realized volatility forecasting and market microstructure noise this paper extends the analytical results for reduced form realized volatility based forecasting in andersen bollerslev and meddahi 2004 to allow for market microstructure frictions and deviations from the basic semi martingale assumption in the observed high frequency returns underlying the realized measures our results builds directly on the powerful eigenfunction representation of the general stochastic volatility class of models originally developed by meddahi 2001 in addition to the traditional realized volatility measure and the role of the underlying sampling frequencies we also explore the forecasting performance of several alternative volatility measures explicitly designed to mitigate the impact of the market microstructure noise our analysis of these alternative robust measures is facilitated by a simple unifled quadratic form representation our results suggest that the detrimental impact of the noise in terms of the accuracy of the forecasts can be substantial and that in empirically realistic situations the linear forecasts based on a simple to implement average estimator deflned by averaging across several sparsely sampled traditional realized volatility measures generally performs on par with best alternative robust measures

the heteroscedastic graded response model with a skewed latent trait testing statistical and substantive hypotheses related to skewed item category functions the graded response model grm samejima estimation of ability using a response pattern of graded scores psychometric monograph no 17 richmond va the psychometric society 1969 can be derived by assuming a linear regression of a continuous variable z on the trait to underlie the ordinal item scores takane de leeuw in psychometrika 52 393 408 1987 traditionally a normal distribution is specified for z implying homoscedastic error variances and a normally distributed in this paper we present the heteroscedastic grm with skewed latent trait which extends the traditional grm by incorporation of heteroscedastic error variances and a skew normal latent trait an appealing property of the extended grm is that it includes the traditional grm as a special case this enables specific tests on the normality assumption of z we show how violations of normality in z can lead to asymmetrical category response functions the ability to test this normality assumption is beneficial from both a statistical and substantive perspective in a simulation study we show the viability of the model and investigate the specificity of the effects we apply the model to a dataset on affect and a dataset on alexithymia

on using perturbation analysis to do sensitivity analysis derivatives versus differences one use of perturbation analysis is to compute the derivative of a performance measure p with respect to a parameter theta for use in iterative optimization schemes to locate local maxima by driving the derivative to zero it has been pointed out that in stochastic approximation contexts there is an advantage in using derivatives as opposed to differences another use of perturbation analysis is just to do a sensitivity analysis with respect to a parameter without relation to any optimization the advantages of using differences rather than derivatives for sensitivity analysis are identified this prompts the use of noninfinitesimal perturbation analysis or other techniques whereby perturbation information can be obtained from a single run

estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error abstract we propose an econometric model that captures the effects of market microstructure on a latent price process in particular we allow for correlation between the measurement error and the return process and we allow the measurement error process to have a diurnal heteroskedasticity we propose a modification of the tsrv estimator of quadratic variation we show that this estimator is consistent with a rate of convergence that depends on the size of the measurement error but is no worse than n 1 6 we investigate in simulation experiments the finite sample performance of various proposed implementations

limited and full information estimation and goodness of fit testing in 2n contingency tables high dimensional contingency tables tend to be sparse and standard goodness of fit statistics such as x2 cannot be used without pooling categories as an improvement on arbitrary pooling for goodness of fit of large 2n contingency tables we propose classes of quadratic form statistics based on the residuals of margins or multivariate moments up to order r these classes of test statistics are asymptotically chi squared distributed under the null hypothesis further the marginal residuals are useful for diagnosing lack of fit of parametric models we show that when r is small r 2 3 the proposed statistics have better small sample properties and are asymptotically more powerful than x2 for some useful multivariate binary models related to these test statistics is a class of limited information estimators based on low dimensional margins we show that these estimators have high efficiency for one commonly used latent trait model for binary data

rbf methods in a stochastic volatility framework for greeks computation abstract in this paper we aim to apply a new proposed meshless approach for heston pde resolution in mathematical finance most classical models may be reformulated as partial differential equations pde which are commonly solved by finite difference and monte carlo methods alternatively bio inspired methods may be considered to select parameters and to solve said pdes in particular we focus on heston model pde and we solve it via radial basis functions rbf methods moreover some considerations on the computation of model parameters through learning approaches have been discussed we aim to price a vanilla call option focusing on the derivation of the formulae for its greeks profiles eventually we conclude rbfs are an accurate alternative method to price derivatives in a stochastic volatility framework especially since they allow for a fast and precise computation of greeks

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

asymptotic robustness study of the polychoric correlation estimation asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied the asymptotic normality of the pseudo maximum likelihood estimator is derived using the two step estimation procedure the t distribution assumption and the skew normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study the numerical results show that the underlying normal distribution can be substantially biased even though skewness and kurtosis are not large the skew normal assumption generally produces a lower bias than the normal assumption thus it is worth using a non normal distributional assumption if the normal assumption is dubious

modeling maxima with autoregressive conditional frechet model abstract this paper introduces a novel dynamic generalized extreme value gev framework for modeling the time varying behavior of maxima in financial time series specifically an autoregressive conditional frechet acf model is proposed in which the maxima are modeled by a frechet distribution with time varying scale parameter volatility and shape parameter tail index conditioned on past information the acf provides a direct and accurate modeling of the time varying behavior of maxima and furthermore offers a new angle to study the tail risk dynamics in financial markets probabilistic properties of acf are studied and a maximum likelihood estimator is used for model estimation with its statistical properties investigated simulations show the flexibility of acf and confirm the reliability of its estimators two real data examples on cross sectional stock returns and high frequency foreign exchange returns are used to demonstrate the acf modeling approach where significant improvement over the static gev has been observed for market tail risk monitoring and conditional var estimation empirical result of acf is consistent with the findings of the dynamic peak over threshold pot literature that the tail index of financial markets varies through time

efficient estimation in semiparametric garch models abstract it is well known that financial data sets exhibit conditional hereroskedasticity garch type models are often used to model this phenomenon since the distribution of the rescaled innovations is generally far from a normal distribution a semiparametric approach is advisable several publications observed that adaptive estimation of the euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter thus suggesting that adaptive estimation of the autoregression parameters is possible indeed we construct adaptive and hence efficient estimators in a general garch in mean type context including integrated garch models our analysis is based on a general lan theorem for time series models published elsewhere in contrast to recent literature about arch models we do not need moment condition

simulating multivariate nonnormal distributions a method for generating multivariate nonnormal distributions with specified intercorrelations and marginal means variances skews and kurtoses is proposed as an example the method is applied to the generation of simulated scores on three psychological tests administered to a single group of individuals

can the random walk model be beaten in out of sample density forecasts evidence from intraday foreign exchange rates abstract it has been documented that random walk outperforms most economic structural and time series models in out of sample forecasts of the conditional mean dynamics of exchange rates in this paper we study whether random walk has similar dominance in out of sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance we first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out of sample setting and provide simulation evidence on its finite sample performance then we conduct a comprehensive empirical analysis on the out of sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates euro dollar and yen dollar it is found that some sophisticated time series models that capture time varying higher order conditional moments such as markov regime switching models have better density forecasts for exchange rates than random walk or modified random walk with garch and student t innovations this finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out of sample applications involving the probability density

modelling price dynamics a hybrid truncated levy flight garch approach abstract arch and garch stochastic processes are widely used in finance and are generally accepted as good approximations when modelling the price dynamics with gaussian conditional probability it can be seen that certain aspects of the empirical data for asset price changes seems to more closely fit a truncated levy flight or garch model but each with individual shortfalls in this paper therefore we combine the garch process with a conditional truncated levy distribution in order to build a hybrid model that most notably describes the price change and associated volatility probability density distributions and scaling behaviour over different time horizons

bootstrapping realized volatility we propose bootstrap methods for a general class of nonlinear transformations of realized volatility which includes the raw version of realized volatility and its logarithmic transformation as special cases we consider the independent and identically distributed i i d bootstrap and the wild bootstrap wb and prove their first order asymptotic validity under general assumptions on the log price process that allow for drift and leverage effects we derive edgeworth expansions in a simpler model that rules out these effects the i i d bootstrap provides a second order asymptotic refinement when volatility is constant but not otherwise the wb yields a second order asymptotic refinement under stochastic volatility provided we choose the external random variable used to construct the wb data appropriately none of these methods provides third order asymptotic refinements both methods improve upon the first order asymptotic theory in finite samples

a hausman test for the presence of market microstructure noise in high frequency data abstract we develop tests that help assess whether a high frequency data sample can be treated as reasonably free of market microstructure noise at a given sampling frequency for the purpose of implementing high frequency volatility and other estimators the tests are based on the hausman principle of comparing two estimators one that is efficient but not robust to the deviation being tested and one that is robust but not as efficient we investigate the asymptotic properties of the test statistic in a general nonparametric setting and compare it with several alternatives that are also developed in the paper empirically we find that improvements in stock market liquidity over the past decade have increased the frequency at which simple uncorrected volatility estimators can be safely employed

testing if the market microstructure noise is fully explained by the informational content of some variables from the limit order book abstract in this paper we build tests for the presence of residual noise in a model where the market microstructure noise is a known parametric function of some variables from the limit order book the tests compare two distinct quasi maximum likelihood estimators of volatility where the related model includes a residual noise in the market microstructure noise or not the limit theory is investigated in a general nonparametric framework in the presence of residual noise we examine the central limit theory of the related quasi maximum likelihood estimation approach

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

large deviation estimates for exceedance times of perpetuity sequences and their dual processes in a variety of problems in pure and applied probability it is relevant to study the large exceedance probabilities of the perpetuity sequence yn b1 a1b2 a1 an 1 bnyn b1 a1b2 a1 an 1 bn where ai bi 0 r ai bi 0 r estimates for the stationary tail distribution of yn yn have been developed in the seminal papers of kesten acta math 131 1973 207 248 and goldie ann appl probab 1 1991 126 166 specifically it is well known that if m supnynm supnyn then p m u cmu p m u cmu as u u while much attention has been focused on extending such estimates to more general settings little work has been devoted to understanding the path behavior of these processes in this paper we derive sharp asymptotic estimates for the normalized first passage time tu logu 1inf n yn u tu log u 1inf n yn u we begin by showing that conditional on tu tu tu tu as u u for a certain positive constant we then provide a conditional central limit theorem for tu tu and study p tu g p tu g as u u for sets g 0 g 0 if g 0 g 0 then we show that p tu g ui g c g p tu g ui g c g as u u for a certain large deviation rate function ii and constant c g c g on the other hand if g g then we show that the tail behavior is actually quite complex and different asymptotic regimes are possible we conclude by extending our results to the corresponding forward process understood in the sense of letac in random matrices and their applications brunswick maine 1984 1986 263 273 amer math soc namely to the reflected process m n max anm n 1 bn 0 mn max anmn 1 bn 0 n z n z using siegmund duality we relate the first passage times of yn yn to the finite time exceedance probabilities of m n mn yielding a new result concerning the convergence of m n mn to its stationary distribution

on the extremes of a class of non linear processes with heavy tailed innovations the aim of this paper is to look at the limiting form of certain empirical point processes induced by a particular class of non linear processes generated by heavy tailed innovations such asymptotic results will be highly useful in obtaining the weak limiting behavior of various functionals of the underlying process including the asymptotic distribution of upper and lower order statistics in particular we investigate the maximum limiting distribution and its corresponding extremal index the results are applied to the study of the extremal properties of bilinear processes

expectation propagation for likelihood free inference many models of interest in the natural and social sciences have no closed form likelihood function which means that they cannot be treated using the usual techniques of statistical inference in the case where such models can be efficiently simulated bayesian inference is still possible thanks to the approximate bayesian computation abc algorithm although many refinements have been suggested abc inference is still far from routine abc is often excruciatingly slow due to very low acceptance rates in addition abc requires introducing a vector of summary statistics s y the choice of which is relatively arbitrary and often require some trial and error making the whole process laborious for the user we introduce in this work the ep abc algorithm which is an adaptation to the likelihood free context of the variational approximation algorithm known as expectation propagation the main advantage of ep abc is that it is faster by a few orders of magnitude than standard algorithms while producing

on the invariance of the lagrange multiplier test with respect to certain changes in the alternative hypothesis this paper examines some implications of the observation that the same lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses a characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification and the consequences for finite sample power properties are examined by monte carlo experiments

financial time series modeling using the hurst exponent abstract this study aims to enhance the understanding of logarithmic asset returns in particular more emphasis is given to the long memory property of financial returns a well documented stylized fact however in the presence of structural breaks other studies suggest that statistical tools such as the autocorrelation function acf can wrongly indicate long memory we propose an insensitive to structural breaks method to test for dependence between distant observations furthermore a model which combines memory in returns and memory in absolute returns is developed in two stages first return series are segmented with respect to changes in the volatility and then the two parameters of the model are estimated to assess the capabilities of the model historical prices of the standard and poor 500 index s p500 financial time stocks exchange 100 index ftse100 deutsche boerse ag german stock index dax and crude oil are used 1 given the estimated parameters and the volatility within each regime 10000 vectors are generated and compared to the original data in terms of the kolmogorov smirnov k s statistical test the obtained results suggest that long memory is present and provide evidence that the additional memory information captured by the model improves financial returns modeling

volatility forecasting and microstructure noise abstract it is common practice to use the sum of frequently sampled squared returns to estimate volatility yielding the so called realized volatility unfortunately returns are contaminated by market microstructure noise several noise corrected realized volatility measures have been proposed we assess to what extent correction for microstructure noise improves forecasting future volatility using a mixed data sampling midas regression framework we study the population prediction properties of various realized volatility measures assuming i i d microstructure noise next we study optimal sampling issues theoretically when the objective is forecasting and microstructure noise contaminates realized volatility we distinguish between conditional and unconditional optimal sampling schemes and find that conditional optimal sampling seems to work reasonably well in practice

value at risk estimation with wavelet based extreme value theory evidence from emerging markets abstract this paper introduces wavelet based extreme value theory evt for univariate value at risk estimation wavelets and evt are combined for volatility forecasting to estimate a hybrid model in the first stage wavelets are used as a threshold in generalized pareto distribution and in the second stage evt is applied with a wavelet based threshold this new model is applied to two major emerging stock markets the istanbul stock exchange ise and the budapest stock exchange bux the relative performance of wavelet based evt is benchmarked against the riskmetrics ewma arma garch generalized pareto distribution and conditional generalized pareto distribution models the empirical results show that the wavelet based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail loss tests the superior forecasting performance of the wavelet based evt model is also consistent with basel ii requirements and this new model can be used by financial institutions as well

estimating quadratic variation when quoted prices change by a constant increment abstract for financial assets whose best quotes almost always change by jumping by the market s price tick size one cent five cents etc this paper proposes an estimator of quadratic variation which controls for microstructure effects it measures the prevalence of alternations where quotes jump back to their just previous price it defines a simple property called uncorrelated alternation which under conditions implies that the estimator is consistent in an asymptotic limit theory where jumps become very frequent and small feasible limit theory is developed and in simulations works well

a reduced form framework for modeling volatility of speculative prices based on realized variation measures abstract building on realized variance and bipower variation measures constructed from high frequency financial prices we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility we decompose the total daily return variability into the continuous sample path variance the variation arising from discontinuous jumps that occur during the trading day as well as the overnight return variance our empirical results based on long samples of high frequency equity and bond futures returns suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long memory har garch model while the overnight returns may be modeled by an augmented garch type structure the dynamic dependencies in the non parametrically identified significant jumps appear to be well described by the combination of an ach model for the time varying jump intensities coupled with a relatively simple log linear structure for the jump sizes finally we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out of sample forecasts for the total return volatility

properties of optimal forecasts under asymmetric loss and nonlinearity abstract evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast we establish instead that a suitable transformation of the forecast error known as the generalized forecast error possesses an equivalent set of properties the paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts

the model confidence set this paper introduces the model confidence set mcs and applies it to the selection of models a mcs is a set of models that is constructed such that it will contain the best model with a given level of confidence the mcs is in this sense analogous to a confidence interval for a parameter the mcs acknowledges the limitations of the data such that uninformative data yield a mcs with many models whereas informative data yield a mcs with only a few models the mcs procedure does not assume that a particular model is the true model in fact the mcs procedure can be used to compare more general objects beyond the comparison of models we apply the mcs procedure to two empirical problems first we revisit the inflation forecasting problem posed by stock and watson 1999 and compute the mcs for their set of inflation forecasts second we compare a number of taylor rule regressions and determine the mcs of the best regression in terms of in sample likelihood criteria

a top bottom price approach to understanding financial fluctuations abstract the presence of sequences of top and bottom tb events in financial series is investigated for the purpose of characterizing such switching points they clearly mark a change in the trend of rising or falling prices of assets to the opposite tendency are of crucial importance for the players decision and also for the market stability previous attempts to characterize switching points have been based on the behavior of the volatility and on the definition of microtrends the approach used herein is based on the smoothing of the original data with a gaussian kernel the events are identified by the magnitude of the difference of the extreme prices by the time lag between the corresponding events waiting time and by the time interval between events with a minimal magnitude return time results from the analysis of the inter day dow jones industrial average index djia from 1928 to 2011 are discussed q gaussian functions with power law tails are found to provide a very accurate description of a class of measures obtained from the series statistics

impact of foreign exchange rate on oil companies risk in stock market during the recent years the importance of effective risk management has become extremely crucial value at risk var is a standard downside measure to explain the behavior of financial series as the garch models have been successfully applied in modeling the volatility structure of securities and other financial assets the var of garch models has turned into an important quantity to study in addition to garch family models the markov regime switching garch mrs garch models are a widely used approach to model financial volatility with potential structural breaks in this paper we evaluated the performance of the mrs garch models with the traditional arma garch family models for estimating var of the stock return of operating companies in the oil industry srocoi in irans stock market under the normal student t and ged distributions our findings showed that the mrs garch models outperform the arma garch family models to capture the characteristics of the srocois volatility additionally we evaluated impact of the foreign exchange rate fluctuations on the var of srocois that were calculated from the optimal models under two regimes usingardl model the results further demonstrated that foreign exchange rate fluctuations have significant and different impacts on the var of srocois across regimes we modeled srocois in irans stock market using mrs garch and arma garch family models mrs garch models under student t and ged distributions have better performance to capture srocois we estimated in sample and out of sample var of srocois from optima models we evaluated impact of the foreign exchange rate fluctuations on the var of srocois foreign exchange rate significantly effect on the var of srocois in different regimes

robust score and portmanteau tests of volatility spillover abstract this paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or garch type feedback the tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent we negligibly trim test equations or components of the equations and construct heavy tail robust score and portmanteau statistics trimming is either simple based on an indicator function or smoothed in particular we develop the tail trimmed sample correlation coefficient for robust inference and prove that its gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness further if spillover occurs within a specified horizon our test statistics obtain power of one asymptotically we discuss the choice of trimming portion including a smoothed p value over a window of extreme observations a monte carlo study shows our tests provide significant improvements over extant garch based tests of spillover and we apply the tests to financial returns data finally based on ideas in patton 2011 we construct a heavy tail robust forecast improvement statistic which allows us to demonstrate that our spillover test can be used as a model specification pre test to improve volatility forecasting

volatility forecast comparison using imperfect volatility proxies the use of a conditionally unbiased but imperfect volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts we motivate our study with analytical results on the distortions caused by some widely used loss functions when used with standard volatility proxies such as squared returns the intra daily range or realised volatility we then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy and derive some useful special cases of this class of robust loss functions the methods are illustrated with an application to the volatility of returns on ibm over the period 1993 to 2003

data based ranking of realised volatility estimators abstract this paper presents new methods for comparing the accuracy of estimators of the quadratic variation of a price process i provide conditions under which the relative accuracy of competing estimators can be consistently estimated as t and show that forecast evaluation tests may be adapted to the problem of ranking these estimators the proposed methods avoid making specific assumptions about microstructure noise and facilitate comparisons of estimators that would be difficult using methods from the extant literature such as those based on different sampling schemes an application to high frequency ibm data between 1996 and 2007 illustrates the new methods

consistent ranking of volatility models abstract we show that the empirical ranking of volatility models can be inconsistent for the true ranking if the evaluation is based on a proxy for the population measure of volatility for example the substitution of a squared return for the conditional variance in the evaluation of arch type models can result in an inferior model being chosen as best with a probability that converges to one as the sample size increases we document the practical relevance of this problem in an empirical application and by simulation experiments our results provide an additional argument for using the realized variance in out of sample evaluations rather than the squared return we derive the theoretical results in a general framework that is not specific to the comparison of volatility models similar problems can arise in comparisons of forecasting models whenever the predicted variable is a latent variable

monte carlo inference in econometric models with symmetric stable disturbances the paper develops markov chain monte carlo methods to perform exact posterior analysis in models with symmetric stable paretian disturbances it is shown how posterior moments and marginal densities of functions of parameters can be computed methodically by combining a gibbs sampler with metropolis independence chains the new method is shown to perform satisfactorily in constructed examples the method is also applied to a set of monthly real exchange rates and the question of difference versus trend stationarity is taken up jointly with the problem of inference about the parameter of the stable distribution

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models

interval estimation of value at risk based on garch models with heavy tailed innovations arch and garch models are widely used to model financial market volatilities in risk management applications considering a garch model with heavy tailed innovations we characterize the limiting distribution of an estimator of the conditional value at risk var which corresponds to the extremal quantile of the conditional distribution of the garch process we propose two methods the normal approximation method and the data tilting method for constructing confidence intervals for the conditional var estimator and assess their accuracies by simulation studies finally we apply the proposed approach to an energy market data set

econometric analysis of realized covariation high frequency based covariance regression and correlation in financial economics this paper analyses multivariate high frequency financial data using realized covariation we provide a new asymptotic distribution theory for standard methods such as regression correlation analysis and covariance it will be based on a fixed interval of time e g a day or week allowing the number of high frequency returns during this period to go to infinity our analysis allows us to study how high frequency correlations regressions and covariances change through time in particular we provide confidence intervals for each of these quantities

the roles of mean residence time on herd behavior in a financial market abstract we investigate the herd behavior of stock prices in a finance system with the heston model based on parameter estimation of the heston model obtained by minimizing the mean square deviation between the theoretical and empirical return distributions we simulate mean residence time of positive return mrtpr plots of mrtpr against the amplitude or mean reversion of volatility demonstrate a phenomenon of herd behavior for a positive cross correlation between noise sources of the heston model also for a negative cross correlation a phenomenon of herd behavior is observed in plots of mrtpr against the long run variance by increasing amplitude or mean reversion of volatility

statistical inference based on pseudo maximum likelihood estimators in elliptical populations in this article we develop statistical inference based on the maximum likelihood method in elliptical populations with an unknown density function the method assuming the multivariate normal distribution using the sample mean and the sample covariance matrix is basically correct even for elliptical populations under a certain kurtosis adjustment but is not statistically efficient especially when the kurtosis of the population distribution has higher than moderate values on the other hand several methods of statistical inference assuming a particular family e g multivariate t distribution of elliptical distributions have been recommended as a robust procedure against outliers or distributions with heavy tails such inference also will be important to maintain a high efficiency of statistical inference in elliptical populations in practice however it is very difficult to choose an appropriate family of elliptical distributions and one may misspecify the family furthermore extra parameters

maximum entropy autoregressive conditional heteroskedasticity model abstract in many applications it has been found that the autoregressive conditional heteroskedasticity arch model under the conditional normal or student s t distributions are not general enough to account for the excess kurtosis in the data moreover asymmetry in the financial data is rarely modeled in a systematic way in this paper we suggest a general density function based on the maximum entropy me approach that takes account of asymmetry excess kurtosis and also of high peakedness the me principle is based on the efficient use of available information and as is well known many of the standard family of distributions can be derived from the me approach we demonstrate how we can extract information functional from the data in the form of moment functions we also propose a test procedure for selecting appropriate moment functions our procedure is illustrated with an application to the nyse stock returns the empirical results reveal that the me approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively

managing distribution changes in time series prediction when a problem is modeled statistically a single distribution model is usually postulated that is assumed to be valid for the entire space nonetheless this practice may be somewhat unrealistic in certain application areas in which the conditions of the process that generates the data may change as far as we are aware however no techniques have been developed to tackle this problem this article proposes a technique for modeling and predicting this change in time series with a view to improving estimates and predictions the technique is applied among other models to the hypernormal distribution recently proposed when tested on real data from a range of stock market indices the technique produces better results that when a single distribution model is assumed to be valid for the entire period of time studied moreover when a global model is postulated it is highly recommended to select the hypernormal distribution parameter in the same likelihood maximization process

a simple r estimation method for semiparametric duration models modeling nonnegative financial variables e g durations between trades traded volumes or asset volatilities is central to a number of studies across financial econometrics and despite the efforts still poses several statistical challenges among them the efficiency aspects of semiparametric estimation in this paper we concentrate on estimation problems in autoregressive conditional duration acd models with unspecified innovation densities exponential quasi likelihood estimators qmle are the usual practice in that context the efficiency of those qmles the only fisher consistent qmles unfortunately rapidly deteriorates away from the reference exponential density a phenomenon that has been emphasized earlier by drost and werker 2003 who propose various semiparametrically efficient procedures to palliate that phenomenon those procedures rely on a general semiparametric approach which typically requires kernel estimation of the underlying innovation density we propose rank based estimators r estimators as a substitute just as the qmle r estimators remain root n consistent irrespective of the underlying density and rely on the choice of a reference density under which they achieve semiparametric efficiency that density however needs not be the exponential one contrary to the semiparametric estimators proposed by drost and werker 2003 r estimators neither require tangent space calculations nor kernel based density estimation numerical results moreover indicate that r estimators based on exponential reference densities uniformly outperform the exponential qmle under such families of innovations as the weibull or burr densities a real data example about modeling the price range of the swiss stock market index concludes the paper

a short note on the estimation of the asymptotic covariance matrix for polychoric correlations by using a taylor expansion of the equations that define the two step estimator for polychoric correlations the asymptotic covariance matrix for the estimated correlations can be derived in a simple and straightforward way

the distribution of realized exchange rate volatility using high frequency data on deutschemark and yen returns against the dollar we construct model free estimates of daily exchange rate volatility and correlation that cover an entire decade our estimates termed realized volatilities and correlations are not only model free but also approximately free of measurement error under general conditions which we discuss in detail hence for practical purposes we may treat the exchange rate volatilities and correlations as observed rather than latent we do so and we characterize their joint distribution both unconditionally and conditionally noteworthy results include a simple normality inducing volatility transformation high contemporaneous correlation across volatilities high correlation between correlation and volatilities pronounced and persistent dynamics in volatilities and correlations evidence of long memory dynamics in volatilities and correlations and remarkably precise scaling laws under temporal aggregation

designing realised kernels to measure the ex post variation of equity prices in the presence of noise this paper shows how to use realised kernels to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions the issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed gaussian limit theorems the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem realised kernels can also be selected to i be analysed using endogenously spaced data such as that in databases on transactions ii allow for market frictions which are endogenous iii allow for temporally dependent noise the finite sample performance of our estimators is studied using simulation while empirical work illustrates their use in practice

time evolution of stochastic processes with correlations in the variance stability in power law tails of distributions abstract we model the time series of the s p500 index by a combined process the ar garch process where ar denotes the autoregressive process which we use to account for the short range correlations in the index changes and garch denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long range correlations in the variance we study the ar garch process with an initial distribution of truncated levy form we find that this process generates a new probability distribution with a crossover from a levy stable power law to a power law with an exponent outside the levy range beyond the truncation cutoff we analyze the sum of n variables of the ar garch process and find that due to the correlations the ar garch process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n a feature which is observed in the probability distribution of the s p500 index we find that this power law stability depends on the characteristic scale in the correlations we also find that inclusion of short range correlations through the ar process is needed to obtain convergence to a limiting gaussian distribution for large n as observed in the data

continuous record asymptotics for rolling sample variance estimators it is widely known that conditional covariances of asset returns change over time researchers doing empirical work have adopted many strategies for accommodating conditional heteroskedasticity among the popular strategies are a chopping the available data into short blocks of time and assuming homoskedasticity within the blocks b performing one sided rolling regressions in which only data from say the preceding five year period is used to estimate the conditional covariance of returns at a given date and c performing two sided rolling regressions in which covariances are estimated for each date using say five years of lags and five years of leads another model garch amounts to a one sided weighted rolling regression we develop continuous record asymptotic approximations for the measurement error in conditional variances and covariances when using these methods we derive asymptotically optimal window lengths for standard rolling regressions and optimal weights for weighted rolling regressions as an empirical example we estimate volatility on the s p 500 stock index using daily data from 1928 to 1990

goodman and kruskal s gamma coefficient for ordinalized bivariate normal distributions we consider a bivariate normal distribution with linear correlation formula see text whose random components are discretized according to two assigned sets of thresholds on the resulting bivariate ordinal random variable one can compute goodman and kruskal s gamma coefficient formula see text which is a common measure of ordinal association given the known analytical monotonic relationship between pearson s formula see text and kendall s rank correlation formula see text for the bivariate normal distribution and since in the continuous case kendall s formula see text coincides with goodman and kruskal s formula see text the change of this association measure before and after discretization is worth studying we consider several experimental settings obtained by varying the two sets of thresholds or equivalently the marginal distributions of the final ordinal variables this study confirming previous findings shows how the gamma coefficient is always larger in absolute value than kendall s rank correlation this discrepancy lessens when the number of categories increases or given the same number of categories when using equally probable categories based on these results a proposal is suggested to build a bivariate ordinal variable with assigned margins and goodman and kruskal s formula see text by ordinalizing a bivariate normal distribution illustrative examples employing artificial and real data are provided

bootstrap refinements for qml estimators of the garch 1 1 parameters a b s t r a c t this paper reconsiders a block bootstrap procedure for quasi maximum likelihood estimation of garch models based on the resampling of the likelihood function as proposed by goncalves and white 2004 maximum likelihood and the bootstrap for nonlinear dynamic models journal of econometrics 119 199 219 first we provide necessary conditions and sufficient conditions in terms of moments of the innovation process for the existence of the edgeworth expansion of the garch 1 1 estimator up to the k th term second we provide sufficient conditions for higher order refinements for equally tailed and symmetric test statistics in particular the bootstrap estimator based on resampling the likelihood has the same higher order improvements in terms of error in the rejection probabilities as those in andrews 2002 higher order improvements of a computationally attractive k step bootstrap for extremum estimators econometrica 70 119 162

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

limited information goodness of fit testing in multidimensional contingency tables we introduce a family of goodness of fit statistics for testing composite null hypotheses in multidimensional contingency tables these statistics are quadratic forms in marginal residuals up to order r they are asymptotically chi square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator for a widely used item response model when r is small and multidimensional tables are sparse the proposed statistics have accurate empirical type i errors unlike pearson s x2 for this model in nonsparse situations the proposed statistics are also more powerful than x2 in addition the proposed statistics are asymptotically chi square when applied to subtables and can be used for a piecewise goodness of fit assessment to determine the source of misfit in poorly fitting models

maximum likelihood diversity combining in partial band noise maximum likelihood diversity combining is investigated for an ffh mfsk spread spectrum system in partial band noise pbn the structure of maximum likelihood diversity reception in pbn plus white gaussian noise is derived it is shown that signal to noise ratio and the noise variance at each hop have to be known to implement this optimum diversity combiner several suboptimum diversity combining schemes are also considered the performance of the optimum combining scheme is evaluated it is shown that adaptive gain control diversity combining actually achieves the optimum performance when interference is not very weak

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

estimation for partially nonstationary multivariate autoregressive models with conditional heteroscedasticity this paper investigates a partially nonstationary multivariate autoregressive model which allows its innovations to be generated by a multivariate arch autoregressive conditional heteroscedastic process three estimators including the least squares estimator a full rank maximum likelihood estimator and a reduced rank maximum likelihood estimator are considered and their asymptotic distributions are derived when the multivariate arch process reduces to the innovation with a constant covariance matrix these asymptotic distributions are the same as those given by ahn reinsel 1990 however in the presence of multivariate arch innovations the asymptotic distributions of the full rank maximum likelihood estimator and the reduced rank maximum likelihood estimator involve two correlated multivariate brownian motions which are different from those given by ahn reinsel 1990 simulation results show that the full rank and reduced rank maximum likelihood estimator are more efficient than the least squares estimator an empirical example shows that the two features of multivariate conditional heteroscedasticity and partial nonstationarity may be present simultaneously in a multivariate time series

item response theory with estimation of the latent population distribution using spline based densities the purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines a spline based density estimation system provides a flexible alternative to existing procedures that use a normal distribution or a different functional form for the population distribution a simulation study shows that the new procedure is feasible in practice and that when the latent distribution is not well approximated as normal two parameter logistic 2pl item parameter estimates and expected a posteriori scores eaps can be improved over what they would be with the normal model an example with real data compares the new method and the extant empirical histogram approach

the econometrics of ultra high frequency data ultra high frequency data is defined to be a full record of transactions and their associated characteristics the transaction arrival times and accompanying measures can be analyzed as marked point processes the acd point process developed by engle and russell 1998 is applied to ibm transactions arrival times to develop semiparametric hazard estimates and conditional intensities combining these intensities with a garch model of prices produces ultra high frequency measures of volatility both returns and variances are found to be negatively influenced by long durations as suggested by asymmetric information models of market micro structure

out of sample forecasts of quadratic variation we compare the forecasts of quadratic variation given by the realized volatility rv and the two scales realized volatility tsrv computed from high frequency data in the presence of market microstructure noise under several different dynamics for the volatility process and assumptions on the noise we show that tsrv largely outperforms rv whether looking at bias variance rmse or out of sample forecasting ability an empirical application to all djia stocks confirms the simulation results

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

modelling high frequency economic time series abstract the minute by minute move of the hang seng index hsi data over a 4 yr period is analysed and shown to possess similar statistical features as those of other markets based on a mathematical theorem pope ching phys fluids a 5 1993 1529 we derive an analytic form for the probability distribution function pdf of index moves from fitted functional forms of certain conditional averages of the time series furthermore following a recent work by stolovitzky and ching phys lett a 255 1999 11 we show that the observed pdf can be reproduced by a langevin process with a move dependent noise amplitude the form of the langevin equation can be determined directly from the market data

econometric analysis of realized volatility and its use in estimating stochastic volatility models summary the availability of intraday data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets called realized volatility to study the stochastic properties of returns here under the assumption of a rather general stochastic volatility model we derive the moments and the asymptotic distribution of the realized volatility error the difference between realized volatility and the discretized integrated volatility which we call actual volatility these properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation intensive methods

limited information estimation and testing of discretized multivariate normal structural models discretized multivariate normal structural models are often estimated using multistage estimation procedures the asymptotic properties of parameter estimates standard errors and tests of structural restrictions on thresholds and polychoric correlations are well known it was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators it is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy a test of the overall model specification is proposed as well as a test of the distributional specification i e discretized multivariate normality also the small sample performance of overall distributional and structural tests as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and or distributional misspecification it is found that relatively small samples are needed for parameter estimates standard errors and structural tests larger samples are needed for the distributional and overall tests furthermore parameter estimates standard errors and structural tests are surprisingly robust to distributional misspecification

measuring volatility with the realized range realized variance being the summation of squared intra day returns has quickly gained popularity as a measure of daily volatility following parkinson 1980 the extreme value method for estimating the variance of the rate of return journal of business 53 61 65 we replace each squared intra day return by the high low range for that period to create a novel and more efficient estimator called the realized range in addition we suggest a bias correction procedure to account for the effects of microstructure frictions based upon scaling the realized range with the average level of the daily range simulation experiments demonstrate that for plausible levels of non trading and bid ask bounce the realized range has a lower mean squared error than the realized variance including variants thereof that are robust to microstructure noise empirical analysis of the s p500 index futures and the s p100 constituents confirms the potential of the realized range

realized range based estimation of integrated variance abstract we provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with the realized range based variance a statistic that replaces every squared return of the realized variance with a normalized squared range if the entire sample path of the process is available and under a set of weak conditions our statistic is consistent and has a mixed gaussian limit whose precision is five times greater than that of the realized variance in practice of course inference is drawn from discrete data and true ranges are unobserved leading to downward bias we solve this problem to get a consistent mixed normal estimator irrespective of non trading effects this estimator has varying degrees of efficiency over realized variance depending on how many observations that are used to construct the high low the methodology is applied to taq data and compared with realized variance our findings suggest that the empirical path of quadratic variation is also estimated better with the realized range based variance

market microstructure noise integrated variance estimators and the accuracy of asymptotic approximations a growing literature has been advocating consistent kernel estimation of integrated variance in the presence of financial market microstructure noise we find that for realistic sample sizes encountered in practice the asymptotic results derived for the proposed estimators may provide unsatisfactory representations of their finite sample properties in addition the existing asymptotic results might not offer sufficient guidance for practical implementations we show how to optimize the finite sample properties of kernel based integrated variance estimators empirically we find that their suboptimal implementation can in some cases lead to little or no finite sample gains when compared to the classical realized variance estimator significant statistical and economic gains can however be recovered by using our proposed finite sample methods

probability of error analyses of a bfsk frequency hopping system with diversity under partial band jamming interference part ii performance of square law nonlinear combining soft decision receivers in this paper error probability analyses are performed for a binary frequency shift keying bfsk system employing l hop bit frequency hopping fh spread spectrum waveforms transmitted over a partial band gaussian noise jamming channel the error probabilities for the l hop bit bfsk fh systems are obtained as the performance measure of the square law linear combining soft decision receiver under the assumption of the worst case partial band jamming the receiver in our analysis assumes no knowledge of jamming state side information both exact and approximate multiple bound parameter chernoff bound solutions are obtained under two separate assumptions with and without the system s thermal noise in the analyses numerical results of the error rates are graphically displayed as a function of signal to jamming power ratio with l and signal to noise ratio as parameters all of our results exact and approximate indicated that the higher number of hops per bit produced higher error probabilities as a result of increased combining losses when the square law linear combining soft decision receiver is employed in demodulating the multihop per bit waveform

a tale of two time scales it is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns however market microstructure poses challenges to this estimation approach as evidenced by recent empirical studies in finance the present work attempts to lay out theoretical grounds that reconcile continuous time modeling and discrete time samples we propose an estimation approach that takes advantage of the rich sources in tick by tick data while preserving the continuous time assumption on the underlying returns under our framework it becomes clear why and where the usual volatility estimator fails when the returns are sampled at the highest frequencies if the noise is asymptotically small our work provides a way of finding the optimal sampling frequency a better approach the two scales estimator works for any size of the noise

on the estimation of polychoric correlations and their asymptotic covariance matrix a general theory for parametric inference in contingency tables is outlined estimation of polychoric correlations is seen as a special case of this theory the asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds computational aspects are also discussed

multivariate functional coefficient regression models for nonlinear vector time series data summary vector time series data are widely found in practice in this paper we propose a multivariate functional coefficient regression model with heteroscedasticity for modeling such data the local linear smoother is employed to estimate the unknown coefficient matrices asymptotic normality 10 of the proposed estimators is established and bandwidth selection is considered to deal with cointegration widely observed in financial markets we propose an error corrected multivariate functional coefficient model simulations show that the proposed estimation procedures capture nonlinear structures of coefficients well analysis of united states interest rates illustrates the proposed methodology 15

the stationary bootstrap abstract this article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations previously a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m dimensional joint distribution of m consecutive observations where m is fixed this procedure has been generalized by constructing a blocks of blocks resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole i e infinite dimensional joint distribution of the stationary sequence of observations these methods share the construction of resampling blocks of observations to form a pseudo time series so that the statistic of interest may be recalculated based on the resampled data set but in the context of applying this method to stationary data it is natural

speckle suppression in sar images using the 2 d garch model a novel bayesian based speckle suppression method for synthetic aperture radar sar images is presented that preserves the structural features and textural information of the scene first the logarithmic transform of the original image is analyzed into the multiscale wavelet domain we show that the wavelet coefficients of sar images have significantly non gaussian statistics that are best described by the 2 d garch model by using the 2 d garch model on the wavelet coefficients we are capable of taking into account important characteristics of wavelet coefficients such as heavy tailed marginal distribution and the dependencies between the coefficients furthermore we use a maximum a posteriori map estimator for estimating the clean image wavelet coefficients finally we compare our proposed method with various speckle suppression methods applied on synthetic and actual sar images and we verify the performance improvement in utilizing the new strategy

error probability analysis of ffh mfsk receivers over frequency selective rician fading channels with partial band noise jamming an optimum maximum likelihood ml receiver structure for a fast frequency hopped m ary frequency shift keying system over frequency selective rician fading channels against partial band noise jamming and additive white gaussian noise is proposed in addition we propose two suboptimum ml receivers and derive their corresponding analytical bit error rate expressions

testing forecast optimality under unknown loss empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function in this article we establish new testable properties that hold when the forecaster s loss function is unknown but testable restrictions can be imposed on the data generating process trading off conditions on the data generating process against conditions on the loss function we propose flexible estimation of the forecaster s loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable we apply our results to the problem of evaluating the federal reserve s forecasts of output growth forecast optimality is rejected if the fed s loss depends only on the forecast error however the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the fed than underpredictions particularly during per