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.     

Identifying financial time series with similar dynamic conditional correlation

One of the main problems in modelling multivariate conditional covariance time series is the parameterization of the correlation structure. If no constraints are imposed, it implies a large number of unknown coefficients. The most popular models propose parsimonious representations, imposing similar correlation structures to all the series or to groups of time series, but the choice of these groups is quite subjective. A statistical approach is proposed to detect groups of homogeneous time series in terms of correlation dynamics for one of the widely used models: the Dynamic Conditional Correlation model. The approach is based on a clustering algorithm, which uses the idea of distance between dynamic conditional correlations, and the classical Wald test, to compare the coefficients of two groups of dynamic conditional correlations. The proposed approach is evaluated in terms of simulation experiments and applied to a set of financial time series.     

Comparison of alternative ACD models via density and interval forecasts: Evidence from the Australian stock market

In this paper a number of alternative autoregressive conditional duration (ACD) models are compared using a sample of data for three major companies traded on the Australian Stock Exchange. The comparison is performed by employing the methodology for evaluating density and interval forecasts, developed by Diebold et al. [F. Diebold, A. Gunther, S. Tay, Evaluating density forecasts with applications to financial risk management, International Economic Review 39 (1998) 863–883] and Christoffersen [P. Christoffersen, Evaluating interval forecasts, International Economic Review 39 (1998) 841–862], respectively. Our main finding is that the generalized gamma and log-normal distributions for the error terms have similar performance and perform better that the exponential and Weibull distributions. Additionally, there seems to be no substantial difference between the standard ACD specification of Engle and Russel [R. Engle, J. Russell, Autoregressive conditional duration: a new model for irregularly-spaced transaction data, Econometrica 66 (1998) 1127–1162] and the log-ACD specification of Bauwens and Giot [L. Bauwens, P. Giot, The logarithmic ACD model: an application to the bid-ask quote process of three NYSE stocks, Annales d’Economie et de Statistique 60 (2000) 117–150].     

Approximate dynamic programming for an inventory problem: Empirical comparison

This study investigates the application of learning-based and simulation-based Approximate Dynamic Programming (ADP) approaches to an inventory problem under the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. Specifically, we explore the robustness of a learning-based ADP method, Sarsa, with a GARCH(1,1) demand model, and provide empirical comparison between Sarsa and two simulation-based ADP methods: Rollout and Hindsight Optimization (HO). Our findings assuage a concern regarding the effect of GARCH(1,1) latent state variables on learning-based ADP and provide practical strategies to design an appropriate ADP method for inventory problems. In addition, we expose a relationship between ADP parameters and conservative behavior. Our empirical results are based on a variety of problem settings, including demand correlations, demand variances, and cost structures.     

A simple multivariate ARCH model specified by random coefficients

This paper provides an alternative formulation of the conditional correlation structure in fitting the multivariate GARCH model. A special case is the multivariate ARCH model with random coefficients. Its coherence structure is derived by the correlations between the random coefficients which play an important role in describing the interested heteroscedastic features. The parameter estimation problem can be solved by maximum likelihood estimation and model selection is via the likelihood ratio test. We consider three real applications: (1) the spot and forward rates of the Deutsche Mark against the US dollars; (2) exchange rates of Deutsche Mark and Japanese Yen against US dollars; (3) the Heng Sang index and SES index.     

A risk map of international tourist regions in Spain

This paper presents a different approach to tourism research at the regional level. Financial econometric techniques are applied to international tourist arrivals, as well as their volatilities, in the five main tourist regions in Spain, using monthly international tourist arrivals during 1997–2007. Univariate time series models are estimated for the conditional means of monthly international tourist arrivals and their volatilities. The estimated conditional volatility models are GARCH(1,1), GJR(1,1) and EGARCH(1,1). Both the second moment and log-moment conditions are calculated to provide diagnostic checks of the estimated models. The conditional mean estimates are generally statistically adequate, and the inferences are valid.     

Volatility dynamics of the US business cycle: A multivariate asymmetric GARCH approach

Most empirical investigations of the business cycles in the United States have excluded the dimension of asymmetric conditional volatility. This paper analyses the volatility dynamics of the US business cycle by comparing the performance of various multivariate generalised autoregressive conditional heteroskedasticity (GARCH) models. In particular, we propose two bivariate GARCH models to examine the evidence of volatility asymmetry and time-varying correlations concurrently, and then apply the proposed models to five sectors of Industrial Production of the United States. Our findings provide strong evidence of asymmetric conditional volatility in all sectors, and some support of time-varying correlations in various sectoral pairs. This has important policy implications for government to consider the effective countercyclical measures during recessions.     

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.     

Sea surface target detection based on complex ARMA-GARCH processes

In financial applications, it is common practice to fit return series by AutoRegressive Moving-Average (ARMA) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors. In this paper, we develop a complex-valued ARMA-GARCH model for the sea clutter modeling application. Compared with the AR-GARCH model, the additionally introduced MA terms make the proposed model capable of considering the dependence of conditional variances of adjacent echo measurements as model coefficients, improving the modeling precision by taking advantage of the strong correlations between adjacent measurements. Based on the complex-valued ARMA-GARCH process for sea clutter modeling, we further develop a sea surface target detection algorithm. By analyzing a large number of the practical sea clutter data, we evaluate its performance and show that the proposed sea surface target detector offers a noticeable improvement for the probability of detection, comparing with the state-of-the-art AR-GARCH detector.     

Joint forecasts of Dow Jones stocks under general multivariate loss function

When forecasts are assessed by a general loss (cost-of-error) function, the optimal point forecast is, in general, not the conditional mean, and depends on the conditional volatility—which, for stock returns, is time-varying. In order to provide forecasts of daily returns of 30 DJIA stocks under a general multivariate loss function, the following issues are addressed. We discuss what conditions define a multivariate loss function, and a simple class of such functions is proposed. Based on suitable combinations of univariate losses, the suggested multivariate functions are convenient for practical applications with many variables. To keep the computational aspect tractable, a flexible multivariate GARCH model is employed in estimating the conditional forecast distributions. The model easily copes with large number of series while allowing for skewness, fat tails, non-ellipticity, and tail dependence. Based on Engle’s DCC GARCH, it uses multivariate affine generalized hyperbolic distributions as conditional probability law, and the number of parameters to be estimated simultaneously does not depend on the number of series. The model is fitted using daily data from 2002 to 2007 (keeping data from 2008 for out-of-sample forecasts), and a bootstrap procedure is used to derive point forecasts under several multivariate loss functions of the proposed type.     

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.     

Modelling time-varying higher moments with maximum entropy density

Since the introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model of Engle [R. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50 (1982) 987–1007], the literature of modelling the conditional second moment has become increasingly popular in the last two decades. Many extensions and alternate models of the original ARCH have been proposed in the literature aiming to capture the dynamics of volatility more accurately. Interestingly, the Quasi Maximum Likelihood Estimator (QMLE) with normal density is typically used to estimate the parameters in these models. As such, the higher moments of the underlying distribution are assumed to be the same as those of the normal distribution. However, various studies reveal that the higher moments, such as skewness and kurtosis of the distribution of financial returns are not likely to be the same as the normal distribution, and in some cases, they are not even constant over time. These have significant implications in risk management, especially in the calculation of Value-at-Risk (VaR) which focuses on the negative quantile of the return distribution. Failed to accurately capture the shape of the negative quantile would produce inaccurate measure of risk, and subsequently lead to misleading decision in risk management. This paper proposes a solution to model the distribution of financial returns more accurately by introducing a general framework to model the distribution of financial returns using maximum entropy density (MED). The main advantage of MED is that it provides a general framework to estimate the distribution function directly based on a given set of data, and it provides a convenient framework to model higher order moments up to any arbitrary finite order k. However this flexibility comes with a high cost in computational time as k increases, therefore this paper proposes an alternative model that would reduce computation time substantially. Moreover, the sensitivity of the parameters in the MED with respect to the dynamic changes of moments is derived analytically. This result is important as it relates the dynamic structure of the moments to the parameters in the MED. The usefulness of this approach will be demonstrated using 5 min intra-daily returns of the Euro/USD exchange rate.     

Several multi-criteria programming methods for classification

In this paper, we propose a general optimization-based model for classification. Then we show that some well-known optimization-based methods for classification, which were developed by Shi et al. [Data mining in credit card portfolio management: a multiple criteria decision making approac. In: Koksalan M, Zionts S, editors. Multiple criteria decision making in the new millennium. Berlin: Springer; 2001. p. 427–36] and Freed and Glover [A linear programming approach to the discriminant problem. Decision Sciences 1981; 12: 68–79; Simple but powerful goal programming models for discriminant problems. European Journal of Operational Research 1981; 7: 44–60], are special cases of our model. Moreover, three new models, MCQP (multi-criteria indefinite quadratic programming), MCCQP (multi-criteria concave quadratic programming) and MCVQP (multi-criteria convex programming), are developed based on the general model. We also propose algorithms for MCQP and MCCQP, respectively. Then we apply these models to three real-life problems: credit card accounts, VIP mail-box and social endowment insurance classification. Extensive experiments are done to compare the efficiency of these methods.     

Forecasting large scale conditional volatility and covariance using neural network on GPU

Forecasting volatility is an important issue in financial econometric analysis. This paper aims to seek a computationally feasible approach for predicting large scale conditional volatility and covariance of financial time series. In the case of multi-variant time series, the volatility is represented by a Conditional Covariance Matrix (CCM). Traditional models for predicting CCM such as GARCH models are incapable of dealing with high-dimensional cases as there are O(N ²) parameters to be estimated in the case of N-variant asset return, and it is difficult to accelerate the computation of estimating these parameters by utilizing modern multi-core architecture. These GARCH models also have difficulties in modeling non-linear properties. The widely used Restricted Boltzmann Machine (RBM) is an energy-based stochastic recurrent neural network and its extended model, Conditional RBM (CRBM), has shown its capability in modeling high-dimensional time series. In this paper, we first propose a CRBM-based approach to forecast CCM and show how to capture the long memory properties in volatility, and then we implement the proposed model on GPU by using CUDA and CUBLAS. Experiment results indicate that the proposed CRBM-based model obtains better forecasting accuracy for low-dimensional volatility and it also shows great potential in modeling for large-scale cases compared with traditional GARCH models.     

Model checking conditional CSL for continuous-time Markov chains

In this paper, we consider the model-checking problem of continuous-time Markov chains (CTMCs) with respect to conditional logic. To the end, we extend Continuous Stochastic Logic introduced in Aziz et al. (2000) [1] to Conditional Continuous Stochastic Logic (CCSL) by introducing a conditional probabilistic operator. CCSL allows us to express a richer class of properties for CTMCs. Based on a parameterized product obtained from the CTMC and an automaton extracted from a given CCSL formula, we propose an approximate model checking algorithm and analyse its complexity.     

Intraday dynamic relationships between CSI 300 index futures and spot markets: a high-frequency analysis

Based on intraday 5-min high-frequency dataset, this paper empirically analyzes the intraday dynamic relationships between China’s CSI 300 index futures and spot markets with vector autoregression (VAR) and multivariate GARCH (MGARCH) models. By comparing four VAR–MGARCH models (dynamic conditional correlation, constant conditional correlation, diagonal and BEKK), the VAR–DCC–MGARCH model is found to fit the data the best and be preferred over the other models. The results of this model show that although there are bidirectional price causal relationships between the CSI 300 index futures and spot markets, the index futures return shock affects the spot market more severely than the spot return shock affects the futures market, indicating that the index futures market dominates the price discovery process between the two markets. There are bidirectional volatility spillovers effects between the CSI 300 index futures and spot markets, and the spillovers effects from index futures to spot almost equal to that from index spot to futures. The time-varying conditional correlations between the CSI 300 index futures and spot markets change from 0.4787 to 0.9594 across time, showing there is a strong positive correlation and linkage effect between the two markets. These results indicate that after a period of time of development, the price discovery performance of the CSI 300 index futures market has begun to function well, and the impact of the CSI 300 index futures market on its underlying spot market has strengthened.     

Asymmetric multivariate normal mixture GARCH

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is shown that the disaggregation of the conditional (co)variance process generated by the model provides substantial intuition. Moreover, the model exhibits a strong performance in calculating out-of-sample Value-at-Risk measures.     

A random effects four-part model, with application to correlated medical costs

In this paper we propose a four-part random effects model, with application to correlated medical cost data. Four joint equations are used to model respectively: (1) the probability of seeking medical treatment, (2) the probability of being hospitalized (conditional on seeking medical treatment), and the actual amount of (3) outpatient and (4) inpatient costs. Our model simultaneously takes account of the inter-temporal (or within-cluster) correlation of each patient and the cross-equation correlation of the four equations, by means of joint linear mixed models and generalized linear mixed models. The estimation is accomplished by the high-order Laplace approximation technique in Raudenbush et al. [Raudenbush, S.W., Yang, M., Yosef, M., 2000. Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. Journal of Computational and Graphical Statistics 9, 141-157] and Olsen and Schafer [Olsen, M.K., Schafer, J.L., 2001. A two-part random effects model for semicontinuous longitudinal data. Journal of the American Statistical Association 96, 730-745]. Our model is used to analyze monthly medical costs of 1397 chronic heart failure patients from the clinical data repository (CDR) at the University of Virginia.     

Joint maximum likelihood estimation of unit root testing equations and GARCH processes: Some finite-sample issues

In recent research [B. Seo, Distribution theory for unit root tests with conditional heteroskedasticity, J. Econometrics 91 (1999) 113–144] has suggested that the examination of the unit root hypothesis in series exhibiting GARCH behaviour should proceed via joint maximum likelihood (ML) estimation of the unit root testing equation and GARCH process. The results presented show the asymptotic distribution of the resulting ML t-test to be a mixture of the Dickey–Fuller and standard normal distributions. In this paper, the relevance of these asymptotic arguments is considered for the finite samples encountered in empirical research. In particular, the influences of sample size, alternative values of the parameters of the GARCH process and the use of the Bollerslev–Wooldridge covariance matrix estimator upon the finite-sample distribution of the ML t-statistic are explored. It is shown that the resulting critical values for the ML t-statistic are similar to those of the Dickey–Fuller distribution rather than the standard normal, unless a large sample size and empirically unrealistic values of the volatility parameter of the GARCH process are considered. Use of the Bollerslev–Wooldridge standard covariance matrix estimator exaggerates this finding, causing a leftward shift in the finite-sample distribution of the ML t-statistic. The results of the simulation analysis are illustrated via an application to U.S. short term interest rates.     

Intradaily dynamic portfolio selection

A portfolio selection model which allocates a portfolio of currencies by maximizing the expected return subject to Value-at-Risk (VaR) constraint is designed and implemented. Based on an econometric implementation using intradaily data, the optimal portfolio allocation is forecasted at regular time intervals. For the estimation of the conditional variance from which the VaR is computed, univariate and multivariate GARCH models are used. Model evaluation is done using two economic criteria and two statistical tests. The result for each model is given by the best forecasted intradaily investment recommendations in terms of the optimal weights of the currencies in the risky portfolio. The results show that estimating the VaR from multivariate GARCH models improves the results of the forecasted optimal portfolio allocation, compared to using a univariate model.