Wai Keung Li - Academia.edu (original) (raw)

Papers by Wai Keung Li

Quantitative Finance, 2011

In this paper, we propose a co-integration model with a logistic mixture auto-regressive equilibr... more 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 (ADF test), used in testing co-integration, cannot give a sound explanation when a time series passes the ADF test. However, its largest root in the AR polynomial is extremely close to, but less than, one, which is most likely the result of a mixture of random-walk and mean-reverting processes in the time series data. With this background, we put an LMAR model into the co-integration framework to identify baskets that have a large spread but are still well co-integrated. A sufficient condition for the stationarity of the LMAR model is given and proved using a Markovian approach. A two-step estimating procedure, combining least-squares estimation and the Expectation-Maximization (EM) algorithm, is given. The Bayesian information criterion (BIC) is used in model selection. The co-integrated LMAR model is applied to basket trading, which is a widely used tool for arbitrage. We use simulation to assess the model in basket trading strategies with the statistical arbitrage feature in equity markets. Data from several sectors of the Hong Kong Hang Seng Index are used in a simulation study on basket trading. Empirical results show that a portfolio using the co-integrated LMAR model has a higher return than portfolios selected by traditional methods. Although the volatility in the return increases, the Sharpe ratio also increases in most cases. This risk–return profile can be explained by the shorter converging period in the co-integrated LMAR model and the larger volatility in the ‘mean-reverting’ regime.

Journal of Time Series Analysis, 1994

. Time series with a changing conditional variance have been found useful in many applications. R... more . Time series with a changing conditional variance have been found useful in many applications. Residual autocorrelations from traditional autoregressive moving-average models have been found useful in model diagnostic checking. By analogy, squared residual autocorrelations from fitted conditional heteroskedastic time series models would be useful in checking the adequacy of such models. In this paper, a general class of squared residual autocorrelations is defined and their asymptotic distribution is obtained. The result leads to some useful diagnostic tools for statisticians using conditional heteroskedastic time series models. Some simulation results and an illustrative example are also reported.

Journal of Time Series Analysis, 1984

For the bilinear time series X , = pX,-,e,-, + en k P 1, formulas for the first k-1 autocorrelati... more For the bilinear time series X , = pX,-,e,-, + en k P 1, formulas for the first k-1 autocorrelations of X : are obtained. These results fill in a gap in Granger and Andersen (1978). Simulation experiments are used to study the applicability of theoretical results and to investigate some more general situations. It is found that if p is not too small, k and 1 may be identified using the autocorrelations of X:. Application to more general situations is also briefly discussed.

Journal of Time Series Analysis, 1997

The autoregressive random variance (ARV) model proposed by Taylor (Financial returns modelled by ... more The autoregressive random variance (ARV) model proposed by Taylor (Financial returns modelled by the product of two stochastic processes, a study of daily sugar prices 1961±79. In Time Series Analysis: Theory and Practice 1 (ed. O. D. Anderson). Amsterdam: North-Holland, 1982, pp. 203±26) is useful in modelling stochastic changes in the variance structure of a time series. In this paper we focus on a general multivariate ARV model. A traditional EM algorithm is derived as the estimation method. The proposed EM approach is simple to program, computationally ef®cient and numerically well behaved. The asymptotic variance±covariance matrix can be easily computed as a by-product using a well-known asymptotic result for extremum estimators. A result that is of interest in itself is that the dimension of the augmented state space form used in computing the variance±covariance matrix can be shown to be greatly reduced, resulting in greater computational ef®ciency. The multivariate ARV model considered here is useful in studying the lead±lag (causality) relationship of the variance structure across different time series. As an example, the leading effect of Thailand on Malaysia in terms of variance changes in the stock indices is demonstrated.

The Statistician, 1996

Possible asymmetric behaviour of stock prices during bear and bull markets are studied by using a... more Possible asymmetric behaviour of stock prices during bear and bull markets are studied by using a threshold type non-linear time series model with conditional heteroscedastic variance. Using Hong Kong data it is demonstrated that the return series could have a conditional mean structure which depends on the rise and fall of the market on a previous day. The findings also shed some light on why it could be difficult to reject the efficient market hypothesis. The threshold model with conditional changing variance is also of interest in other financial applications.

Journal of the American Statistical Association, 1999

Journal of Statistical Planning and Inference, 1997

This paper considers a time series model with a piecewise linear conditional mean and a piecewise... more This paper considers a time series model with a piecewise linear conditional mean and a piecewise linear conditional variance which is a natural extension of Tong&amp;#x27;s threshold autoregressive model. The model has potential applications in modelling asymmetric behaviour in volatility in the financial market. Conditions for stationarity and ergodicity are derived. Asymptotic properties of the maximum likelihood estimator and two

Econometric Reviews, 2009

In this article, a multivariate threshold varying conditional correlation (TVCC) model is propose... more In this article, a multivariate threshold varying conditional correlation (TVCC) model 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 allows for dynamic conditional correlations. Techniques of model identification, estimation and model checking are developed. Some simulation results are reported on the finite sample distribution of the maximum likelihood estimate of the TVCC model. Real examples demonstrate the asymmetric behaviour of the mean and the variance in financial time series and the ability of the TVCC model to capture these phenomena.

Communications in Statistics - Simulation and Computation, 1988

An algorithm to compute the autocovariance functions of periodic autoregressive moving average mo... more An algorithm to compute the autocovariance functions of periodic autoregressive moving average models is proposed. As a result, an easily implemented algorithm for the exact likelihood of these models is rendered possible.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008

An attempt is made in this study to estimate the noise level present in a chaotic time series. Th... more 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 Hénon map, the Lorenz equation, the Duffing equation, the Rossler equation and the Chua's circuit whose dynamical characteristics are known a priori. Different levels of noise are added to the artificial chaotic time series and the estimated results indicate good performance of the proposed method. Finally, the proposed method is applied to estimate the noise level present in some real world data sets.

Canadian Journal of Statistics, 2007

The authors show how to extend univariate mixture autoregressive models to a multivariate time se... more The authors show how to extend univariate mixture autoregressive models to a multivariate time series context. Similar to the univariate case, the multivariate model consists of a mixture of stationary or nonstationary autoregressive components. The authors give the first and second order stationarity conditions for a multivariate case up to order 2. They also derive the second order stationarity condition for the univariate mixture model up to arbitrary order. They describe an EM algorithm for estimation, as well as a diagnostic checking procedure. They study the performance of their method via simulations and include a real application. A propos d'un modèle de mélange autorégressif vectoriel Résumé : Les auteurs montrent comment les modèles de mélange autorégressifs univariés peuventêtré etendus au cas de séries chronologiques multivariées.À l'instar du cas univarié, le modèle multivarié est composé d'un mélange de processus autorégressifs, stationnaires ou non. Les auteurs donnent les conditions de stationnarité de premier et de deuxième ordre des modèles multivariés de degré 1 et 2. Ils précisent aussi les conditions de stationnarité du deuxième ordre pour un modèle de mélange univarié de degré arbitraire. Ils décrivent un algorithme de type EM aux fins d'estimation, ainsi qu'un test diagnostic. Ils examinent la performance de leur procédure au moyen de simulations et présentent une application concrète.

Biometrika, 2001

Biometrika is currently published by Biometrika Trust.

Biometrics, 2011

Introductory Time Series with R, by Cowpertwait, P. S. P. & Metcalfe, A. V., New York : Sprin... more Introductory Time Series with R, by Cowpertwait, P. S. P. & Metcalfe, A. V., New York : Springer-Verlag, 2009.

We consider surveys with one or more callbacks and use a series of logistic regressions to model ... more We consider surveys with one or more callbacks and use a series of logistic regressions to model the probabilities of nonresponse at first contact and subsequent callbacks. These probabilities are allowed to depend on covariates as well as the categorical variable of interest and so the nonresponse mechanism is nonignorable. Explicit formulae for the score functions and information matrices are

We suggest using independent component analysis (ICA) to decompose multivariate time series into ... more We suggest using independent component analysis (ICA) to decompose multivariate time series into statistically independent time series. Then, we propose to use ICA-GARCH models which are computationally efficient to estimate the multivariate volatilities. The experimental results show that the ICA-GARCH models are more effective than existing methods, including DCC, PCA-GARCH, and EWMA. We also apply the proposed models to compute value at risk (VaR) for risk management applications. The backtesting and the out-of-sample tests validate the performance of ICA-GARCH models for value at risk estimation.