Memory GARCH Research Articles

Forecasting conditional volatility based on hybrid GARCH-type models with long memory, regime switching, leverage effect and heavy-tail: Further evidence from equity market

The properties of clustering, long memory, switching regime, leverage effect and heavy tail in volatility dynamic behavior are induced by important stylized facts in financial markets. There is still a controversy whether incorporating these properties could improve the modelling and forecasting performance of volatility. We construct hybrid volatility models via three perspectives including short memory, long memory and Markov switching GARCH with leverage effect and heavy tail, and empirically compare their performance of in-sample estimation, out-of-sample forecast and risk measurement based on trading data of Chinese equity market index. The out-of-sample forecast results indicate that the FIEGARCH model with innovation distribution of GED outperforms the competing models, and the backtesting results of VaR and ES confirm that this model performs well in the application of risk measurement.

An improved FIGARCH model with the fractional differencing operator (1-νL)d

In this study, we propose a new volatility model called the product memory GARCH model by replacing (1 − L)d in the FIGARCH model of Baillie et al. (1996) with (1 − νL)d for 0 ≤ ν ≤ 1, where the impulse response function in its ARCH(∞) process has a decay rate in the form of the product of a geometric memory rate and a hyperbolic memory rate when the lags increase. Under the ARCH(∞) framework, the non-negativity constraints, the existence of the second, fourth, sixth, and eighth moments, and the memory length are investigated, and the Gaussian quasi-maximum likelihood estimation is also discussed. This improved model is of considerable significance in the evolution of GARCH-type models and financial econometrics.

How does news sentiment affect the states of Japanese stock return volatility?

This paper examines the impact of public news sentiment on the volatility states of firm-level returns on the Japanese Stock market. We firstly adopt a novel Markov Regime Switching Long Memory GARCH (MRS-LMGARCH), which is employed to estimate the latent volatility states of intraday stock return. By using the RavenPack Dow Jones News Analytics database, we fit discrete choice models to investigate the impact of news sentiment on changes of volatility states of the constituent stocks in the TOPIX Core 30 Index. Our findings suggest that news occurrence and sentiment, especially those of macro-economic news, are a key factor that significantly drives the volatility state of Japanese stock returns. This provides essential information for traders of the Japanese stock market to optimize their trading strategies and risk management plans to combat volatility.

Semiparametric GARCH models with long memory applied to value-at-risk and expected shortfall

In this paper new semiparametric GARCH models with long memory are in- troduced. The estimation of the nonparametric scale function is carried out by an adapted version of the SEMIFAR algorithm (Beran et al., 2002). Recurring on the revised recommendations by the Basel Committee to measure market risk in the banks' trading books (Basel Committee on Banking Supervision, 2013), the semi- parametric GARCH models are applied to obtain rolling one-step ahead forecasts for the Value at Risk (VaR) and Expected Shortfall (ES) for market risk assets. In addition, standard regulatory traffic light tests (Basel Committee on Banking Supervision, 1996) and a newly introduced traffic light test for the ES are carried out for all models. The practical relevance of our proposal is demonstrated by a comparative study. Our results indicate that semiparametric long memory GARCH models are an attractive alternative to their conventional, parametric counterparts.

Risk spillovers and hedge strategies between global crude oil markets and stock markets: Do regime switching processes combining long memory and asymmetry matter?

This paper investigates risk spillovers and hedge strategies between global crude oil markets and stock markets. In the paper, we propose a multivariate long memory and asymmetry GARCH framework that integrates state-dependent regime switching in the mean process with multivariate long memory and asymmetry GARCH in the variance process. Our results first show that there are linear risk spillovers running from the US stock markets to the WTI oil market in the short term. However, the linear risk spillover effect running from the oil market to the US stock market can only exist in the long term. In addition, there is a bidirectional linear risk spillover effect between the European stock markets and the Brent oil market in the short and long terms. Furthermore, there is no linear risk spillover effect between the Dubai oil market and the Chinese stock market. Second, the nonlinear risk spillovers running from the WTI oil market to the US stock market can be found in the tranquil regime. Moreover, there is also a nonlinear risk spillover effect running from the European stock markets to the Brent oil market in the tranquil regime. In addition, the nonlinear risk spillover effect running from the Brent oil markets to the European stock market can be found in the crisis regime. Furthermore, there is bidirectional nonlinear Granger causality between the Dubai crude oil market and the Chinese stock market in the tranquil regime. Finally, dynamic hedge effectiveness shows that the regime switching process combined with long memory and asymmetry behavior seems to be a plausible and feasible way to conduct hedge strategies between the global crude oil markets and stock markets.

Modelling and forecasting long memory time series with Exponential and Switching GARCH models

There is some evidence that structural change or stochastic regime switching and long memory are intimately related concepts. However, long memory and regime switching in a stochastic process are properties that could be easily confused in a financial study. Using a modelling approach, the aim is to distinguish regime switching behaviour from long memory for the financial time series. In an empirical study the forecasting performance of symmetric, asymmetric, long memory and Markov switching GARCH model are compared using Tehran stock market daily returns. The results indicate that in out of sample performance, long memory exponential GARCH (FIEGARCH) model outperforms the competing models. To ensure the validity of the results, the value at risk (VaR) forecasts are obtained for each model and a loss function is calculated. A simple rule for distinguishing between long memory and structural break in financial and economic time series is suggested.

Risk transmission between natural gas market and stock markets: portfolio and hedging strategy analysis

This paper investigates the risk transmission and hedging strategies between natural gas market and stock markets. We propose a multivariate GARCH framework which combines regime switching with multivariate long memory and asymmetry GARCH. Results show that there exists granger causality from natural gas market to the Chinese stock markets in crisis regime. Dynamic correlations between these markets are vulnerable to extreme weather, government policies and financial crisis. When looking at the optimal design of a natural gas-stock portfolio, we find that investors in stock markets should have more stocks than natural gas asset in order to reduce their portfolio risk.

Stationarity and functional central limit theorem for ARCH([formula omitted]) models

In this paper, we study the stationarity and functional central limit theorem for (random coefficient) ARCH(∞) models including HYAPGARCH and mixture memory GARCH models. Those models are able to cover long memory property with fewer parameters and have finite variances. The functional central limit theorems for ut and the squared processes ut2 and σt2 are proved. Sufficient conditions for L2-NED property to hold are established and the FCLT for mixture memory GARCH model as an example of a random coefficient ARCH(∞) process is derived via L2-NED condition.

Oil price volatility forecast with mixture memory GARCH

We expand the literature of volatility and Value-at-Risk forecasting of oil price returns by comparing the recently proposed Mixture Memory GARCH (MMGARCH) model to other discrete volatility models (GARCH, RiskMetrics, EGARCH, APARCH, FIGARCH, HYGARCH, and FIAPARCH). We incorporate an Expectation-Maximization algorithm for parameter estimation of the MMGARCH and find different structures in volatility level as well as shock persistence. MMGARCH is also able to cover asymmetric and long memory effects. Furthermore, a dissimilar memory structure in variance of WTI and Brent crude oil prices is observed which is supported by additional tests. Parameter estimation and comparison of the models reveal significant long memory and asymmetry in oil price returns. In regard of variance forecasting and Value-at-Risk prediction, it is shown that MMGARCH outperforms the aforementioned models due to its dynamic approach in varying the volatility level and memory of the process. We find MMGARCH superior for application in risk management as a result of its flexibility in adjusting to variance shifts and shocks.

Modeling Latin-American stock markets volatility: Varying probabilities and mean reversion in a random level shift model

Following Xu and Perron (2014), I applied the extended RLS model to the daily stock market returns of Argentina, Brazil, Chile, Mexico and Peru. This model replaces the constant probability of level shifts for the entire sample with varying probabilities that record periods with extremely negative returns. Furthermore, it incorporates a mean reversion mechanism with which the magnitude and the sign of the level shift component vary in accordance with past level shifts that deviate from the long-term mean. Therefore, four RLS models are estimated: the Basic RLS, the RLS with varying probabilities, the RLS with mean reversion, and a combined RLS model with mean reversion and varying probabilities. The results show that the estimated parameters are highly significant, especially that of the mean reversion model. An analysis of ARFIMA and GARCH models is also performed in the presence of level shifts, which shows that once these shifts are taken into account in the modeling, the long memory characteristics and GARCH effects disappear. Also, I find that the performance prediction of the RLS models is superior to the classic models involving long memory as the ARFIMA(p,d,q) models, the GARCH and the FIGARCH models. The evidence indicates that except in rare exceptions, the RLS models (in all its variants) are showing the best performance or belong to the 10% of the Model Confidence Set (MCS). On rare occasions the GARCH and the ARFIMA models appear to dominate but they are rare exceptions. When the volatility is measured by the squared returns, the great exception is Argentina where a dominance of GARCH and FIGARCH models is appreciated.

Oil Price Volatility Forecast with Mixture Memory GARCH

First Version: 03/11/2015This Version: 04/01/2016We expand the literature of volatility and Value-at-Risk forecasting of oil price returns by comparing the recently proposed Mixture Memory GARCH (MMGARCH) model to other discrete volatility models (GARCH, FIGARCH, and HYGARCH). We incorporate an Expectation-Maximization algorithm for parameter estimation of the MMGARCH and find regimes that differ in volatility level as well as shock persistence. Furthermore, we observe dissimilar memory structure in variance of WTI and Brent crude oil prices which is confirmed by altering the mixture components. In regard of variance forecasting and Value-at-Risk prediction, we show that MMGARCH outperforms the aforementioned models due to its dynamic approach in varying the volatility level and memory of the process. We find MMGARCH superior for application in risk management as a result of its flexibility in adjusting to variance shifts and shocks.

Empirical Stylized Facts Modelling and Forecast Evaluations for Energy and Stock Markets

This paper applies autoregressive heteroscedasticity (ARCH) family models for the purpose of comparing stylized facts such as volatility clustering, leverage effect, long memory volatility and risk-return tradeoff for energy and stock markets. Empirical results have found that the presences of volatility clustering in both markets and the impact of volatility shocks to the conditional volatility display hyperbolic rather than exponential rate of decay. Meanwhile, only stock markets denote the leverage effect, which implies that ‘bad’ news has a greater impact on volatility than ‘good’ news at the same magnitude. Additionally, empirical results also highlighted that Kerosene and Brent crude oil are the only energy commodities exhibit risk-return tradeoff. For forecast evaluations, the FIAPARCH model indicates superior out of sample forecasts over short and long time horizon for stock markets. Nevertheless, FIAPARCH model suits better over long term as compared to short term for energy markets. Finally, the Superior Predictive Ability (SPA) tests suggested that overall asymmetric long memory GARCH models display higher forecasting accuracy than the standard GARCH models.

Evaluation of Value-at-Risk Estimation Using Long Memory Volatility Models: Evidence from Stock Exchange of Thailand

This paper examines the accuracy of Value-at-Risk (VaR) estimation in the Stock Exchange of Thailand. We apply standard conditional volatility models (GARCH) and the GARCH model with long memory process (FIGARCH) in calculation of VaR. The empirical results from R|S statistics show that there is significant evidence of long memory process in volatility but not in mean of SET50 index returns. Comparing accuracy of VaR estimation, the results from the Kupiec-LR test show that 1-day ahead 1% VaR values calculated using FIGARCH(1,d,1) model with normal innovations are more accurate than those generated using short memory GARCH(1,1) models. Considering the Bank of International Settlement (BIS)’s regulatory back-testing, the results also confirm that the long memory models provide better performance than those of the standard GARCH models. In summary, our empirical results indicate that long-range memory could provide better performance in risk management than that of standard GARCH in the case of Stock Exchange of Thailand. However, our results from FIGARCH still do not outperform those of the asymmetric GARCH.

Volatility Modeling Using GARCH: Theory and Practice

This paper explains why a two-component GARCH model as proposed by Ding and Granger (1996) or Engle and Lee (1999) can be an ideal alternative model for practitioners in modeling stock return volatility. I show that the two-component GARCH model can easily capture the slow hyperbolic decay of the sample autocorrelation function for the absolute or squared returns that is commonly found in empirical data. Compared to the alternative long memory GARCH model, the two-component GARCH model is easy to estimate and implement.

Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period value-at-risk (VaR) and expected shortfall (ES) across 20 stock indices worldwide. The dataset is composed of daily data covering the period from 1989 to 2009. The research addresses the question of whether or not accounting for long memory in the conditional variance specification improves the accuracy of the VaR and ES forecasts produced, particularly for longer time horizons. Accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-day-ahead, 10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Additionally, the results suggest that underestimation of the true VaR figure becomes less prevalent as the forecasting horizon increases. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered for the 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons. Finally, the rolling-sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models. Hence, the parameters' time-variant characteristic cannot be entirely due to the news information arrival process of the market; a portion must be due to the FIGARCH modelling process itself.

Misspecification tests for periodic long memory GARCH models

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asymptotically. Because of that, this paper analyses the real size and power of the likelihood ratio and the Lagrange multiplier misspecification tests when periodic long memory GARCH models are involved. The performance of these tests is studied by means of Monte Carlo simulations with respect to the class of generalized long memory GARCH models. For this class of models, analytical derivatives are developed. An application to the USD/JPY exchange rate is also provided.

On functional central limit theorems for dependent, heterogeneous arrays with applications to tail index and tail dependence estimation

We establish invariance principles for a large class of dependent, heterogeneous arrays. The theory equally covers conventional arrays, and inherently degenerate tail arrays popularly encountered in the extreme value theory literature including sample means and covariances of tail events and exceedances. For tail arrays we trim dependence assumptions down to a minimum leaving non-extremes and joint distributions unrestricted, covering geometrically ergodic, mixing, and mixingale processes, in particular linear and nonlinear distributed lags with long or short memory, linear and nonlinear GARCH, and stochastic volatility. Of practical importance the limit theory can be used to characterize the functional limit distributions of a tail index estimator, the tail quantile process, and a bivariate extremal dependence estimator under substantially general conditions.

Misspecification Tests for Periodic Long Memory GARCH Models

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asymptotically. Because of that, this paper analyzes the performance of the Likelihood Ratio and the Lagrange Multiplier misspecification tests for Periodic Long Memory GARCH models. The real size and power of these tests are studied by means of Monte Carlo simulations with respect to the class of Generalized Long Memory GARCH models. An application to the USD/JPY exchange rate is also provided.

Long Memory GARCH Processes: Empirical Evidence from the Tunisian Stock Exchange Market

This paper deals with statistics' and econometrics' properties of fractionally integrated GARCH (FIGARCH). We compare these characteristics with those of traditional models. We insist on the GARCH exponential/IGARCH infinite decrease of volatility impact. Then, we apply it on three Tunisian exchange rate series between 1994 and 2006. As Beine, Laurent and Lecourt (2002), the contributions of the FIGARCH model are extended by accounting for the observed kurtosis through a student-t based maximum likelihood estimation. This estimation improves the goodness of fit properties of this model and may lead to different interest parameters estimates.

The impulse response function of the long memory GARCH process

In this article we derive convenient representations for the cumulative impulse response function of the long memory GARCH( p, d, q) (LMGARCH) process. Our results extend the results in Baillie et al. (1996) [Baillie, R.T., Bollerslev, T., Mikkelsen, H.O. 1996. Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 74, 3–30.] on the first order LMGARCH. Using the derived impulse response functions we compare the persistence of shocks to the conditional variance in various GARCH models of interest such as stable, integrated and LMGARCH.