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

complex valued wavelet lifting and applications abstractsignals with irregular sampling structures arise naturally in many fields in applications such as spectral decomposition and nonparametric regression classical methods often assume a regular sampling pattern thus cannot be applied without prior data processing this work proposes new complex valued analysis techniques based on the wavelet lifting scheme that removes one coefficient at a time our proposed lifting transform can be applied directly to irregularly sampled data and is able to adapt to the signal s characteristics as our new lifting scheme produces complex valued wavelet coefficients it provides an alternative to the fourier transform for irregular designs allowing phase or directional information to be represented we discuss applications in bivariate time series analysis where the complex valued lifting construction allows for coherence and phase quantification we also demonstrate the potential of this flexible methodology over real valued analysis in the nonparametric re

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

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

particle filters for partially observed diffusions in this paper we introduce novel particle filters for a class of partially observed continuous time dynamic models where the signal is given by a multivariate diffusion process we consider a variety of observation schemes including diffusion observed with error observation of a subset of the components of the multivariate diffusion and arrival times of a poisson process whose intensity is a known function of the diffusion cox process unlike currently available methods our particle filters do not require approximations of the transition and or the observation density using time discretisations instead they build on recent methodology for the exact simulation of the diffusion process and the unbiased estimation of the transition density as described in beskos et al 2006 in particular we introduce the generalised poisson estimator which generalises the poisson estimator of beskos et al 2006 thus our filters avoid the systematic biases caused by time discretisations and they have significant computational advantages over alternative continuous time filters these advantages are supported theoretically by a central limit theorem

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

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 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

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

an analogue of row removal for diagrammatic cherednik algebras we prove an analogue of james donkin row removal theorems for diagrammatic cherednik algebras this is one of the first results concerning the graded decomposition numbers of these algebras over fields of arbitrary characteristic as a special case our results yield a new reduction theorem for graded decomposition numbers and extension groups for cyclotomic q schur algebras

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

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

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

kleshchev s decomposition numbers for diagrammatic cherednik algebras we construct a family of graded isomorphisms between certain subquotients of diagrammatic cherednik algebras as the quantum characteristic multicharge level degree and weighting are allowed to vary this provides new structural information even in the case of the classical q schur algebra this also allows us to prove some of the first results concerning the graded decomposition numbers of these algebras over fields of arbitrary characteristic

local multiplicative bias correction for asymmetric kernel density estimators abstract we consider semiparametric asymmetric kernel density estimators when the unknown density has support on 0 we provide a unifying framework which relies on a local multiplicative bias correction and contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature this framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification we further develop a specification test to determine if a density belongs to a particular parametric family the proposed estimators outperform rival non and semiparametric estimators in finite samples and are easy to implement we provide applications to loss data from a large swiss health insurer and brazilian income data

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

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

pseudo maximum likelihood methods applications to poisson models pseudo maximum likelihood techniques are applied to basic poisson models and to poisson models with specification errors in the latter case it is shown that consistent and asymptotically normal estimators can be obtained without specifying the p d f of the disturbances these estimators are compared both from the finite sample and the asymptotic point of view quasi generalized pml estimators which asymptotically dominate all pml estimators are also proposed finally bivariate and panel data poisson models are discussed the analysis of economic behavior often leads to the study of characteristics taking a small number of positive values the classical linear model is not adapted to explain how such discrete variables depend on other quantitative or qualitative variables the reasons are similar to those usually given in the case of an endogenous qualitative variable the shape of the observation set does not correspond to a linear model the assumption of normality of the disturbances cannot be made since the endogenous variables take a small number of values with strictly positive probabilities and the prediction formulae which are deduced from a linear model give impossible values in the models considered in the literature to describe discrete variables cox and lewis 2 el sayyad 3 frome kutner and beauchamp 4 gilbert 5 hausman hall and griliches 8 see also lancaster 12 the endogenous variable is assumed to have a poisson distribution conditional upon the exogenous variables the parameter of this distribution is a function of the values of the exogenous variables the choice of such a model is justified if the dependent variable counts the occurrence of a given event during a fixed period and if the usual assumptions of the poisson process are satisfied for instance the model is adapted to describe daily numbers of oil tankers arrivals in a port the number of accidents at work by factory or the number of patents applied for and received by firms hausman hall and griliches 8

finite sample properties of the qmle for the log acd model application to australian stocks this paper concerns the properties of the quasi maximum likelihood estimator qmle of the logarithmic autoregressive conditional duration log acd model proofs of consistency and asymptotic normality of qmle for the log acd model with log normal density are presented this is an important issue as the log acd is used widely for testing various market microstructure models and effects knowledge of the distribution of the qmle is crucial for purposes of valid inference and diagnostic checking the theoretical results developed in the paper are evaluated using monte carlo experiments the experimental results also provide insights into the finite sample properties of the log acd model under different distributional assumptions finally this paper presents two extensions to the log acd model to accommodate asymmetric effects the usefulness of these novel models will be evaluated empirically using data from australian stocks

the distribution of first passage times and durations in forex and future markets abstract possible distributions are discussed for intertrade durations and first passage processes in financial markets the view point of renewal theory is assumed in order to represent market data with relatively long durations two types of distributions are used namely a distribution derived from the mittag leffler survival function and the weibull distribution for the mittag leffler type distribution the average waiting time residual life time is strongly dependent on the choice of a cut off parameter t max whereas the results based on the weibull distribution do not depend on such a cut off therefore a weibull distribution is more convenient than a mittag leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations on the other hand we find that the gini index is rather independent of the cut off parameter based on the above considerations we propose a good candidate for describing the distribution of first passage time in a market the weibull distribution with a power law tail this distribution compensates the gap between theoretical and empirical results more efficiently than a simple weibull distribution it should be stressed that a weibull distribution with a power law tail is more flexible than the mittag leffler distribution which itself can be approximated by a weibull distribution and a power law indeed the key point is that in the former case there is freedom of choice for the exponent of the power law attached to the weibull distribution which can exceed 1 in order to reproduce decays faster than possible with a mittag leffler distribution we also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory moreover we discuss the limitation of our distributions by applying our distribution to the analysis of the btp future and calculating the average waiting time we find that our distribution is applicable as long as durations follow a weibull law for short times and do not have too heavy a tail

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

relaxation dynamics of aftershocks after large volatility shocks in the ssec index abstract the relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high frequency data sets of the shanghai stock exchange composite ssec index compared with previous relevant work we have defined main financial shocks based on large volatilities rather than large crashes we find that the occurrence rate of aftershocks with the magnitude exceeding a given threshold for both daily volatility constructed using 1 minute data and minutely volatility using intra minute data decays as a power law the power law relaxation exponent increases with the volatility threshold and is significantly greater than 1 taking financial volatility as the counterpart of seismic activity the power law relaxation in financial volatility deviates remarkably from the omori law in geophysics

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

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

nonlinear garch model and 1 f noise abstract auto regressive conditionally heteroskedastic arch family models are still used by practitioners in business and economic policy making as a conditional volatility forecasting models furthermore arch models still are attracting an interest of the researchers in this contribution we consider the well known garch 1 1 process and its nonlinear modifications reminiscent of ngarch model we investigate the possibility to reproduce power law statistics probability density function and power spectral density using arch family models for this purpose we derive stochastic differential equations from the garch processes in consideration we find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics we show that linear garch 1 1 process has power law distribution but its power spectral density is brownian noise like however the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 f form including 1 f noise

a multiple indicators model for volatility using intra daily data many ways exist to measure and model financial asset volatility in principle as the frequency of the data increases the quality of forecasts should improve yet there is no consensus about a true or best measure of volatility in this paper we propose to jointly consider absolute daily returns daily high low range and daily realized volatility to develop a forecasting model based on their conditional dynamics as all are non negative series we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function the estimation results show significant interactions between the indicators we also show that one month ahead forecasts match well both in and out of sample the market based volatility measure provided by an average of implied volatilities of index options as measured by vix

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 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

functional data analysis for clients segmentation tasks functional analysis of variance fanova is used to test whether there are some effects in cash flow processes that could be attributed to some categorical variable two data sets are under investigation first data set represents cash flow processes with geographical and the second one with merchant type attributes

empirical shape function of limit order books in the chinese stock market abstract we have analyzed the statistical probabilities of limit order book lob shape through building the book using the ultra high frequency data from 23 liquid stocks traded on the shenzhen stock exchange in 2003 we find that the averaged lob shape has a maximum away from the same best price for both buy and sell sides of the lob the lob shape function has nice exponential form in the right tail the buy side of the lob is found to be abnormally thicker for the price levels close to the same best although there are much more sell orders on the book we also find that the lob shape functions for both buy and sell sides have periodic peaks with a period of five the 1 min averaged volumes at fixed tick level follow log normal distributions except for the left tails which display power law behaviors exhibit abnormal intraday patterns with increasing trend and possess long memory that cannot be explained by the intraday patterns academic implications of our empirical results are also briefly discussed

schubert calculus and torsion explosion the author observes that certain numbers occurring in schubert calculus for sl also occur as entries in intersection forms controlling decompositions of soergel bimodules in higher rank these numbers grow exponentially this observation gives many counter examples to the expected bounds in lusztig s conjecture on the characters of simple rational modules for sl over fields of positive characteristic the examples also give counter examples to the james conjecture on decomposition numbers for symmetric groups

testing for jumps when asset prices are observed with noise a swap variance approach abstract this paper proposes a new test for jumps in asset prices that is motivated by the literature on variance swaps formally the test follows by a direct application of ito s lemma to the semi martingale process of asset prices and derives its power from the impact of jumps on the third and higher order return moments intuitively the test statistic reflects the cumulative gain of a variance swap replication strategy which is known to be minimal in the absence of jumps but substantial in the presence of jumps simulations show that the jump test has nice properties and is generally more powerful than the widely used bi power variation test an important feature of our test is that it can be applied in analytically modified form to noisy high frequency data and still retain power as a by product of our analysis we obtain novel analytical results regarding the impact of noise on bi power variation an empirical illustration using ibm trade data is also included

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

categorifications and cyclotomic rational double affine hecke algebras varagnolo and vasserot conjectured an equivalence between the category mathcal o for crdaha s and a subcategory of an affine parabolic category o of type a we prove this conjecture as applications we prove a conjecture of rouquier on the dimension of simple modules of crdaha s and a conjecture of chuang miyachi on the koszul duality for the category mathcal o of crdaha s

modelling non homogeneous poisson processes with almost periodic intensity functions summary we propose a model for the analysis of non stationary point processes with almost periodic rate of occurrence the model deals with the arrivals of events which are unequally spaced and show a pattern of periodicity or almost periodicity such as stock transactions and earthquakes we model the rate of occurrence of a non homogeneous poisson process as the sum of sinusoidal functions plus a baseline consistent estimates of frequencies phases and amplitudes which form the sinusoidal functions are constructed mainly by the bartlett periodogram the estimates are shown to be asymptotically normally distributed computational issues are discussed and it is shown that the frequency estimates must be resolved with order o t 1 to guarantee the asymptotic unbiasedness and consistency of the estimates of phases and amplitudes where t is the length of the observation period the prediction of the next occurrence is carried out and the mean squared prediction error is calculated by monte carlo integration simulation and real data examples are used to illustrate the theoretical results and the utility of the model