detrended fluctuation analysis of intertrade durations abstract the intraday pattern long memory and multifractal nature of the intertrade durations which are defined as the waiting times between two consecutive transactions are investigated based upon the limit order book data and order flows of 23 liquid chinese stocks listed on the shenzhen stock exchange in 2003 an inverse u shaped intraday pattern in the intertrade durations with an abrupt drop in the first minute of the afternoon trading is observed based on a detrended fluctuation analysis we find a crossover of power law scaling behaviors for small box sizes trade numbers in boxes and large box sizes and strong evidence in favor of long memory in both regimes in addition the multifractal nature of intertrade durations in both regimes is confirmed by a multifractal detrended fluctuation analysis for individual stocks with a few exceptions in the small duration regime the intraday pattern has little influence on the long memory and multifractality

scaling and memory in the non poisson process of limit order cancelation abstract the order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order driven markets we investigate the dynamics of order cancelation by studying the statistical properties of inter cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the shenzhen stock exchange of china in year 2003 three types of cancelations are considered including cancelation of any limit orders of buy limit orders and of sell limit orders we find that the distributions of the inter cancelation durations of individual stocks can be well modeled by weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks complex intra day patterns are also unveiled in the inter cancelation durations the detrended fluctuation analysis dfa and the multifractal dfa show that the inter cancelation durations possess long term memory and multifractal nature which are not influenced by the intra day patterns no clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale these findings indicate that the cancelation of limit orders is a non poisson process which has potential worth in the construction of order driven market models

on the definition of the strategic stability of equilibria a new definition of strategic stability is shown to satisfy all of the requirements given by elon kohlberg and jean francois mertens 1986 the definition follows the general form of the original definition of kohlberg and mertens but rather than working with perturbations of the payoffs or strategy space works directly with perturbations to the best reply correspondence with the appropriate topology on this space of perturbations the resulting definition does satisfy all of the requirements given by kohlberg and mertens it is shown that one does not have much freedom in the topology one uses

a micro movement model with bayes estimation via filtering application to measuring trading noises and costs abstract we highlight a general hybrid system as the micromovement model for asset price using counting processes recently introduced with its bayes estimation via filtering we construct a new simple micromovement model and apply it to analyze trade by trade stock price data in the light of the series of works initiated by christie and schultz why do nasdaq market makers avoid odd eighth quotes finance 49 1994 1813 1840 through the new model we propose more reasonable but computationally intensive measures for trading noise including clustering noise and non clustering noise and for trading cost we employ bayes estimation via filtering to obtain parameter estimates of the new model and to provide numerical measures of trading noise and trading cost for three stocks from four chosen periods our empirical results support the important findings in christie harris schultz why did nasdaq market makers stop avoiding odd eighth quotes finance 49 1994 1841 1860 barclay christie harris kandel schultz the effects of market reform on the trading costs and depths of nasdaq stocks j finance 54 1 1999 1 34

essential components of nash equilibria for games parametrized by payoffs and strategies abstract we study the stability of nash equilibria for games in normal form parameterized by continuous and quasi concave payoffs and compact convex strategy sets in euclidean spaces and we establish an existence theorem for essential connected components of nash equilibria which includes corresponding results in the literature as special cases

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

the effects of random and discrete sampling when estimating continuous time diffusions high frequency financial data are not only discretely sampled in time but the time separating successive observations is often random we analyze the consequences of this dual feature of the data when estimating a continuous time model in particular we measure the additional effects of the randomness of the sampling intervals over and beyond those due to the discreteness of the data we also examine the effect of simply ignoring the sampling randomness we find that in many situations the randomness of the sampling has a larger impact than the discreteness of the data

activity spectrum from waiting time distribution in high frequency financial data not only returns but also waiting times between trades are random variables in this work we analyze the spectra of the waiting time processes for tick by tick trades the numerical problem strictly related with the real inversion of laplace transforms is analyzed by using tikhonov s regularization method we also analyze these spectra by a rough method using a comb of dirac s delta functions

econometric analysis of multivariate realised qml estimation of the covariation of equity prices under asynchronous trading estimating the covariance between assets using high frequency data is challenging due to market microstructure effects and asynchronous trading in this paper we develop a multivariate realised quasi likelihood qml approach carrying out inference as if the observations arise from an asynchronously observed vector scaled brownian model observed with error under stochastic volatility the resulting realised qml estimator is positive semi definite uses all available data is consistent and asymptotically mixed normal the quasi likelihood is computed using a kalman filter and optimised using a relatively simple em algorithm which scales well with the number of assets we derive the theoretical properties of the estimator and prove that it achieves the efficient rate of convergence we show how to make itobtain the non parametric efficiency bound for this problem the estimator is also analysed usingmonte carlo methods and applied to equity data with varying levels of liquidity

numerical integration of related hankel transforms by quadrature and continued fraction expansion an algorithm is presented for the accurate evaluation of hankel or bessel transforms of algebraically related kernel functions defined here as the non bessel function portion of the integrand that is more widely applicable than the standard digital filter methods without enormous increases in computational burden the algorithm performs the automatic integration of the product of the kernel and bessel functions between the asymptotic zero crossings of the latter and sums the series of partial integrations using a continued fraction expansion equivalent to an analytic continuation of the series the integrands may be saved to allow the rapid computation of related transforms without recalculating the kernel or bessel functions and the integration steps use interlacing quadrature formulas so that no function evaluations are wasted when it is necessary to increase the order of the quadrature rule the continued fraction algorithm allows very slowly divergent or even formally divergent integrals to be computed quite easily the local error is controlled at each step in the algorithm and accuracy is limited largely by machine resolution the algorithm is written in fortran and is listed in an appendix along with a driver program that illustrates its features the driver program and subroutine are available from the seg business offtce

continuous time analysis of fleeting discrete price moves abstractthis article proposes a novel model of financial prices where i prices are discrete ii prices change in continuous time iii a high proportion of price changes are reversed in a fraction of a second our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve the resulting cadlag price process is a piecewise constant semimartingale with finite activity finite variation and no brownian motion component we use moment based estimations to fit four high frequency futures datasets and demonstrate the descriptive power of our proposed model this model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals supplementary materials for this article are available online

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

nonparametric specification tests for conditional duration models this paper deals with the testing of autoregressive conditional duration acd models by gauging the distance between the parametric density and hazard rate functions implied by the duration process and their non parametric estimates we derive the asymptotic justification using the functional delta method for fixed and gamma kernels and then investigate the finite sample properties through monte carlo simulations although our tests display some size distortion bootstrapping suffices to correct the size without compromising their excellent power we show the practical usefulness of such testing procedures for the estimation of intraday volatility patterns

a nonlinear autoregressive conditional duration model with applications to financial transaction data abstract this paper presents a new model that improves upon several inadequacies of the original autoregressive conditional duration acd model considered in engle and russell econometrica 66 5 1998 1127 1162 we propose a threshold autoregressive conditional duration tacd model to allow the expected duration to depend nonlinearly on past information variables conditions for the tacd process to be ergodic and existence of moments are established strong evidence is provided to suggest that fast transacting periods and slow transacting periods of nyse stocks have quite different dynamics based on the improved model we identify multiple structural breaks in the transaction duration data considered and those break points match nicely with real economic events

testing for unobserved heterogeneity in exponential and weibull duration models abstract we examine the use of the likelihood ratio lr statistic to test for unobserved heterogeneity in duration models based on mixtures of exponential or weibull distributions we consider both the uncensored and censored duration cases the asymptotic null distribution of the lr test statistic is not the standard chi square as the standard regularity conditions do not hold instead there is a nuisance parameter identified only under the alternative and a null parameter value on the boundary of the parameter space as in cho and white 2007a we accommodate these and provide methods delivering consistent asymptotic critical values we conduct a number of monte carlo simulations comparing the level and power of the lr test statistic to an information matrix im test due to chesher 1984 and lagrange multiplier lm tests of kiefer 1985 and sharma 1987 our simulations show that the lr test statistic generally outperforms the im and lm tests we also revisit the work of van den berg and ridder 1998 on unemployment durations and of ghysels et al 2004 on interarrival times between stock trades and as it turns out affirm their original informal inferences

a misspecification test for multiplicative error models of non negative time series processes in recent years analysis of financial time series focuses largely on data related to market trading activity apart from modeling of the conditional variance of returns within the generalized autoregressive conditional heteroskedasticity garch family of models presently attention is also devoted to that of other market variables for instance volumes number of trades or financial durations to this end a large group of researchers focus their studies on a class of model that is referred to in the literature as the multiplicative error model mem which is considered particularly for modeling non negative time series processes the goal of the current paper is to establish an alternative misspecification test for the mem of non negative time series processes in the literature although several procedures are available to perform hypothesis testing for the mem the newly proposed testing procedure is particularly useful in the context of the mem of waiting times between financial events since its outcomes have a number of important implications on the fundamental concept of point processes finally the current paper makes a number of statistical contributions especially in making a head way into nonparametric hypothesis testing of unobservable variables

garch models without positivity constraints exponential or log garch this paper provides a probabilistic and statistical comparison of the log garch and egarch models which both rely on multiplicative volatility dynamics without positivity constraints we compare the main probabilistic properties strict stationarity existence of moments tails of the egarch model which are already known with those of an asymmetric version of the log garch the quasi maximum likelihood estimation of the log garch parameters is shown to be strongly consistent and asymptotically normal similar estimation results are only available for particular egarch models and under much stronger assumptions the comparison is pursued via simulation experiments and estimation on real data

estimating continuous time processes subject to time deformation an application to postwar u s gnp abstract a class of time series models is presented in which variables evolve on a data based rather than calendar time scale the discrete calendar time model thus obtained exhibits time varying parameters and conditional heteroscedasticity using a procedure based on the kalman filter univariate models are estimated for postwar u s real gross national product gnp and short and long term interest rates the results indicate significant time scale nonlinearities

fitting a two phase threshold multiplicative error model abstract the recent literature on financial time series analysis has devoted considerable attention to nonnegative time series such as financial durations realized volatility and squared returns the class of models referred to as the multiplicative error models mem is particularly suited to model such nonnegative time series we develop a lack of fit test for fitting a two phase threshold model for the conditional mean function in an mem the proposed testing procedure can also be applied to a class of autoregressive conditional heteroscedastic threshold models we evaluate the test in a simulation study the testing procedure is illustrated by using two data examples

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

an open source full 3d electromagnetic modeler for 1d vti media in python empymod abstractthe python code empymod computes the 3d electromagnetic field in a layered earth with vertical transverse isotropy by combining and extending two earlier presented algorithms in this journal the bottleneck in frequency and time domain calculations of electromagnetic responses derived in the wavenumber frequency domain is the transformations from the wavenumber to the space domain and from the frequency to the time domain the so called hankel and fourier transforms three different hankel transform methods quadrature quadrature with extrapolation qwe and filters and four different fourier transform methods fast fourier transform fft fftlog qwe and filters are included in empymod which allows us to compare these different methods in terms of speed and precision the best transform in terms of speed and precision depends on the modeled frequencies published digital filters for the hankel transform are very fast and precise for frequencies in the range of controlled source electromag

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

intraday value at risk an asymmetric autoregressive conditional duration approach abstract we propose to compute the intraday value at risk ivar for stocks using real time transaction data tick by tick data filtered by price duration are modeled using a two state asymmetric autoregressive conditional duration aacd model and the ivar is calculated using monte carlo simulation based on the estimated aacd model backtesting results for the new york stock exchange nyse show that the ivar calculated using the aacd method outperforms those using the dionne et al 2009 and giot 2005 methods

the hessian method highly efficient simulation smoothing in a nutshell abstract i introduce the hessian highly efficient simulation smoothing in a nutshell method for numerically efficient simulation smoothing in state space models with univariate states given a vector of parameters the vector of states 1 n is gaussian and the observed vector y y 1 y n need not be i describe a procedure to construct a close approximation q y to the target density p y it requires code to compute five derivatives of log p y t t with respect to t t 1 n and is not otherwise model specific since q y is proper fully normalised and simulable it can be used as an importance density for importance sampling is or as a proposal density for markov chain monte carlo mcmc hessian is an acronym but it also refers to the sparse hessian matrix of log p y with respect to the hessian method is based on sparse matrix operations rather than the kalman filter i construct q y and a related approximation q y of p y for two stochastic volatility models two stochastic count models and a stochastic duration model i illustrate their use for numerical approximation of likelihood function values and marginal likelihoods using is and for posterior inference using is and mcmc compared with other simulation smoothing methods the hessian method is highly numerically efficient in an is application featuring a student s t stochastic volatility model and n 8851 daily log returns the efficiency of is for numerical approximation of the elements of the posterior mean e y is between 80 and 100

fitting the empirical distribution of intertrade durations based on the analysis of a tick by tick data set used in the previous work by one of the authors djia stocks traded at nyse in october 1999 in this paper we reject the hypothesis that tails of the empirical intertrade distribution are described by a power law we further argue that the tsallis q exponentials are a viable tool for fitting and describing the unconditional distribution of empirical intertrade durations and they compare well to the weibull distribution

causality effects in return volatility measures with random times we provide a structural approach to identify instantaneous causality effects between durations and stock price volatility so far in the literature instantaneous causality effects have either been excluded or cannot be identified separately from granger type causality effects by giving explicit moment conditions for observed returns over random duration intervals we are able to identify an instantaneous causality effect the documented causality effect has significant impact on inference for tick by tick data we find that instantaneous volatility forecasts for e g ibm stock returns must be decreased by as much as 40 when not having seen the next quote change before its conditionally median time also instantaneous volatilities are found to be much higher than indicated by standard volatility assessment procedures using tick by tick data for ibm a naive assessment of spot volatility based on observed returns between quote changes would only account for 60 of the actual volatility for less liquidly traded stocks at nyse this effect is even stronger

statistical analysis of the overnight and daytime return we investigate the two components of the total daily return close to close the overnight return close to open and the daytime return open to close as well as the corresponding volatilities of the 2215 new york stock exchange stocks for the 20 year period from 1988 to 2007 the tail distribution of the volatility the long term memory in the sequence and the cross correlation between different returns are analyzed our results suggest that i the two component returns and volatilities have features similar to that of the total return and volatility the tail distribution follows a power law for all volatilities and long term correlations exist in the volatility sequences but not in the return sequences ii the daytime return contributes more to the total return both the tail distribution and the long term memory of the daytime volatility are more similar to that of the total volatility compared to the overnight records in addition the cross correlation between the daytime return and the total return is also stronger iii the two component returns tend to be anticorrelated moreover we find that the cross correlations between the three different returns total overnight and daytime are quite stable over the entire 20 year period

statistical properties dynamic conditional correlation and scaling analysis evidence from dow jones and nasdaq high frequency data abstract this paper investigates statistical properties of high frequency intraday stock returns across various frequencies both time series and panel data are utilized to explore the properties of probability distribution dynamic conditional correlations and scaling analysis in dow jones industrial average djia and nasdaq intraday returns across 10 min 30 min 60 min 120 min and 390 min frequencies the evidence shows that both returns and volatility standard deviation increase with the increasing scaling from 10 min to 390 min intervals by fitting an ar 1 garch 1 1 model to intraday data we find that ar 1 coefficients are negative for djia returns and positive for nasdaq exhibiting a positive and negative feedback strategy in djia and nasdaq respectively the evidence also shows that these coefficients are statistically significant for either including or excluding opening returns for the 10 min and 30 min frequencies by examining the dynamic conditional correlation between the djia and the nasdaq across different frequencies a positive correlation ranging from 0 6 to 0 8 was found in addition the variance of the dynamic correlation coefficients is decreasing and appears to be stable for the 2001 2003 period finally both returns on djia and nasdaq satisfy the stable levy distributions implying that both markets can converge to equilibrium by self governing mechanism after shocks results of this work provide relevant implications for investors and policy makers

estimation of endogenously sampled time series the case of commodity price speculation in the steel market abstract we consider the problem of estimating a markov process that is endogenously sampled we observe a discrete time markov process p t at a set of random times t 1 t n that depend on the outcome of a probabilistic sampling rule that depends on the state of the process and other observed covariates x t we focus on a particular example where p t is the daily wholesale price of a standardized steel product the endogenous sampling problem arises from the fact that we only observe p t on the days the firm purchases steel we show how to solve this problem under two different assumptions about firm behavior 1 optimality the timing of steel purchases is governed by an optimal purchasing strategy that maximizes expected discounted profits and 2 potential suboptimality we allow the firm to use any randomized markovian purchasing strategy in the latter case the estimation problem becomes semi parametric and we use the method of sieves to estimate a flexible parametric approximation to the firm s purchasing behavior that best fits the data without imposing optimality we show how estimation of this model becomes tractable under either of these assumptions using the method of simulated moments msm we simulate realizations of wholesale steel prices and sample them in the same way as they are sampled in the actual data i e only on days where purchases occur we use the msm estimator to estimate a truncated lognormal ar 1 model of the wholesale price processes for particular types of steel plate and test and reject the assumption that the firm is behaving optimally

residual based rank specification tests for ar garch type models this paper derives the asymptotic distribution for a number of rank based and classical residual specification tests in ar garch type models we consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation residual symmetry and no structural breaks we also apply our method to backtesting value at risk for these tests we show that generally no size correction is needed in the asymptotic test distribution when applied to ar garch residuals obtained through gaussian quasi maximum likelihood estimation to be precise we give exact expressions for the limiting null distribution of the test statistics applied to standardized residuals and find that standard critical values often though not always lead to conservative tests for this result we give simple necessary and sufficient conditions simulations show that our asymptotic approximations work well for a large number of ar garch models and parameter values we also show that the rank based tests often though not always have superior power properties over the classical tests even if they are conservative an empirical application illustrates the relevance of these tests to the ar garch models for weekly stock market return indices of some major and emerging countries

asymptotic spectral theory for nonlinear time series we consider asymptotic problems in spectral analysis of stationary causal processes limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given instead of the commonly used strong mixing conditions in our asymptotic spectral theory we impose conditions only involving conditional moments which are easily verifiable for a variety of nonlinear time series

autoregressive conditional duration a new model for irregularly spaced transaction data this paper proposes a new statistical model for the analysis of data which arrive at irregular intervals the model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates the conditional intensity is developed and compared with other self exciting processes because the model focuses on the expected duration between events it is called the autoregressive conditional duration acd model asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to arch model results strong evidence is provided for duration clustering for the financial transaction data analyzed both deterministic time of day effects and stochastic effects are important the model is applied to the arrival times of trades and therefore is a model of transaction volume and also to the arrival of other events such as price changes models for the volatility of prices are estimated with price based durations and examined from a market microstructure point of view

a bayesian chi squared test for hypothesis testing abstract a new bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss the proposed test statistic may be regarded as the bayesian version of the lagrange multiplier test its asymptotic distribution is obtained based on a set of regular conditions and follows a chi squared distribution when the null hypothesis is correct the new statistic has several important advantages that make it appealing in practical applications first it is well defined under improper prior distributions second it avoids jeffrey lindley s paradox third it always takes a non negative value and is relatively easy to compute even for models with latent variables fourth its numerical standard error is relatively easy to obtain finally it is asymptotically pivotal and its threshold values can be obtained from the chi squared distribution the method is illustrated using some real examples in economics and finance

optimal predictions of powers of conditionally heteroscedastic processes in conditionally heteroskedastic models the optimal prediction of powers or logarithms of the absolute process has a simple expression in terms of the volatility process and an expectation involving the independent process a standard procedure for estimating this prediction is to estimate the volatility by gaussian quasi maximum likelihood qml in a first step and to use empirical means based on rescaled innovations to estimate the expectation in a second step this paper proposes an alternative one step procedure based on an appropriate non gaussian qml estimation of the model and establishes the asymptotic properties of the two approaches their performances are compared for finite order garch models and for the infinite arch for the standard garch p q and the asymmetric power garch p q it is shown that the are of the estimators only depends on the prediction problem and some moments of the independent process an application to indexes of major stock exchanges is proposed

the multi state latent factor intensity model for credit rating transitions a new empirical reduced form model for credit rating transitions is introduced it is a parametric intensity based duration model with multiple states and driven by exogenous covariates and latent dynamic factors the model has a generalized semi markov structure designed to accommodate many of the stylized facts of credit rating migrations parameter estimation is based on monte carlo maximum likelihood methods for which the details are discussed in this paper a simulation experiment is carried out to show the effectiveness of the estimation procedure an empirical application is presented for transitions in a 7 grade rating system the model includes a common dynamic component that can be interpreted as the credit cycle asymmetric effects of this cycle across rating grades and additional semi markov dynamics are found to be statistically significant finally we investigate whether the common factor model suffices to capture systematic risk in rating transition data by introducing multiple factors in the model

weak convergence for a type of conditional expectation application to the inference for a class of asset price models we prove weak convergence ofa type ofconditional expectation which provides a straightforward proofofgoggin s theorem and f proves the consistency of integrated likelihood posterior and bayes factor for a class of transactional asset price models recently developed 2004 elsevier ltd all rights reserved

is the fast hankel transform faster than quadrature the fast hankel transform fht implemented with digital filters has been the algorithm of choice in em geophysics for a few decades however other disciplines have predominantly relied on methods that break up the hankel transform integral into a sum of partial integrals that are each evaluated with quadrature the convergence of the partial sums is then accelerated through a nonlinear sequence transformation while such a method was proposed for geophysics nearly three decades ago it was demonstrated to be much slower than the fht this work revisits this problem by presenting a new algorithm named quadrature with extrapolation qwe the qwe method recasts the quadrature sum into a form conceptually similar to the fhtapproach by using a fixed point quadrature rule the sum of partial integrals is efficiently accelerated using the shanks transformation computed with wynn s algorithm a matlab implementation of the qwe algorithm is compared with the fht method for accuracy and speed on a suite of relevant modeling problems including frequency domain controlledsource em time domain em and a large loop magnetic source problem surprisingly the qwe method is faster than the fht for all three problems however when the integral needs to be evaluated at many offsets and the lagged convolution variant of the fht is applicable the fht is significantly faster than the qwe method for divergent integrals such as those encountered in the large loop problem the qwe method can provide an accurate answer when the fht method fails

well posed ky fan s point quasi variational inequality and nash equilibrium problems abstract we give a unified approach to hadamard well posedness for some nonlinear problems such as those of ky fan s point and quasi variational inequality as applications we obtain some well posed theorems for nash equilibrium points

modelling volatility recurrence intervals in the chinese commodity futures market abstract the law of extreme event occurrence attracts much research the volatility recurrence intervals of chinese commodity futures market prices are studied the results show that the probability distributions of the scaled volatility recurrence intervals have a uniform scaling curve for different thresholds q so we can deduce the probability distribution of extreme events from normal events the tail of a scaling curve can be well fitted by a weibull form which is significance tested by ks measures both short term and long term memories are present in the recurrence intervals with different thresholds q which denotes that the recurrence intervals can be predicted in addition similar to volatility volatility recurrence intervals also have clustering features through monte carlo simulation we artificially synthesise arma garch class sequences similar to the original data and find out the reason behind the clustering the larger the parameter d of the figarch model the stronger the clustering effect is finally we use the fractionally integrated autoregressive conditional duration model fiacd to analyse the recurrence interval characteristics the results indicated that the fiacd model may provide a method to analyse volatility recurrence intervals

optimization problem for a portfolio with an illiquid asset lie group analysis abstract management of a portfolio that includes an illiquid asset is an important problem of modern mathematical finance one of the ways to model illiquidity among others is to build an optimization problem and assume that one of the assets in a portfolio cannot be sold until a certain finite infinite or random moment of time this approach arises a certain amount of models that are actively studied at the moment working in the merton s optimal consumption framework with continuous time we consider an optimization problem for a portfolio with an illiquid a risky and a risk free asset our goal in this paper is to carry out a complete lie group analysis of pdes describing value function and investment and consumption strategies for a portfolio with an illiquid asset that is sold in an exogenous random moment of time with a prescribed liquidation time distribution the problem of such type leads to three dimensional nonlinear hamilton jacobi bellman hjb equations such equations are not only tedious for analytical methods but are also quite challenging form a numeric point of view to reduce the three dimensional problem to a two dimensional one or even to an ode one usually uses some substitutions yet the methods used to find such substitutions are rarely discussed by the authors we find the admitted lie algebra for a broad class of liquidation time distributions in cases of hara and log utility functions and formulate corresponding theorems for all these cases we use found lie algebras to obtain reductions of the studied equations several of similar substitutions were used in other papers before whereas others are new to our knowledge this method gives us the possibility to provide a complete set of non equivalent substitutions and reduced equations

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

generalized arma models with martingale difference errors the analysis of non gaussian time series has been studied extensively and has many applications many successful models can be viewed as special cases or variations of the generalized autoregressive moving average garma models of benjamin et al 2003 where a link function similar to that used in generalized linear models is introduced and the conditional mean under the link function assumes an arma structure under such a model the transformed time series under the same link function assumes an arma form as well unfortunately unless the link function is an identity function the error sequence defined in the transformed arma model is usually not a martingale difference sequence in this paper we extend the garma model in such a way that the resulting arma model in the transformed space has a martingale difference sequence as its error sequence the benefit of such an extension are four folds it has easily verifiable conditions for stationarity and ergodicity its gaussian pseudo likelihood estimator is consistent standard time series model building tools are ready to use and its mle s asymptotic distribution can be established we also proposes two new classes of non gaussian time series models under the new framework the performance of the proposed models is demonstrated with simulated and real examples

diagnostic checking in arma models with uncorrelated errors we consider tests for lack of fit in arma models with nonindependent innovations in this framework the standard box pierce and ljung box portmanteau tests can perform poorly specifically the usual text book formulas for asymptotic distributions are based on strong assumptions and should not be applied without careful consideration in this article we derive the asymptotic covariance matrix of a vector of autocorrelations for residuals of arma models under weak assumptions on the noise the asymptotic distribution of the portmanteau statistics follows a consistent estimator of and a modification of the portmanteau tests are proposed this allows us to construct valid asymptotic significance limits for the residual autocorrelations and asymptotically valid goodness of fit tests when the underlying noise process is assumed to be noncorrelated rather than independent or a martingale difference a set of monte carlo experiments and an application to the standard poor 500 returns illustrate the p

fluctuations in time intervals of financial data from the view point of the gini index abstract we propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the gini index we show the explicit form of the gini index for a weibull distribution a good candidate to describe the first passage time of foreign exchange rate the analytical expression of the gini index compares well with the value obtained from empirical data

bayes estimation via filtering for a simple micro movement model of asset price with discrete noises abstract a simple partially observed model for micro movement of stock prices is proposed the micro movement refers to the transactional price behavior the model can be framed as a filtering problem with counting process observations under this framework the whole sample path is observable and is used for parameter estimation based on the filtering equation we construct a recursive algorithm to compute the approximate posterior and the bayes estimates the consistencies of the recursive algorithm and of bayes estimates are proven bayes estimates for transaction prices of microsoft are obtained with a financial application

diffusion entropy technique applied to the study of the market activity abstract the present work briefly summarizes the results obtained in palatella et al eur phys j b 38 2004 671 using the diffusion entropy technique and adds some new results regarding the dow jones index time series we show that time distances between peaks of volatility or activity are distributed following an asymptotic power law which ultimately recovers an exponential behavior we discuss these results in comparison with the tarch model the ornstein uhlenbeck stochastic volatility model and a multi agent model we conclude that both arch and stochastic volatility models better describe the observed experimental evidences

generalised structured models summary we present a general class of nonlinear regression and time series models that we call generalised structured models the class is a natural generalisation of generalised additive models and it includes generalised interaction models structured volatility models visual garch generalised autoregressive conditional heteroscedasticity models and varying coefficient models we discuss estimation principles including smoothing splines and a generalisation of the projection approach of mammen et al 1999 we finish the paper with some theoretical considerations about the asymptotic performance of the estimator for the general class of generalised structured models

probabilistic forecasts of volatility and its risk premia abstract the object of this paper is to produce distributional forecasts of asset price volatility and its associated risk premia using a non linear state space approach option and spot market information on the latent variance process is captured by using dual model free variance measures to define a bivariate observation equation in the state space model the premium for variance diffusive risk is defined as linear in the latent variance in the usual fashion whilst the premium for variance jump risk is specified as a conditionally deterministic dynamic process driven by a function of past measurements the inferential approach adopted is bayesian implemented via a markov chain monte carlo algorithm that caters for the multiple sources of non linearity in the model and for the bivariate measure the method is applied to spot and option price data on the s p500 index from 1999 to 2008 with conclusions drawn about investors required compensation for variance risk during the recent financial turmoil the accuracy of the probabilistic forecasts of the observable variance measures is demonstrated and compared with that of forecasts yielded by alternative methods to illustrate the benefits of the approach it is used to produce forecasts of prices of derivatives on volatility itself in addition the posterior distribution is augmented by information on daily returns to produce value at risk predictions linking the variance risk premia to the risk aversion parameter in a representative agent model probabilistic forecasts of approximate relative risk aversion are also produced

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

intra day variability of the stock market activity versus stationarity of the financial time series abstract in this paper we propose a new approach to a well known phenomena of intra day activity pattern on the stock market we suggest that seasonality of inter transaction times has a more significant impact than intra day pattern of volatility our aim is not to remove the intra day pattern from the data but to describe its impact on autocorrelation function estimators we obtain an exact analytical formula relating estimators of the autocorrelation functions of non stationary seasonal process to its stationary counterpart hence we prove that the day seasonality of inter transaction times extends the memory of the process that is autocorrelation of both price returns and their absolute values relaxation to zero is longer

nonparametric filtering of conditional state price densities abstract this paper studies the use of noisy high frequency data to estimate the time varying state price density implicit in european option prices a dynamic kernel estimator of the conditional pricing function and its derivatives is proposed that can be used for model free risk measurement infill asymptotic theory is derived that applies when the pricing function is either smoothly varying or driven by diffusive state variables trading times and moneyness levels are modeled by marked point processes that capture intraday trading patterns a simulation study investigates the performance of the estimator using a varying plug in bandwidth in various scenarios empirical analysis using s p 500 e mini european option quotes reveals significant time variation at intraday frequencies an application towards delta and minimum variance hedging further illustrates the use of the estimator

the stochastic conditional duration model a latent variable model for the analysis of financial durations we introduce a class of models for the analysis of durations which we call stochastic conditional duration scd models these models are based on the assumption that the durations are generated by a dynamic stochastic latent variable the model yields a wide range of shapes of hazard functions the estimation of the parameters is performed by quasi maximum likelihood and using the kalman filter the model is applied to trade price and volume durations of stocks traded at nyse we also investigate the relation between price durations spread trade intensity and volume c 2003 elsevier b v all rights reserved

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

a hybrid fast hankel transform algorithm for electromagnetic modeling a hybrid fast hankel transform algorithm has been developed that uses several complementary features of two existing algorithms anderson s digital filtering or fast hankel transform fht algorithm and chave s quadrature and continued fraction algorithm a hybrid fht subprogram called hybfht written in standard fortran 77 provides a simple user interface to call either subalgorithm the hybrid approach is an attempt to combine the best features of the two subalgorithms in order to minimize the user s coding requirements and to provide fast execution and good accuracy for a large class of electromagnetic problems involving various related hankel transform sets with multiple arguments special cases of hankel transforms of double order and double argument are discussed where use of hybfht is shown to be advantageous for oscillatory kernel functions

a long range memory stochastic model of the return in financial markets abstract we present a nonlinear stochastic differential equation sde which mimics the probability density function pdf of the return and the power spectrum of the absolute return in financial markets absolute return as a measure of market volatility is considered in the proposed model as a long range memory stochastic variable the sde is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework the proposed stochastic model generates time series of the return with two power law statistics i e the pdf and the power spectral density reproducing the empirical data for the one minute trading return in the nyse

the dynamic mixed hitting time model for multiple transaction prices and times we propose a structural model for durations between events and a vector of associated marks using a multivariate brownian motion successive passage times of one latent brownian component relative to random boundaries define durations the other correlated brownian components generate the marks our model embeds the class of stochastic conditional scd and autoregressive conditional acd duration models which impose testable restrictions on the relation between the conditional expectation and conditional volatility of durations we strongly reject the scd and acd specifications for both a very liquid and less liquid nyse traded stock and characterize causality relations between volatilities and durations

on linear intensity models for mixed doubly stochastic poisson and self exciting point processes a flexible family of parametric models for intensity processes is introduced to represent a causal relationship between a point process and another stochastic process algorithms for the maximum likelihood computation and the procedure of model selection are discussed

option pricing with a general marked point process this paper examines the impact of a random number of price changes on the options valuation the model introduces the structure of the general marked point processes mpp this kind of model allows us to take account of more general distributions of interarrival times than usual jump diffusion models in particular stock price variations can be correlated with the times of transactions thus the investors can decide to trade according to the history of market values and the sizes of price variations can also depend on the past times of transactions by using the special decomposition of predictable processes with respect to a marked point process the determination of all risk neutral probabilities is detailed derivative prices are calculated in this context with different basic examples

estimation of continuous time markov processes sampled at random time intervals we introduce a family of generalized method of moments estimators of the parameters of a continuous time markov process observed at random time intervals the results include strong consistency asymptotic normality and a characterization of standard errors sampling is at an arrival intensity that is allowed to depend on the underlying markov process and on the parameter vector to be estimated we focus on financial applications including tick based sampling allowing for jump diffusions regime switching diffusions and reflected diffusions

filtered likelihood for point processes abstract point processes are widely used in finance and economics to model the timing of defaults market transactions unemployment spells births and a range of other events we develop and analyze likelihood estimators for the parameters of a marked point process and incompletely observed explanatory factors that influence the arrival intensity and mark distribution we establish an approximation to the likelihood and analyze the convergence and large sample properties of the associated estimators numerical results illustrate the behavior of our estimators

information theoretic optimality of observation driven time series models for continuous responses we investigate information theoretic optimality properties of the score function of the predictive likelihood as a device for updating a real valued time varying parameter in a univariate observation driven model with continuous responses we restrict our attention to models with updates of one lag order the results provide theoretical justification for a class of score driven models which includes the generalized autoregressive conditional heteroskedasticity model as a special case ourmain contribution is to show that only parameter updates based on the score will always reduce the local kullback leibler divergence between the true conditional density and themodel implied conditional density this result holds irrespective of the severity of modelmisspecification we also show that use of the score leads to a considerably smaller global kullback leibler divergence in empirically relevant settings we illustrate the theory with an application to time varying volatility models we show that the reduction in kullback leibler divergence across a range of different settings can be substantial compared to updates based on for example squared lagged observations

a measure of market volatility based on f transform abstract volatility is a tool of fundamental importance for capturing price movements in financial markets in general terms volatility is the tendency of prices to vary along a period of time measuring volatility is a quantitative proxy of uncertainty in prices there are different definitions of volatility measure one of the most common is based on the standard deviation of daily returns in this paper we propose an alternative definition based on f transform and its inverse the method is compatible with the theory of risk originally proposed by duncan luce as experimental setting we considered the nifty 50 stock market index within the period september 2000 and february 2017 results show that the proposed measure is smoother and better correlated between stocks

modeling non stationarities in high frequency financial time series abstract we study tick by tick financial returns for the ftse mib index of the italian stock exchange borsa italiana we confirm previously detected non stationarities scaling properties reported before for other high frequency financial data are only approximately valid as a consequence of our empirical analyses we propose a simple model for non stationary returns based on a non homogeneous normal compound poisson process it turns out that our model can approximately reproduce several stylized facts of high frequency financial time series moreover using monte carlo simulations we analyze order selection for this class of models using three information criteria akaike s information criterion aic the bayesian information criterion bic and the hannan quinn information criterion hq for comparison we perform a similar monte carlo experiment for the acd autoregressive conditional duration model our results show that the information criteria work best for small parameter numbers for the compound poisson type models whereas for the acd model the model selection procedure does not work well in certain cases

a monte carlo approach to filtering for a class of marked doubly stochastic poisson processes marked doubly stochastic poisson processes are a particular type of marked point processes that are characterized by the number of events in any time interval as being conditionally poisson distributed given another positive stochastic process called intensity here we consider a subclass of these processes in which the intensity is assumed to be a deterministic function of another nonexplosive marked point process in particular we will investigate an intensity jump process with an exponential decay having an analytic form for the distribution of the times and sizes of the jumps which can be seen as a generalization of the classical shot noise process assuming that the intensity is unobservable interest here is in its filtering that is in the computation of its conditional distribution over a whole time interval given an observed trajectory of realized events because in general this computation cannot be performed analytically we propose a simulation method that provides an approximate solut