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 insample and out-of-sample forecast evaluations. The forecasted results are used in the determination of value-at-risk for S&P500 market.

Principal component analysis reduces dimensionality; however, uncorrelated components imply the existence of variables with weights of opposite signs. This complicates the application in data envelopment analysis. To overcome problems due to signs, a modification to the component axes is proposed and was verified using Monte Carlo simulations.

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.

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.

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.