Forecasting conditional correlations in stock,bond and foreign exchange markets

The paper forecasts conditional correlations between three classes of international financial assets, namely stock, bond and foreign exchange. Two countries are considered, namely Australia and New Zealand. Forecasting will be conducted using three multivariate GARCH models, namely the CCC model [T. Bollerslev, Modelling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model, Rev. Econ. Stat. 72 (1990) 498–505], VARMA-GARCH model [S. Ling, M. McAleer, Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory 19 (2003) 280–310], and VARMA-AGARCH model [M. McAleer, S. Hoti, F. Chan, Structure and asymptotic theory for multivariate asymmetric volatility, Econometric Rev., in press]. A rolling window technique is used to forecast 1-day ahead conditional correlations. To evaluate the impact of model specification on conditional correlations forecasts, this paper calculates and compares the correlations between conditional correlations forecasts resulted from the three models. The paper finds the evidence of volatility spillovers and asymmetric effect of negative and positive shock on the conditional variance in most pairs of series. However, it suggests that incorporating volatility spillovers and asymmetric do not contribute to better conditional correlations forecasts.     

Model and distribution uncertainty in multivariate GARCH estimation: A Monte Carlo analysis

Multivariate GARCH models are in principle able to accommodate the features of the dynamic conditional covariances; nonetheless the interaction between model parametrization of the second conditional moment and the conditional density of asset returns adopted in the estimation determines the fitting of such models to the observed dynamics of the data. Alternative MGARCH specifications and probability distributions are compared on the basis of forecasting performances by means of Monte Carlo simulations, using both statistical and financial forecasting loss functions.     

Real time detection of structural breaks in GARCH models

A sequential Monte Carlo method for estimating GARCH models subject to an unknown number of structural breaks is proposed. Particle filtering techniques allow for fast and efficient updates of posterior quantities and forecasts in real time. The method conveniently deals with the path dependence problem that arises in these types of models. The performance of the method is shown to work well using simulated data. Applied to daily NASDAQ returns, the evidence favors a partial structural break specification in which only the intercept of the conditional variance equation has breaks compared to the full structural break specification in which all parameters are subject to change. The empirical application underscores the importance of model assumptions when investigating breaks. A model with normal return innovations result in strong evidence of breaks; while more flexible return distributions such as t-innovations or a GARCH-jump mixture model still favor breaks but indicate much more uncertainty regarding the time and impact of them.     

Computational intelligence approaches and linear models in case studies of forecasting exchange rates

Artificial neural networks and fuzzy systems, have gradually established themselves as a popular tool in approximating complicated nonlinear systems and time series forecasting. This paper investigates the hypothesis that the nonlinear mathematical models of multilayer perceptron and radial basis function neural networks and the Takagi–Sugeno (TS) fuzzy system are able to provide a more accurate out-of-sample forecast than the traditional auto regressive moving average (ARMA) and ARMA generalized auto regressive conditional heteroskedasticity (ARMA-GARCH) linear models. Using series of Brazilian exchange rate (R$/US$) returns with 15 min, 60 min and 120 min, daily and weekly basis, the one-step-ahead forecast performance is compared. Results indicate that forecast performance is strongly related to the series’ frequency and the forecasting evaluation shows that nonlinear models perform better than their linear counterparts. In the trade strategy based on forecasts, nonlinear models achieve higher returns when compared to a buy-and-hold strategy and to the linear models.     

Multivariate mixed normal conditional heteroskedasticity

A new multivariate volatility model where the conditional distribution of a vector time series is given by a mixture of multivariate normal distributions is proposed. Each of these distributions is allowed to have a time-varying covariance matrix. The process can be globally covariance stationary even though some components are not covariance stationary. Some theoretical properties of the model such as the unconditional covariance matrix and autocorrelations of squared returns are derived. The complexity of the model requires a powerful estimation algorithm. A simulation study compares estimation by maximum likelihood with the EM algorithm. Finally, the model is applied to daily US stock returns.     

Bayesian changepoint and time-varying parameter learning in regime switching volatility models

This paper proposes a combined state and piecewise time-varying parameter learning technique in regime switching volatility models using multiple changepoint detection. This approach is a Sequential Monte Carlo method for estimating GARCH & EGARCH based volatility models with an unknown number of changepoints. Modern auxiliary particle filtering techniques are used to calculate the posterior densities and online forecasts. This approach also automatically deals with the common ancestral path dependence problem faced in these type volatility models. The model is tested on Borsa Istanbul (BIST) formerly known as Istanbul Stock Exchange (ISE) market data using daily log returns. A full structural changepoint specification is defined in which all parameters of the conditional variance of the volatility models are dynamic. Finally, it is shown with simulation experiments that the proposed approach partitions the series into several regimes and learns the parameters of each regime's volatility model in parallel with the multiple changepoint detection process.     

A Student-<Emphasis Type="Italic">t</Emphasis> Full Factor Multivariate GARCH Model

We extend the full-factor multivariate GARCH model of Vrontos et al. (Econom J 6:312–334, 2003a) to account for fat tails in the conditional distribution of financial returns, using a multivariate Student-t error distribution. For the new class of Student-t full factor multivariate GARCH models, we derive analytical expressions for the score, the Hessian matrix and the Information matrix. These expressions can be used within classical inferential procedures in order to obtain maximum likelihood estimates for the model parameters. This fact, combined with the parsimonious parameterization of the covariance matrix under the full factor multivariate GARCH models, enables us to apply the models in high dimensional problems. We provide implementation details and illustrations using financial time series on eight stocks of the US market.     

Computational intelligence approaches and linear models in case studies of forecasting exchange rates

Artificial neural networks and fuzzy systems, have gradually established themselves as a popular tool in approximating complicated nonlinear systems and time series forecasting. This paper investigates the hypothesis that the nonlinear mathematical models of multilayer perceptron and radial basis function neural networks and the Takagi–Sugeno (TS) fuzzy system are able to provide a more accurate out-of-sample forecast than the traditional auto regressive moving average (ARMA) and ARMA generalized auto regressive conditional heteroskedasticity (ARMA-GARCH) linear models. Using series of Brazilian exchange rate (R$/US$) returns with 15 min, 60 min and 120 min, daily and weekly basis, the one-step-ahead forecast performance is compared. Results indicate that forecast performance is strongly related to the series’ frequency and the forecasting evaluation shows that nonlinear models perform better than their linear counterparts. In the trade strategy based on forecasts, nonlinear models achieve higher returns when compared to a buy-and-hold strategy and to the linear models.     

A generalized Dynamic Conditional Correlation model for portfolio risk evaluation

We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle [R.F. Engle, Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business and Economic Statistics 20 (2002) 339–350] and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al.[L. Cappiello, R.F. Engle, K. Sheppard, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 25 (2006) 537–572]. The model we propose introduces a block structure in parameter matrices that allows for interdependence with a reduced number of parameters. Our model nests the Flexible Dynamic Conditional Correlation model of Billio et al. [M. Billio, M. Caporin, M. Gobbo, Flexible dynamic conditional correlation multivariate GARCH for asset allocation, Applied Financial Economics Letters 2 (2006) 123–130] and is named Quadratic Flexible Dynamic Conditional Correlation Multivariate GARCH. In the paper, we provide conditions for positive definiteness of the conditional correlations. We also present an empirical application to the Italian stock market comparing alternative correlation models for portfolio risk evaluation.     

A new algorithm based on copulas for VaR valuation with empirical calculations

This paper concerns the application of copula functions in VaR valuation. The copula function is used to model the dependence structure of multivariate assets. After the introduction of the traditional Monte Carlo simulation method and the pure copula method we present a new algorithm based on mixture copula functions and the dependence measure, Spearman’s rho. This new method is used to simulate daily returns of two stock market indices in China, Shanghai Stock Composite Index and Shenzhen Stock Composite Index, and then empirically calculate six risk measures including VaR and conditional VaR. The results are compared with those derived from the traditional Monte Carlo method and the pure copula method. From the comparison we show that the dependence structure between asset returns plays a more important role in valuating risk measures comparing with the form of marginal distributions.     

Bayesian analysis of stochastic volatility models with mixture-of-normal distributions

Stochastic volatility (SV) models usually assume that the distribution of asset returns conditional on the latent volatility is normal. This article analyzes SV models with a mixture-of-normal distributions in order to compare with other heavy-tailed distributions such as the Student-t distribution and generalized error distribution (GED). A Bayesian method via Markov-chain Monte Carlo (MCMC) techniques is used to estimate parameters and Bayes factors are calculated to compare the fit of distributions. The method is illustrated by analyzing daily data from the Yen/Dollar exchange rate and the Tokyo stock price index (TOPIX). According to Bayes factors, we find that while the t distribution fits the TOPIX better than the normal, the GED and the normal mixture, the mixture-of-normal distributions give a better fit to the Yen/Dollar exchange rate than other models. The effects of the specification of error distributions on the Bayesian confidence intervals of future returns are also examined. Comparison of SV with GARCH models shows that there are cases that the SV model with the normal distribution is less effective to capture leptokurtosis than the GARCH with heavy-tailed distributions.     

Heavy-tailed mixture GARCH volatility modeling and Value-at-Risk estimation

This paper presents a heavy-tailed mixture model for describing time-varying conditional distributions in time series of returns on prices. Student-t component distributions are taken to capture the heavy tails typically encountered in such financial data. We design a mixture MT(m)-GARCH(p, q) volatility model for returns, and develop an EM algorithm for maximum likelihood estimation of its parameters. This includes formulation of proper temporal derivatives for the volatility parameters. The experiments with a low order MT(2)-GARCH(1, 1) show that it yields results with improved statistical characteristics and economic performance compared to linear and nonlinear heavy-tail GARCH, as well as normal mixture GARCH. We demonstrate that our model leads to reliable Value-at-Risk performance in short and long trading positions across different confidence levels.     

Improving forecasts of GARCH family models with the artificial neural networks: An application to the daily returns in Istanbul Stock Exchange

In the study, we discussed the ARCH/GARCH family models and enhanced them with artificial neural networks to evaluate the volatility of daily returns for 23.10.1987–22.02.2008 period in Istanbul Stock Exchange. We proposed ANN-APGARCH model to increase the forecasting performance of APGARCH model. The ANN-extended versions of the obtained GARCH models improved forecast results. It is noteworthy that daily returns in the ISE show strong volatility clustering, asymmetry and nonlinearity characteristics.     

On asymmetric generalised t stochastic volatility models

In stochastic volatility (SV) models, asset returns conditional on the latent volatility are usually assumed to have a normal, Student-t or exponential power (EP) distribution. An earlier study uses a generalised t (GT) distribution for the conditional returns and the results indicate that the GT distribution provides a better model fit to the Australian Dollar/Japanese Yen daily exchange rate than the Student-t distribution. In fact, the GT family nests a number of well-known distributions including the commonly used normal, Student-t and EP distributions. This paper extends the SV model with a GT distribution by incorporating general volatility asymmetry. We compare the empirical performance of nested distributions of the GT distribution as well as different volatility asymmetry specifications. The new asymmetric GT SV models are estimated using the Bayesian Markov chain Monte Carlo (MCMC) method to obtain parameter and log-volatility estimates. By using daily returns from the Standard and Poors (S&P) 500 index, we investigate the effects of the specification of error distributions as well as volatility asymmetry on parameter and volatility estimates. Results show that the choice of error distributions has a major influence on volatility estimation only when volatility asymmetry is not accounted for.     

Measuring actual daily volatility from high frequency intraday returns of the S&P futures and index observations

In this study 10 min frequency realized variance series are used to forecast the volatility of S&P 500 index (SPX) daily returns. The logarithm-transformed realized variances are modeled directly in the AR(FI)MA model specification in which the structure of the model is optimized using the AICc criterion. As reported in previous literature, the approximately normal structure of distribution of the logarithm-transformed realized variance series can be modeled directly in structure of the AR(FI)MA process. However, in this study, it is recognized the statistically significant non-normal property of the logarithm-transformed realized variances. Hence, to forecast volatility the non-normality is exploited to improve efficiency of volatility forecasts. It is also observed that in the context of the AR(FI)MA model specification the futures and index based deseasonalized returns for the realized variance estimates improve the forecast performance. Considering the seasonality effect and the distributional properties of the estimated realized variance series, it is evident that the information content of the futures (ES) high frequency observations produces the most accurate forecasts.     

Bayesian estimation of the Gaussian mixture GARCH model

Bayesian inference and prediction for a generalized autoregressive conditional heteroskedastic (GARCH) model where the innovations are assumed to follow a mixture of two Gaussian distributions is performed. The mixture GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. Bayesian prediction of the Value at Risk is also addressed providing point estimates and predictive intervals. The method is illustrated using the Swiss Market Index.     

Fat tails and asymmetry in financial volatility models

Although the generalised autoregressive conditional heteroskedasticity (GARCH) model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme observations, outliers and skewness in returns. This paper examines the GARCH model under various non-normal error distributions in order to evaluate skewness and leptokurtosis. The empirical results show that GARCH models estimated using asymmetric leptokurtic distributions are superior to their counterparts estimated under normality, in terms of: (i) capturing skewness and leptokurtosis; (ii) the maximized log-likelihood values; and (iii) isolating the ARCH and GARCH parameter estimates from the adverse effects of outliers. Overall, the flexible asymmetric Student’s t-distribution performs best in capturing the non-normal aspects of the data.     

A hybrid modeling approach for forecasting the volatility of S&P 500 index return

Forecasting volatility is an essential step in many financial decision makings. GARCH family of models has been extensively used in finance and economics, particularly for estimating volatility. The motivation of this study is to enhance the ability of GARCH models in forecasting the return volatility. We propose two hybrid models based on EGARCH and Artificial Neural Networks to forecast the volatility of S&P 500 index. The estimates of volatility obtained by an EGARCH model are fed forward to a Neural Network. The input to the first hybrid model is complemented by historical values of other explanatory variables. The second hybrid model takes as inputs both series of the simulated data and explanatory variables. The forecasts obtained by each of those hybrid models have been compared with those of EGARCH model in terms of closeness to the realized volatility. The computational results demonstrate that the second hybrid model provides better volatility forecasts.     

Modelling conditional correlations in the volatility of Asian rubber spot and futures returns

Asia is presently the most important market for the production and consumption of natural rubber. World prices of rubber are subject to not only to changes in demand, but also speculation regarding future markets. Japan and Singapore are the major future markets for rubber, while Thailand is one of the world's largest producers of rubber. As rubber prices are influenced by external markets, it is important to analyse the relationship between the relevant markets in Thailand, Japan and Singapore. The analysis is conducted using several alternative multivariate GARCH models. The empirical results indicate that the constant conditional correlations arising from the CCC model lie in the low to medium range. The results from the VARMA-GARCH model and the VARMA-AGARCH model suggest the presence of volatility spillovers and asymmetric effects of positive and negative return shocks on conditional volatility. Finally, the DCC model suggests that the conditional correlations can vary dramatically over time. In general, the dynamic conditional correlations in rubber spot and futures returns shocks can be independent or interdependent.     

Change Point Detection in GARCH Models for Voice Activity Detection

This paper presents a robust algorithm for voice activity detection (VAD) based on change point detection in a generalized autoregressive conditional heteroscedasticity (GARCH) process. GARCH models are new statistical methods that are used especially in economic time series and are a popular choice to model speech signals and their changing variances. Change point detection is also important in economic sciences. In this paper, no distinct probability functions are assumed for speech and noise distributions. Also, to detect speech/nonspeech intervals, no likelihood ratio test (LRT) is employed. For testing parameter constancy in GARCH models, the algorithm of the Cramer-von Mises (CVM) test is described. This test is a nonparametric test and is based on the empirical quantiles. We show that VAD is related to the parameter constancy test in GARCH process, and we illustrate several examples.