Asymmetries in conditional mean and variance: modelling stock returns by asMA‐asQGARCH

We propose a nonlinear time series model where both the conditional mean and the conditional variance are asymmetric functions of past information. The model is particularly useful for analysing financial time series where it has been noted that there is an asymmetric impact of good news and bad news on volatility (risk) transmission. We introduce a coherent framework for testing asymmetries in the conditional mean and the conditional variance, separately or jointly. To this end we derive both a Wald and a Lagrange multiplier test. Some of the new asymmetric model's moment properties are investigated. Detailed empirical results are given for the daily returns of the composite index of the New York Stock Exchange. There is strong evidence of asymmetry in both the conditional mean and the conditional variance functions. In a genuine out‐of‐sample forecasting experiment the performance of the best fitted asymmetric model, having asymmetries in both conditional mean and conditional variance, is compared with an asymmetric model for the conditional mean, and with no‐change forecasts. This is done both in terms of conditional mean forecasting as well as in terms of risk forecasting. Finally, the paper presents some evidence of asymmetries in the index stock returns of the Group of Seven (G7) industrialized countries. Copyright © 2004 John Wiley & Sons, Ltd.     

Volatility forecasting with double Markov switching GARCH models

This paper investigates inference and volatility forecasting using a Markov switching heteroscedastic model with a fat‐tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. The motivation for extending the Markov switching GARCH model, previously developed to capture mean asymmetry, is that the switching variable, assumed to be a first‐order Markov process, is unobserved. The proposed model extends this work to incorporate Markov switching in the mean and variance simultaneously. Parameter estimation and inference are performed in a Bayesian framework via a Markov chain Monte Carlo scheme. We compare competing models using Bayesian forecasting in a comparative value‐at‐risk study. The proposed methods are illustrated using both simulations and eight international stock market return series. The results generally favor the proposed double Markov switching GARCH model with an exogenous variable. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting Hong Kong's container throughput: an error‐correction model

A three‐player oligopoly model is devised to capture the competitive interaction between operators of the Hong Kong container terminals, the Hong Kong midstream and the Singapore container terminals in providing container handling services. The oligopoly model is then estimated statistically and thereby the structural parameters can be identified. The results of the estimation confirm a substitutability between the services supplied by operators of different types (terminal versus midstream) and different locations (Hong Kong versus Singapore). Moreover, the model proposed in this article generates forecasts of demand for Hong Kong's container handling services that are more accurate than those reported by the government authority, and suggests an earlier construction of new terminals to meet future demand. Copyright © 2002 John Wiley & Sons, Ltd.     

Bias in the estimation of non‐linear transformations of the integrated variance of returns

Volatility models such as GARCH, although misspecified with respect to the data‐generating process, may well generate volatility forecasts that are unconditionally unbiased. In other words, they generate variance forecasts that, on average, are equal to the integrated variance. However, many applications in finance require a measure of return volatility that is a non‐linear function of the variance of returns, rather than of the variance itself. Even if a volatility model generates forecasts of the integrated variance that are unbiased, non‐linear transformations of these forecasts will be biased estimators of the same non‐linear transformations of the integrated variance because of Jensen's inequality. In this paper, we derive an analytical approximation for the unconditional bias of estimators of non‐linear transformations of the integrated variance. This bias is a function of the volatility of the forecast variance and the volatility of the integrated variance, and depends on the concavity of the non‐linear transformation. In order to estimate the volatility of the unobserved integrated variance, we employ recent results from the realized volatility literature. As an illustration, we estimate the unconditional bias for both in‐sample and out‐of‐sample forecasts of three non‐linear transformations of the integrated standard deviation of returns for three exchange rate return series, where a GARCH(1, 1) model is used to forecast the integrated variance. Our estimation results suggest that, in practice, the bias can be substantial. Copyright © 2006 John Wiley & Sons, Ltd.     

Comparison of two non‐parametric models for daily traffic forecasting in Hong Kong

The most up‐to‐date annual average daily traffic (AADT) is always required for transport model development and calibration. However, the current‐year AADT data are not always available. The short‐term traffic flow forecasting models can be used to predict the traffic flows for the current year. In this paper, two non‐parametric models, non‐parametric regression (NPR) and Gaussian maximum likelihood (GML), are chosen for short‐term traffic forecasting based on historical data collected for the annual traffic census (ATC) in Hong Kong. These models are adapted as they are more flexible and efficient in forecasting the daily vehicular flows in the Hong Kong ATC core stations (in total of 87 stations). The daily vehicular flows predicted by these models are then used to calculate the AADT of the current year, 1999. The overall prediction and comparison results show that the NPR model produces better forecasts than the GML model using the ATC data in Hong Kong. Copyright © 2006 John Wiley _ Sons, Ltd.     

Modeling and forecasting aggregate stock market volatility in unstable environments using mixture innovation regressions

We perform Bayesian model averaging across different regressions selected from a set of predictors that includes lags of realized volatility, financial and macroeconomic variables. In our model average, we entertain different channels of instability by either incorporating breaks in the regression coefficients of each individual model within our model average, breaks in the conditional error variance, or both. Changes in these parameters are driven by mixture distributions for state innovations (MIA) of linear Gaussian state‐space models. This framework allows us to compare models that assume small and frequent as well as models that assume large but rare changes in the conditional mean and variance parameters. Results using S&P 500 monthly and quarterly realized volatility data from 1960 to 2014 suggest that Bayesian model averaging in combination with breaks in the regression coefficients and the error variance through MIA dynamics generates statistically significantly more accurate forecasts than the benchmark autoregressive model. However, compared to a MIA autoregression with breaks in the regression coefficients and the error variance, we fail to provide any drastic improvements.     

A Double‐threshold GARCH Model for the French Franc/Deutschmark exchange rate

This paper combines and generalizes a number of recent time series models of daily exchange rate series by using a SETAR model which also allows the variance equation of a GARCH specification for the error terms to be drawn from more than one regime. An application of the model to the French Franc/Deutschmark exchange rate demonstrates that out‐of‐sample forecasts for the exchange rate volatility are also improved when the restriction that the data it is drawn from a single regime is removed. This result highlights the importance of considering both types of regime shift (i.e. thresholds in variance as well as in mean) when analysing financial time series. Copyright © 2000 John Wiley & Sons, Ltd.     

A threshold factor multivariate stochastic volatility model

A new multivariate stochastic volatility model is developed in this paper. The main feature of this model is to allow threshold asymmetry in a factor covariance structure. The new model provides a parsimonious characterization of volatility and correlation asymmetry in response to market news. Statistical inferences are drawn from Markov chain Monte Carlo methods. We introduce news impact analysis to analyze volatility asymmetry with a factor structure. This analysis helps us to study different responses of volatility to historical market information in a multivariate volatility framework. Our model is successful when applied to an extensive empirical study of twenty stocks. Copyright © 2009 John Wiley & Sons, Ltd.     

Stochastic Multivariate Mixture Covariance Model

Stochastic covariance models have been explored in recent research to model the interdependence of assets in financial time series. The approach uses a single stochastic model to capture such interdependence. However, it may be inappropriate to assume a single coherence structure at all time t. In this paper, we propose the use of a mixture of stochastic covariance models to generalize the approach and offer greater flexibility in real data applications. Parameter estimation is performed by Bayesian analysis with Markov chain Monte Carlo sampling schemes. We conduct a simulation study on three different model setups and evaluate the performance of estimation and model selection. We also apply our modeling methods to high‐frequency stock data from Hong Kong. Model selection favors a mixture rather than non‐mixture model. In a real data study, we demonstrate that the mixture model is able to identify structural changes in market risk, as evidenced by a drastic change in mixture proportions over time. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting realized volatility of oil futures market: A new insight

In this study we propose several new variables, such as continuous realized semi‐variance and signed jump variations including jump tests, and construct a new heterogeneous autoregressive model for realized volatility models to investigate the impacts that those new variables have on forecasting oil price volatility. In‐sample results indicate that past negative returns have greater effects on future volatility than that of positive returns, and our new signed jump variations have a significantly negative influence on the future volatility. Out‐of‐sample empirical results with several robust checks demonstrate that our proposed models can not only obtain better performance in forecasting volatility but also garner larger economic values than can the existing models discussed in this paper.     

Forecasting Volatility with Many Predictors

This study investigates the forecasting performance of the GARCH(1,1) model by adding an effective covariate. Based on the assumption that many volatility predictors are available to help forecast the volatility of a target variable, this study shows how to construct a covariate from these predictors and plug it into the GARCH(1,1) model. This study presents a method of building a covariate such that the covariate contains the maximum possible amount of predictor information of the predictors for forecasting volatility. The loading of the covariate constructed by the proposed method is simply the eigenvector of a matrix. The proposed method enjoys the advantages of easy implementation and interpretation. Simulations and empirical analysis verify that the proposed method performs better than other methods for forecasting the volatility, and the results are quite robust to model misspecification. Specifically, the proposed method reduces the mean square error of the GARCH(1,1) model by 30% for forecasting the volatility of S&P 500 Index. The proposed method is also useful in improving the volatility forecasting of several GARCH‐family models and for forecasting the value‐at‐risk. Copyright © 2013 John Wiley & Sons, Ltd.     

Volatility Forecasting via MIDAS,HAR and their Combination: An Empirical Comparative Study for IBOVESPA

In this paper we compare several multi‐period volatility forecasting models, specifically from MIDAS and HAR families. We perform our comparisons in terms of out‐of‐sample volatility forecasting accuracy. We also consider combinations of the models' forecasts. Using intra‐daily returns of the BOVESPA index, we calculate volatility measures such as realized variance, realized power variation and realized bipower variation to be used as regressors in both models. Further, we use a nonparametric procedure for separately measuring the continuous sample path variation and the discontinuous jump part of the quadratic variation process. Thus MIDAS and HAR specifications with the continuous sample path and jump variability measures as separate regressors are estimated. Our results in terms of mean squared error suggest that regressors involving volatility measures which are robust to jumps (i.e. realized bipower variation and realized power variation) are better at forecasting future volatility. However, we find that, in general, the forecasts based on these regressors are not statistically different from those based on realized variance (the benchmark regressor). Moreover, we find that, in general, the relative forecasting performances of the three approaches (i.e. MIDAS, HAR and forecast combinations) are statistically equivalent. Copyright © 2014 John Wiley & Sons, Ltd.     

Forecasting volatility

In this paper, we investigate the time series properties of S&P 100 volatility and the forecasting performance of different volatility models. We consider several nonparametric and parametric volatility measures, such as implied, realized and model‐based volatility, and show that these volatility processes exhibit an extremely slow mean‐reverting behavior and possible long memory. For this reason, we explicitly model the near‐unit root behavior of volatility and construct median unbiased forecasts by approximating the finite‐sample forecast distribution using bootstrap methods. Furthermore, we produce prediction intervals for the next‐period implied volatility that provide important information about the uncertainty surrounding the point forecasts. Finally, we apply intercept corrections to forecasts from misspecified models which dramatically improve the accuracy of the volatility forecasts. Copyright © 2006 John Wiley & Sons, Ltd.     

Predictable Return Distributions

Using quantile regression this paper explores the predictability of the stock and bond return distributions as a function of economic state variables. The use of quantile regression allows us to examine specific parts of the return distribution such as the tails and the center, and for a sufficiently fine grid of quantiles we can trace out the entire distribution. A univariate quantile regression model is used to examine the marginal stock and bond return distributions, while a multivariate model is used to capture their joint distribution. An empirical analysis on US data shows that economic state variables predict the stock and bond return distributions in quite different ways in terms of, for example, location shifts, volatility and skewness. Comparing the different economic state variables in terms of their out‐of‐sample forecasting performance, the empirical analysis also shows that the relative accuracy of the state variables varies across the return distribution. Density forecasts based on an assumed normal distribution with forecasted mean and variance is compared to forecasts based on quantile estimates and, in general, the latter yields the best performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian Analysis of a Threshold Stochastic Volatility Model

This paper proposes a parsimonious threshold stochastic volatility (SV) model for financial asset returns. Instead of imposing a threshold value on the dynamics of the latent volatility process of the SV model, we assume that the innovation of the mean equation follows a threshold distribution in which the mean innovation switches between two regimes. In our model, the threshold is treated as an unknown parameter. We show that the proposed threshold SV model can not only capture the time‐varying volatility of returns, but can also accommodate the asymmetric shape of conditional distribution of the returns. Parameter estimation is carried out by using Markov chain Monte Carlo methods. For model selection and volatility forecast, an auxiliary particle filter technique is employed to approximate the filter and prediction distributions of the returns. Several experiments are conducted to assess the robustness of the proposed model and estimation methods. In the empirical study, we apply our threshold SV model to three return time series. The empirical analysis results show that the threshold parameter has a non‐zero value and the mean innovations belong to two separately distinct regimes. We also find that the model with an unknown threshold parameter value consistently outperforms the model with a known threshold parameter value. Copyright © 2016 John Wiley & Sons, Ltd.     

Realized Volatility Forecast of Stock Index Under Structural Breaks

We investigate the realized volatility forecast of stock indices under the structural breaks. We utilize a pure multiple mean break model to identify the possibility of structural breaks in the daily realized volatility series by employing the intraday high‐frequency data of the Shanghai Stock Exchange Composite Index and the five sectoral stock indices in Chinese stock markets for the period 4 January 2000 to 30 December 2011. We then conduct both in‐sample tests and out‐of‐sample forecasts to examine the effects of structural breaks on the performance of ARFIMAX‐FIGARCH models for the realized volatility forecast by utilizing a variety of estimation window sizes designed to accommodate potential structural breaks. The results of the in‐sample tests show that there are multiple breaks in all realized volatility series. The results of the out‐of‐sample point forecasts indicate that the combination forecasts with time‐varying weights across individual forecast models estimated with different estimation windows perform well. In particular, nonlinear combination forecasts with the weights chosen based on a non‐parametric kernel regression and linear combination forecasts with the weights chosen based on the non‐negative restricted least squares and Schwarz information criterion appear to be the most accurate methods in point forecasting for realized volatility under structural breaks. We also conduct an interval forecast of the realized volatility for the combination approaches, and find that the interval forecast for nonlinear combination approaches with the weights chosen according to a non‐parametric kernel regression performs best among the competing models. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal sampling frequency for volatility forecast models for the Indian stock markets

This paper evaluates the performance of conditional variance models using high‐frequency data of the National Stock Index (S&P CNX NIFTY) and attempts to determine the optimal sampling frequency for the best daily volatility forecast. A linear combination of the realized volatilities calculated at two different frequencies is used as benchmark to evaluate the volatility forecasting ability of the conditional variance models (GARCH (1, 1)) at different sampling frequencies. From the analysis, it is found that sampling at 30 minutes gives the best forecast for daily volatility. The forecasting ability of these models is deteriorated, however, by the non‐normal property of mean adjusted returns, which is an assumption in conditional variance models. Nevertheless, the optimum frequency remained the same even in the case of different models (EGARCH and PARCH) and different error distribution (generalized error distribution, GED) where the error is reduced to a certain extent by incorporating the asymmetric effect on volatility. Our analysis also suggests that GARCH models with GED innovations or EGRACH and PARCH models would give better estimates of volatility with lower forecast error estimates. Copyright © 2008 John Wiley & Sons, Ltd.     

Empirical analysis and forecasting of volatility dynamics in high‐frequency returns with time‐varying components

We study intraday return volatility dynamics using a time‐varying components approach, and the method is applied to analyze IBM intraday returns. Empirical evidence indicates that with three additive components—a time‐varying mean of absolute returns and two cosine components with time‐varying amplitudes—together they capture very well the pronounced periodicity and persistence behaviors exhibited in the empirical autocorrelation pattern of IBM returns. We find that the long‐run volatility persistence is driven predominantly by daily level shifts in mean absolute returns. After adjusting for these intradaily components, the filtered returns behave much like a Gaussian noise, suggesting that the three‐components structure is adequately specified. Furthermore, a new volatility measure (TCV) can be constructed from these components. Results from extensive out‐of‐sample rolling forecast experiments suggest that TCV fares well in predicting future volatility against alternative methods, including GARCH model, realized volatility and realized absolute value. Copyright © 2009 John Wiley & Sons, Ltd.     

Single‐index and portfolio models for forecasting value‐at‐risk thresholds

The variance of a portfolio can be forecast using a single index model or the covariance matrix of the portfolio. Using univariate and multivariate conditional volatility models, this paper evaluates the performance of the single index and portfolio models in forecasting value‐at‐risk (VaR) thresholds of a portfolio. Likelihood ratio tests of unconditional coverage, independence and conditional coverage of the VaR forecasts suggest that the single‐index model leads to excessive and often serially dependent violations, while the portfolio model leads to too few violations. The single‐index model also leads to lower daily Basel Accord capital charges. The univariate models which display correct conditional coverage lead to higher capital charges than models which lead to too many violations. Overall, the Basel Accord penalties appear to be too lenient and favour models which have too many violations. Copyright © 2008 John Wiley & Sons, Ltd.     

A Bayesian structural model for predicting algal blooms

A Bayesian structural model with two components is proposed to forecast the occurrence of algal blooms, multivariate mean‐reverting diffusion process (MMRD), and a binary probit model with latent Markov regime‐switching process (BPMRS). The model has three features: (a) forecast of the occurrence probability of algal bloom is directly based on oceanographic parameters, not the forecasting of special indicators in traditional approaches, such as phytoplankton or chlorophyll‐a; (b) augmentation of daily oceanographic parameters from the data collected every 2 weeks is based on MMRD. The proposed method solves the problem of unavailability of daily oceanographic parameters in practice; (c) BPMRS captures the unobservable factors which affect algal bloom occurrence and therefore improve forecast accuracy. We use panel data collected in Tolo Harbour, Hong Kong, to validate the model. The model demonstrates good forecasting for out‐of‐sample rolling forecasts, especially for algal bloom appearing for a longer period, which severely damages fisheries and the marine environment.