Wai Keung Li

Education University of Hong Kong | ied · Department of Mathematics and Information Technology (MIT)

There has been growing interest in extending the popular threshold time series models to include a buffer zone for regime transition. However, almost all attention has been on buffered autoregressive models. Note that the classical moving average (MA) model plays an equally important role as the autoregressive model in classical time series analysi...

This paper first constructs a new generalized Hausman test for detecting the structural change in a multiplicative form of covariance matrix time series model. This generalized Hausman test is asymptotically pivotal, and it has non-trivial power to detect a broad class of alternatives. Moreover, this paper proposes a new semiparametric covariance m...

We propose a new Conditional BEKK matrix-F (CBF) model for the time-varying realized covariance (RCOV) matrices. This CBF model is capable of capturing the heavy-tailed RCOV, which is an important stylized fact but could be handled inadequately by the Wishart-based models. Moreover, we give a systematical study on the probabilistic properties and s...

Asymmetric power GARCH models have been widely used to study the higher order moments of financial returns, while their quantile estimation has been rarely investigated. This paper introduces a simple monotonic transformation on its conditional quantile function to make the quantile regression tractable. The asymptotic normality of the resulting qu...

We consider the Autoregressive Conditional Marked Duration (ACMD) model and apply it to 16 stocks traded in Hong Kong Stock Ex-change (SEHK). By examining the orderings of appropriate sets of model parameters, market microstructure phenomena can be explained. To sub-stantiate these conclusions, likelihood ratio test is used for testing the sig-nifi...

This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the innovations of both time series. Under regular conditions, the limiting null distributions of our HSIC-based tests are e...

Modeling and forecasting covariance matrices of asset returns play a crucial role in many financial fields, such as portfolio allocation and asset pricing. The availability of high frequency intraday data enables the modeling of the realized covariance matrix directly. However, most models in the literature suffer from the curse of dimension- ality...

The proposition of tail risk as a new asset pricing factor has gained traction in recent years. Recent work by Almeida, Ardison, Garcia, and Vicente (Nonparametric tail risk, stock returns, and the macroeconomy. J. Financ. Economet., 2017, 15(3), 333–376) proxies the cross-sectional variation in returns by Fama-French portfolios, which are further...

Variable screening for censored survival data is most challenging when both survival and censoring times are correlated with an ultrahigh‐dimensional vector of covariates. Existing approaches to handling censoring often make use of inverse probability weighting by assuming independent censoring with both survival time and covariates. This is a conv...

We distinguish the evaluation methods for two main kinds of investment strategies, namely, passive and active portfolio management. Passive portfolio management aims at tracking an underlying index as close as possible with the most important measure being the tracking error. To claim the tracking error not exceeding a certain threshold, we apply t...

A fuzzy portfolio selection model is considered with a view to incorporating ambiguity about model and data structure. The model features the uncertainty about the exit time of each risky asset within a pre- specified investment horizon and also the presence of transaction costs. However, departing from the traditional paradigm where the transactio...

In this article, we propose a generalized threshold conditional autoregressive Wishart (GTCAW) model to analyze the dynamics of the realized covariance (RCOV) matrices. This model extends the idea of [29] to a threshold framework. It is believed that, as in many financial time series, the dynamic of RCOV matrices exhibits nonlinearity and may be be...

This article investigates a portmanteau test statistic for checking model adequacy of smooth transition autoregressive (STAR) models. The asymptotic distribution of residual autocorrelations and the least‐squares estimators are also derived. Hence, the correct asymptotic standard errors for residual autocorrelations are also obtained facilitating m...

Asymmetric power GARCH models have been widely used to study the higher order moments of financial returns, while their quantile estimation has been rarely investigated. This paper introduces a simple monotonic transformation on its conditional quantile function to make the quantile regression tractable. The asymptotic normality of the resulting qu...

We propose a new Conditional BEKK matrix-F (CBF) model for the time-varying realized covariance (RCOV) matrices. This CBF model is capable of capturing heavy-tailed RCOV, which is an important stylized fact but could not be handled adequately by the Wishart-based models. To further mimic the long memory feature of the RCOV, a special CBF model with...

Recently, inference about high-dimensional integrated covariance matrices (ICVs) based on noisy high-frequency data has emerged as a challenging problem. In the literature, a pre-averaging estimator (PA-RCov) is proposed to deal with the microstructure noise. Using the large-dimensional random matrix theory, it has been established that the eigenva...

With the rapid development of internet economy, transparent logistics is stepping into a prosperity period with massive transportation data generated and collected every day. In this paper, we focus on the segmentation of GPS trajectory data generated in logistics transportation to analyze the vehicle behaviors and extract business affair informati...

Buffered autoregression is an extension of the classical threshold autoregression by allowing a buffer region for regime changes. In this paper, we study asymptotic statistical inference for the two-regime Buffered Autoregressive (BAR) model with autoregressive unit roots. We propose a Sup-LR test for the nonlinear buffer effect in the possible pre...

This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the innovations of both time series. Under regular conditions, the limiting null distributions of our HSIC-based tests are e...

time series models with heavy-tailed innovations has been widely discussed, but corresponding goodness-of-fit tests have attracted less attention, primarily because the autocorrelation function commonly used in constructing goodness-of-fit tests necessarily imposes certain moment conditions on the innovations. As a bounded random variable has finit...

This paper extends the work of Yuen et al. (2013), who obtained explicit results for the discount-free Gerber–Shiu function for a compound binomial risk model in the presence of delayed claims and a randomized dividend strategy with a zero threshold level. Specifically, we establish a recursion method for computing the Gerber–Shiu expected discount...

Realized moments of higher order computed from intraday returns are introduced in recent years. The literature indicates that realized skewness is an important factor in explaining future asset returns. However, the literature mainly focuses on the whole market and on the monthly or weekly scale. In this paper, we conduct an extensive empirical ana...

This paper introduces a new model called the buffered autoregressive model with generalized autoregressive conditional heteroscedasticity (BAR-GARCH). The proposed model, as an extension of the BAR model in Li et al. (2015), can capture the buffering phenomena of time series in both the conditional mean and variance. Thus, it provides us a new way...

Pairs trading can be regarded as conditional mean reversion strategies. The conditions are usually imposed in two stages: Identification of pairs’ relationship and the opening (and closing) mechanism sequentially as a ‘pass or fail’ test. Nevertheless, as cointegration relationship is often not a ‘yes or no’ question but a ‘strong or weak’ one, dic...

We extend a current result in the literature by introducing a parametric family of matrix-valued cross-covariance functions, which would help describe multivariate space–time dependence structures for any number of variables. All the direct and cross-covariance functions belong to the Matérn class. The smoothness, space–time separability and scale...

The Matern class is an important class of covariance functions in spatial statistics. With the recent flourishing trend in modelling spatio-temporal data, indepth theoretical development of spatio-temporal covariograms is needed. In this paper, theories under the infill asymptotic framework concerning estimation issues of a generally non-separable...

Ian McLeod’s contributions to time series are both broad and influential. His work has put Canada and the University of Western Ontario on the map in the time series community. This article strives to give a partial picture of McLeod’s diverse contributions and their impact by reviewing the development of portmanteau statistics, long memory (persis...

We derive the asymptotic distribution of residual autocorrelations for the Weibull autoregressive conditional duration (ACD) model, and this leads to a portmanteau test for the adequacy of the fitted Weibull ACD model. The finite-sample performance of this test is evaluated by simulation experiments and a real data example is also reported.

This paper proposes a conditional heteroscedastic model with a new piecewise linear structure such that the regime-switching mechanism has a buffer zone where regime-switching is delayed. The Gaussian quasi-maximum likelihood estimation (QMLE) is considered, and its asymptotic behaviors, including the strong consistency and the asymptotic distribut...

Dispersion regression is often used to predict the expected deviance in a generalised linear model. Using the individual deviance residual as the response variable in that model is considered the standard approach in dispersion modelling. In this paper, we investigate an alternative approach by fitting the dispersion model on the individual Pearson...

Spatio-temporal processes involving more than one variable emerge in various fields. Any serious attempt of statistical inference and prediction for multivariate data require knowledge about the dependency structures within and across variables. In this work, we provide general conditions leading to positive semi-definiteness of the overall matrix-...

To appear. Please find it here: doi:10.5705/ss.202015.0037

This volume reviews and summarizes some of A. I. McLeod's significant contributions to time series analysis. It also contains original contributions to the field and to related areas by participants of the festschrift held in June 2014 and friends of Dr. McLeod. Covering a diverse range of state-of-the-art topics, this volume well balances applied...

This paper proposes a mixture double autoregressive model by introducing the flexibility of mixture models to the double autoregressive model, a novel conditional heteroscedastic model recently proposed by Ling (2004). To make it more flexible, the mixing proportions are further assumed to be time varying, and probabilistic properties including str...

It is well known that in finance variances and covariances of asset returns move together over time. Recently, much interest has been aroused by an approach involving the use of the realized covariance (RCOV) matrix constructed from high-frequency returns as the ex-post realization of the covariance matrix of low-frequency returns. For the analysis...

This article proposes a novel Pearson-type quasi-maximum likelihood estimator (QMLE) of GARCH(p, q) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not just the heavy-tailed but also the skewed innovations. Under strict stationarity and some weak moment...

In many situations, we may encounter time series that are non-negative. Examples include trading duration, volume transaction and price volatility in finance, waiting time in a queue in social sciences, and daily/hourly rainfall in natural sciences. The vector multiplicative error model (VMEM) is a natural choice for modeling such time series in a...

In this paper, we introduce valid parametric covariance models for univariate and multivariate spatio-temporal random fields. In contrast to the traditional models, we allow the model parameters to vary over time. Since variables in applications usually exhibit seasonality or changes in dependency structures, the allowance of varying parameters wou...

This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condit...

The problem of heavy tail in regression models is studied. It is proposed that regression models are estimated by a standard procedure and a statistical check for heavy tail using residuals is conducted as a tool for regression diagnostic. Using the peaks-over-threshold approach, the generalized Pareto distribution quantifies the degree of heavy ta...

Generalized Threshold Model (GTM) is a non-linear time series model which generalizes the Threshold Autoregressive Model (TAR) to implement the idea of the Generalized Linear Model under the threshold time series framework. However, the dispersion parameter is usually assumed as constant in the context of Generalized Linear Model which does not hol...

The estimation for time series models with heavy-tailed innovations has been widely discussed in the literature, while the corresponding goodness-of-fit tests have attracted less attention. This is mainly because the commonly used autocorrelation function in constructing goodness-of-fit tests necessarily imposes certain moment conditions on the inn...

Correlation stress testing is motivated by a well-known phenomenon: correlations change under financial crises. The adjustment of correlation matrices may be required to evaluate the potential impact of these changes. Very often, some correlations are explicitly adjusted (core correlations), with the remainder left unspecified (peripheral correlati...

********************************************************************* Free eprints available at http://www.tandfonline.com/eprint/VqdItQfIC7ccVPsh5kqP/full ********************************************************************* This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the ob...

This paper investigates a quasi-likelihood ratio (LR) test for the thresholds in buffered autoregressive processes. Under the null hypothesis of no threshold, the LR test statistic converges to a function of a centered Gaussian process. Under local alternatives, this LR test has nontrivial asymptotic power. A bootstrap method is proposed to obtain...

Excess zeros and overdispersion are common phenomena that limit the use of traditional Poisson regression models for modeling count data. Both excess zeros and overdispersion caused by unobserved heterogeneity are accounted for by the proposed zero-inflated Poisson (ZIP) regression mixture model. To estimate the parameters of the model, an EM algor...

A testing problem of homogeneity in gamma mixture models is studied. It is found that there is a proportion of the penalized likelihood ratio test statistic that degenerates to zero. The limiting distribution of this statistic is found to be the chi-bar-square distributions. The degeneration is due to the negative-definiteness of a complicated rand...

Correlation stress testing refers to the correlation matrix adjustment to evaluate potential impact of the changes in correlations under financial crises. There are two categories, sensitivity tests and scenario tests. For a scenario test, the correlation matrix is adjusted to mimic the situation under an underlying stress event. It is only natural...

We propose a new volatility model, which is called the mixture memory generalized autoregressive conditional heteroskedasticity (MM-GARCH) model. The MM-GARCH model has two mixture components, of which one is a short-memory GARCH and the other is the long-memory fractionally integrated GARCH. The new model, a special ARCH( ∞ ) process with random c...

This paper describes a novel statistical approach to derive ecologically relevant sediment quality guidelines (SQGs) from field data using a nonparametric empirical Bayesian method (NEBM). We made use of the Norwegian Oil Industrial Association database and extracted concurrently obtained data on species density and contaminant levels in sediment s...

This paper studies the asymptotic theory of least squares estimation in a threshold moving average model. Under some mild conditions, it is shown that the estimator of the threshold is n-consistent and its limiting distribution is related to a two-sided compound Poisson process, whereas the estimators of other coefficients are strongly consistent a...

Radial basis function (RBF) networks are considered in this study to simulate and forecast a chaotic time series. In order to evaluate the performance of the RBF networks, a new method is developed to calculate the generalized degree of freedom (GDF), which is used to obtain an unbiased estimation of variance of the fitted model error for the netwo...

We consider a model which allows data-driven threshold selection in extreme value analysis. A mixture exponential distribution is employed as the thin-tailed distribution in view of the special structure of insurance claims, where individuals are often grouped into categories. An EM algorithm-based procedure is described in model fitting. We then d...

In this study, the correlation sum and the correlation integral for chaotic time series using the Supremum norm and the Euclidean norm are discussed. The correlation integrals are then used to develop governing equations for the correlation sum, noise level and correlation dimension in which the correlation dimension and the noise level are linearl...

The classical autocorrelation function may not be an effective and informative means in revealing the dependence features of a binary time series {y}. Recently, the autopersistence functions defined as APF0(k) = P(yt k = 1 | yt = 0) and APF1(k) = P(yt k = 1 | yt = 1), k = 1, 2,…, have been proposed as alternatives to the autocorrelation function fo...

In this article, a Multivariate Threshold Generalized Autoregressive Conditional Het-eroscedasticity model with time-varying correlation (VC-MTGARCH) is proposed. The model extends the idea of Engle (2002) and Tse & Tsui (2002) to a threshold framework. This model retains the interpretation of the univariate threshold GARCH model and al-lows for dy...

Davidson (2004) recently proposed the hyperbolic GARCH model to capture the phenomenon of longrange dependence in volatility, with the extent of such dependence measured by the geometric or hyperbolic decay of the coefficients in an ARCH(∞) model. In this article, we reinterpret the hyperbolic GARCH model by building a link with the common GARCH mo...

Artificial Neural Networks (ANNs) are now widely used in many areas of science, medicine, finance and engineering. Analysis and prediction of time series of hydrological/and meteorological data is one such application. Problems that still exist in the application of ANN's are the lack of transparency and the expertise needed for training. An evolut...

Construction of nonlinear time series models with a flexible probabilistic structure is an important challenge for statisticians. Applications of such a time series model include ecology, economics and finance. In this paper we consider a threshold model for all the first four conditional moments of a time series. The nonlinear structure in the con...

In this paper, we propose a co-integration model with a logistic mixture auto-regressive equilibrium error (co-integrated LMAR), in which the equilibrium relationship among cumulative returns of different financial assets is modelled by a logistic mixture autoregressive time series model. The traditional autoregression (AR) based unit root test (AD...

Zero-inflated data are an often observed phenomenon in empirical studies of different scientific fields. Data are considered as zero-inflated if the observed values of a random vector contain significantly more zeros than expected. The excessive existing zeros, especially when it occurs to the dependent variable in a regression model, discourage st...

This paper derives the asymptotic null distribution of a quasilikelihood ratio test statistic for an autoregressive moving average model against its threshold extension. The null hypothesis is that of no threshold, and the error term could be dependent. The asymptotic distribution is rather complicated, and all existing methods for approximating a...

This paper derives the asymptotic null distribution of a quasilikelihood ratio test statistic for an autoregressive moving average model against its threshold extension. The null hypothesis is that of no threshold, and the error term could be dependent. The asymptotic distribution is rather complicated, and all existing methods for approximating a...

This paper considers the least squares estimation and es-tablishes its asymptotic theory for threshold autoregressive and moving-average models. Under some mild conditions, it is shown that the estimator of the threshold is n-consistent and after normalization it converges weakly to the smallest minimizer of a compound Poisson process, while the es...

In the financial market, the volatility of financial assets plays a key role in the problem of measuring market risk in many investment decisions. Insights into economic forces that may contribute to or amplify volatility are thus important. The financial market is characterized by regime switching between phases of low volatility and phases of hig...

The idea of statistical learning can be applied in financial risk management. In recent years, value-at-risk (VaR) has become the standard tool for market risk measurement and management. For better VaR estimation, Engle and Manganelli (2004) introduced the conditional autoregressive value-at-risk (CAViaR) model to estimate the VaR directly by quan...

We propose a threshold model extending the generalized Pareto distribution for exceedances over a threshold. The threshold is solely determined within the model and is shown to be super-consistent under the maximum product of spacings estimation method. We apply the model to some insurance data and demonstrate the merit of having a full parametric...

A method of estimating the Kolmogorov-Sinai (KS) entropy, herein referred to as the modified correlation entropy, is presented. The method can be applied to both noise-free and noisy chaotic time series. It has been applied to some clean and noisy data sets and the numerical results show that the modified correlation entropy is closer to the KS ent...

The estimation and diagnostic checking of the fractional autoregressive integrated moving average with hyperbolic generalized autoregressive conditional heteroscedasticity (ARFIMA–HYGARCH) model is considered. The ARFIMA–HYGARCH model is a long-memory model for the conditional mean that also allows for long memory in the conditional variance, the l...

As a data mining technique, independent component analysis (ICA) is used to separate mixed data signals into statistically independent sources. In this chapter, we apply ICA for modeling multivariate volatility of financial asset returns which is a useful tool in portfolio selection and risk management. In the finance literature, the generalized au...

In this article, a multivariate threshold varying conditional correlation (TVCC) model is proposed. The model extends the idea of Engle (2002) and Tse and Tsui (2002) to a threshold framework. This model retains the interpretation of the univariate threshold GARCH model and allows for dynamic conditional correlations. Techniques of model identifica...

In this paper we use Ching's multivariate Markov,chain model to model the dependency of rating transitions of several credit entities. The model is an enhancement of the multivariate Markov chain model for ratings considered by Siu et al. Our model is more parsimonious, flexible and empirically competent than the model used by Silt et al. We adopt...

In many regions, monthly (or bimonthly) rainfall data can be considered as deterministic while daily rainfall data may be treated as random. As a result, deterministic models may not sufficiently fit the daily data because of the strong stochastic nature, while stochastic models may also not reliably fit into daily rainfall time series because of t...

This paper considers a local least absolute deviation estimation for unit root processes with generalized autoregressive conditional heteroskedastic (GARCH) errors and derives its asymptotic properties under only finite second-order moment for both errors and innovations. When the innovations are symmetrically distributed, the asymptotic distributi...

Extensions of Tong's threshold approach to other fields of statistics abound. Among these, the application of the threshold approach to model volatility changes in financial time series has been particularly noteworthy. This paper aims to give a brief survey on this vast and important development since the birth of the threshold autoregression mode...

We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterizing the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculati...

In this paper, we first introduce the use of an interactive hidden Markov model (IHMM) for modeling and analyzing default data in a sector. Under the IHMM, transitions of the hidden risk states of the sector depend on the observed number of bonds in the sector that default in the current time period. This incorporates the feedback effect of the num...

Generalized linear models are applied in a data-rich environment and the principle component method is applied to reduce the number of covariants. Autoregressive (AR) time series models are considered in the framework of generalized linear models and these results are extended to autoregressive moving average (ARMA) models. In generalized autoregre...

The double autoregressive model finds its use in the modelling of conditional heteroscedasticity of time series data. In view of its growing popularity, the goodness-of-fit of the model is examined. The asymptotic distributions of the residual and squared residual autocorrelations are derived. Two test statistics are then constructed which can be u...

A test for independence of multivariate time series based on the mutual information measure is proposed. First of all, a test for independence between two variables based on i.i.d. (time-independent) data is constructed and is then extended to incorporate higher dimensions and strictly stationary time series data. The smoothed bootstrap method is u...

This paper proposes a new mixture GARCH model with a dynamic mixture proportion. The mixture Gaussian distribution of the error can vary from time to time. The Bayesian Information Criterion and the EM algorithm are used to estimate the number of parameters as well as the model parameters and their standard errors. The new model is applied to the S...

Searching for an effective dimension reduction space is an important problem in regression, especially for high dimensional data. We propose an adaptive approach based on semiparametric models, which we call the (conditional) minimum average variance estimation (MAVE) method, within quite a general setting. The MAVE method has the following advanta...

ABSTRACT The distribution of the cross-correlations of squared residuals from Box-Jenkins models is considered in very general conditions, and the asymptotic distribution is derived. A test for a lagged relationship in volatility for economic time series under instantaneous causality is proposed, and its empirical behaviour is studied. An example i...

The autoregressive conditional intensity model proposed by Russell (1998) is a promising option for fitting multivariate high frequency irregularly spaced data. The authors acknowledge the validity of this model by showing the independence of its generalized residuals, a crucial assumption of the model formulation not readily recognized by research...

An attempt is made in this study to estimate the noise level present in a chaotic time series. This is achieved by employing a linear least-squares method that is based on the correlation integral form obtained by Diks in 1999. The effectiveness of the method is demonstrated using five artificial chaotic time series, the Henon map, the Lorenz equat...