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Using the nearest neighbor truncation (NNT) approach, this study investigates the realized volatility transmission between the Malaysian Islamic market with various global sectoral Islamic stock markets by extending the heterogeneous autoregressive (HAR) with GARCH, asymmetric effects and jump-robust volatility estimator established in a multivariate setting. The multivariate HAR-GARCH model is capable to capture the persistence and time-varying volatility of realized volatility while NNT approach allows for an asymptotic limit theory in the presence of jumps. Using intraday data, the findings suggest the daily realized volatilities of the Islamic equities rely significantly on their own short-, mid- and long-term volatility components. Besides, there is an evidence of volatility spillover in majority of the pairwise but with low magnitude. The findings also confirm the vital role of conditional heteroscedasticity in the volatility series in explaining the measured volatility transmission of the Islamic stock indices. Hence, this study provides useful insight to understand the portfolio risk of Shariah-compliant equities in making better-informed portfolio allocation.

The availability of ultra-high-frequency data has sparked enormous parametric and nonparametric volatility estimators in financial time series analysis. However, some high-frequency volatility estimators are suffering from biasness issues due to the abrupt jumps and microstructure effect that often observed in nowadays global financial markets. Hence, we motivate our studies with two long-memory time series models using various high-frequency multipower variation volatility proxies. The forecast evaluations are illustrated using the S&P500 data over the period from year 2008 to 2013. Our empirical studies found that higher-power variation volatility proxies provide better in-sample and out-of-sample performances as compared to the widely used realized volatility and fractionally integrated ARCH models. Finally, these empirical findings are used to estimate the one-day-ahead value-at-risk of S&P500.

This study aims to examine the benefits of combining realized volatility, higher power variation volatility and nearest neighbour truncation volatility in the forecasts of financial stock market of DAX. A structural break heavy-tailed heterogeneous autoregressive model under the heterogeneous market hypothesis specification is employed to capture the stylized facts of high-frequency empirical data. Using selected averaging forecast methods, the forecast weights are assigned based on the simple average, simple median, least squares and mean square error. The empirical results indicated that the combination of forecasts in general shown superiority under four evaluation criteria regardless which proxy is set as the actual volatility. As a conclusion, we summarized that the forecast performance is influenced by three factors namely the types of volatility proxy, forecast methods (individual or averaging forecast) and lastly the type of actual forecast value used in the evaluation criteria.

One of the main applications of conditional volatility modeling and forecasting of financial assets is the value-at-risk (VaR) estimation that is used by financial institutions for reporting the daily capital in risk. It remains a question on whether realized volatility (RV) models that incorporate the use of intraday data produce better VaR forecasts compared to methodologies that are based solely on daily returns. This study provides extensive comparison of out-of-sample volatility and VaR forecast performance on three equity market indices: S&P500, FTSE100, and DAX30 using 13 risk models that consist of 5 GARCH specifications, 4 ARFIMAX specifications and 4 HARX specifications. The out-of-sample volatility forecasts are evaluated by various loss functions and simple scoring procedures in order to identity the model that produces the overall best volatility forecasts. For VaR forecasts, the models are evaluated using a two-stage backtesting procedure where the models undergo unconditional and conditional coverage tests to eliminate underperforming models and the qualified models are then evaluated using the quadratic probability score (QPS) function that is computed based on various VaR loss functions. The results showed that RV models outperform GARCH models for volatility forecasts, but a simple EGARCH model outperforms the rest models for most of the VaR forecasts. The results also indicated that capturing the asymmetric behavior of volatility dynamics is essential for accurate volatility and VaR forecasts. The findings of this study provide useful information for market risk regulation, financial risk management and further investigations such as extension to derivative markets and options pricing.

High frequency financial data modelling has become one of the important research areas in the field of financial econometrics. However, the possible structural break in volatile financial time series often trigger inconsistency issue in volatility estimation. In this study, we propose a structural break heavy-tailed heterogeneous autoregressive (HAR) volatility econometric model with the enhancement of jump-robust estimators. The breakpoints in the volatility are captured by dummy variables after the detection by Bai–Perron sequential multi breakpoints procedure. In order to further deal with possible abrupt jump in the volatility, the jump-robust volatility estimators are composed by using the nearest neighbor truncation approach, namely the minimum and median realized volatility. Under the structural break improvements in both the models and volatility estimators, the empirical findings show that the modified HAR model provides the best performing in-sample and out-of-sample forecast evaluations as compared with the standard HAR models. Accurate volatility forecasts have direct influential to the application of risk management and investment portfolio analysis.

This study aims to propose an improved modelling framework for high frequency volatitliy in financial stock market. Extended heterogeneous autoregressive (HAR) and fractionally integrated autoregressive moving average (ARFIMA) models are introduced to model the S&P500 index using various realized volatility measures that are robust to jumps. These measures are the tripower variation volatility, and the realized volatities integrated with the nearest neighbor truncation (NNT) approach, namely the minimum and the median realized volatilities. In order to capture volatility clustering and the asymmetric property of various realized volatilities, the HAR and ARFIMA models are extended with asymmetric GARCH threshold specification. In addition, the asymmetric innovations of various realized volatilities are characterized by a skewed student-t distribution. The empirical findings show that the extended model returns the best performance in the in-sample and out-of-sample forecast evaluations. The forecasted results are used in the determination of value-at-risk for S&P500 market.

Long-memory parameter estimation using log-periodogram regression relies largely on the frequency bandwidth and the order of estimation. Literature shows that a data-dependent plug-in method for the bandwidth significantly increases the MSE’s. In a long memory time series with mild short range effect, a simple approach to determine the bandwidth size is suggested based on the spectral analysis. Monte Carlo simulation results and empirical applications show that the proposed bandwidth selection performs satisfactorily.

This study explores the multipower variation integrated volatility estimates using high frequency data in financial stock market. The different combinations of multipower variation estimators are robust to drastic financial jumps and market microstructure noise. In order to examine the informationally market efficiency, we proposed a rolling window estimate procedures of Hurst parameter using the modified rescale-range approach. In order to test the robustness of the method, we have selected the S&P500 as the empirical data. The empirical study found that the long memory cascading volatility is fluctuating across the studied period and drastically trim down after the subprime mortgage crisis. This time-varying long memory analysis allow us to understand the informationally market efficiency before and after the subprime mortgage crisis in U.S.

Without an efficient financial risk management, it may cause massive consequences to a financial institution as well as individual. Therefore, developing a methodology which gives precise estimates to reduce the exposure of risk to a minimum is of great importance. This paper uses an asymmetric BEKK-GARCH model to examine the return and volatility linkages between the FTSE Bursa Malaysia Emas Shariah (FBMS) index and the sectoral indices under a normal market. The findings suggest that the FBMS plays a leading role in the mean return spillover effect. There is a strong evidence of significant transmission of past shocks, volatilities and leverage effects are observed on the current conditional variance-covariance in all the pair-wise models. These empirical results are helpful in quantifying the cross-market risk evaluation, risk minimizing weight and cross-market hedge ratio for strategizing appropriate portfolio selection.