Multivariate Financial Time Series Research Articles

Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory

Nonlinear functions of multivariate financial time series can exhibit long memory and fractional cointegration. However, tools for analysing these phenomena have principally been justified under assumptions that are invalid in this setting. Determination of asymptotic theory under more plausible assumptions can be complicated and lengthy. We discuss these issues and present a Monte Carlo study, showing that asymptotic theory should not necessarily be expected to provide a good approximation to finite-sample behavior.

Robust M-Estimation of Multivariate GARCH models

In empirical work on multivariate financial time series, it is common to postulate a Multivariate GARCH model. We show that the popular Gaussian quasi-maximum likelihood estimator of MGARCH models is very sensitive to outliers in the data. We propose to use robust M-estimators and provide asymptotic theory for M-estimators of MGARCH models. The Monte Carlo study and empirical application document the good robustness properties of the M-estimator with a fat-tailed Student t loss function and volatility models with the property of bounded innovation propagation.

Testing multivariate distributions in GARCH models

In this paper, we consider testing distributional assumptions in multivariate GARCH models based on empirical processes. Using the fact that joint distribution carries the same amount of information as the marginal together with conditional distributions, we first transform the multivariate data into univariate independent data based on the marginal and conditional cumulative distribution functions. We then apply the Khmaladze's martingale transformation (K-transformation) to the empirical process in the presence of estimated parameters. The K-transformation eliminates the effect of parameter estimation, allowing a distribution-free test statistic to be constructed. We show that the K-transformation takes a very simple form for testing multivariate normal and multivariate t-distributions. The procedure is applied to a multivariate financial time series data set.

Modelling the Dynamic Dependence Structure in Multivariate Financial Time Series

Abstract. The dependence structure in multivariate financial time series is of great importance in portfolio management. By studying daily return histories of 17 exchange‐traded index funds, we identify important features of the data, and we propose two new models to capture these features. The first is an extension of the multivariate BEKK (Baba, Engle, Kraft, Kroner) model, which includes a multivariate t‐type error distribution with different degrees of freedom. We demonstrate that this error distribution is able to accommodate different levels of heavy‐tailed behaviour and thus provides a better fit than models based on a multivariate t‐with a common degree of freedom. The second model is copula based, and can be regarded as an extension of the standard and the generalized dynamic conditional correlation model [Engle, Journal of Business and Economics Statistics (2002) Vol. 17, 425–446; Cappiello et al. (2003) Working paper, UCSD] to a Student copula. Model comparison is carried out using criteria including the Akaike information criteria and Bayesian information criteria. We also evaluate the two models from an asset‐allocation perspective using a three‐asset portfolio as an example, constructing optimal portfolios based on the Markowitz theory. Our results indicate that, for our data, the proposed models both outperform the standard BEKK model, with the copula model performing better than the extension of the BEKK model.

A Multivariate Integer Count Hurdle Model: Theory and Application to Exchange Rate Dynamics

In this paper we propose a model for the conditional multivariate density of integer count variables defined on the set Zn. Applying the concept of copula functions, we allow for a general form of dependence between the marginal processes which is able to pick up the complex nonlinear dynamics of multivariate financial time series at high frequencies. We use the model to estimate the conditional bivariate density of the high frequency changes of the EUR/GBP and the EUR/USD exchange rates.

Extremal financial risk models and portfolio evaluation

It is difficult to find an existing single model which is able to simultaneously model exceedances over thresholds in multivariate financial time series. A new modeling approach, which is a combination of max-stable processes, GARCH processes, and Markov processes, is proposed. Combining Markov processes and max-stable processes defines a new statistical model which has the flexibility of modeling cross-sectional tail dependencies between risk factors and tail dependencies across time. The new model also models asymmetric behaviors of negative and positive returns on financial assets. An important application of the proposed method is to calculate value at risk (VaR) and evaluate portfolio combinations under VaR constraints. Result comparisons between VaRs based on the new approach and VaRs based on some existing methods such as variance–covariance approach and historical simulation approach suggest that some existing methods substantially underestimate the risks during recession and expansion time.

Synchronizing multivariate financial time series

Prices or returns of financial assets are most often collected in local times of the trading markets. The need to synchronize multivariate time series of financial prices or returns is motivated by the fact that information continues to flow for closed markets while others are still open. We propose here a synchronization technique together with further modelling of synchronized returns: The overall method can then be described in terms of a new model for asynchronous returns. Besides the nice interpretation of synchronization, the method potentially increases the predictive performance of many reasonable models and is more appropriate for the calculation of portfolio risk measures such as for example the expected shortfall. We found empirically that this was the case when synchronizing the CCC-GARCH(1,1) model for a 7-dimensional time series of daily exchange rate returns. Since multivariate analysis is generally important for analyzing time-changing portfolios and for better portfolio predictions (even when portfolio weights are time-constant), synchronization is a valuable technique for a variety of problems with multivariate financial data.

Bayesian Dynamic Factor Models and Portfolio Allocation

We discuss the development of dynamic factor models for multivariate financial time series, and the incorporation of stochastic volatility components for latent factor processes. Bayesian inference and computation is developed and explored in a study of the dynamic factor structure of daily spot exchange rates for a selection of international currencies. The models are direct generalizations of univariate stochastic volatility models and represent specific varieties of models recently discussed in the growing multivariate stochastic volatility literature. We discuss model fitting based on retrospective data and sequential analysis for forward filtering and short-term forecasting. Analyses are compared with results from the much simpler method of dynamic variance-matrix discounting that, for over a decade, has been a standard approach in applied financial econometrics. We study these models in analysis, forecasting, and sequential portfolio allocation for a selected set of international exchange-rate-return time series. Our goals are to understand a range of modeling questions arising in using these factor models and to explore empirical performance in portfolio construction relative to discount approaches. We report on our experiences and conclude with comments about the practical utility of structured factor models and on future potential model extensions.

RANDOM MATRIX THEORY AND FINANCIAL CORRELATIONS

We show that results from the theory of random matrices are potentially of great interest when trying to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate financial time series. We find a remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). Finally, we give a specific example to show how this idea can be sucessfully implemented for improving risk management.

A first application of independent component analysis to extracting structure from stock returns.

This paper explores the application of a signal processing technique known as independent component analysis (ICA) or blind source separation to multivariate financial time series such as a portfolio of stocks. The key idea of ICA is to linearly map the observed multivariate time series into a new space of statistically independent components (ICs). We apply ICA to three years of daily returns of the 28 largest Japanese stocks and compare the results with those obtained using principal component analysis. The results indicate that the estimated ICs fall into two categories, (i) infrequent large shocks (responsible for the major changes in the stock prices), and (ii) frequent smaller fluctuations (contributing little to the overall level of the stocks). We show that the overall stock price can be reconstructed surprisingly well by using a small number of thresholded weighted ICs. In contrast, when using shocks derived from principal components instead of independent components, the reconstructed price is less similar to the original one. ICA is shown to be a potentially powerful method of analyzing and understanding driving mechanisms in financial time series. The application to portfolio optimization is described in Chin and Weigend (1998).