The Hurst exponent is a key parameter for characterizing the long memory of high-frequency time series. However, traditional estimators often exhibit systematic biases due to the influence of high-frequency endogenous noise and low-frequency trend shifts. Theoretical derivations show that endogenous noise contemporaneously correlated with the latent signal possesses a spectral density in the first-differenced series that is asymptotically equivalent to a squared sine functional form. Accordingly, the proposed estimator incorporates a corresponding spectral density component to fit the high-frequency error. Simultaneously, the model introduces a SCAD penalty term to control the low-frequency spectral divergence caused by structural breaks, thereby mitigating spurious long memory in parameter estimation. Monte Carlo simulations demonstrate that the Penalized Mixture Whittle estimator yields smaller finite-sample biases and root mean square errors in scenarios involving both trend disturbances and endogenous noise. Empirical analysis shows that the estimates obtained using this method are robust to changes in sampling frequency. In further volatility forecasting experiments on commodity futures, the linear forecasting model constructed based on the parameter set achieves higher prediction accuracy than benchmark models such as HAR, as confirmed by the Diebold-Mariano test. This paper provides an effective econometric tool for high-frequency data inference in the presence of composite statistical disturbances.

Owing to the liberalisation of financial markets, the impact of international capital flows on the Chinese stock market has become substantial. This study investigates the effects of economic policy uncertainty (EPU), geopolitical risk (GPR), consumer sentiment (CCI), macroeconomic fundamentals (MECI), and money supply (M2) on the correlations between the stock and exchange rate markets. The negative correlation between these two markets has become more pronounced in recent years. Moreover, EPU, GPR, CCI, and MECI negatively impact long-term stock-exchange rate correlations, while M2 has a positive impact. Portfolios of stock-exchange rates effectively reduce risk, especially when considering structural breaks.

This study examines the price discovery patterns in the three BRICS countries’ stock index futures markets that were launched after 2000 – China, India, and Russia. We detect two structural breaks in these three futures price series and their underlying spot price series, and use them to form subsamples. Employing a Vector Error Correction Model (VECM) and the Hasbrouck (1995) test, we find the price discovery function of stock index futures markets generally improves over time in China and India, but declines in Russia. A closer examination not only confirms the findings of Yang et al. (2012) and Hou and Li (2013) regarding price discovery in China’s stock index markets, but also reveals the inconsistency of futures’ leading role in the price discovery process. Further, we find some evidence of day-of-the-week effects in earlier part of the sample in China, but not in India or Russia. And our GARCH model results show bidirectional volatility spillover between futures and spot in China and India, but only unidirectional in Russia.

The short history and market segmentation characteristic of China stock markets not surprisingly make the market indicators behave in certain way. In this paper, we tabulate the belief that the regulatory and instrumental policy changes in China structurally break the market indices. This is proven and break points are detected with a focus on Shanghai Stock Exchange in the first part of this paper. Whereas, the stochastic trend nature of the market remains even when the structural breakpoints are detected and after it is tested against various kinds of deterministic trends. It, to some extent, implies the efficiency of Shanghai market with regards to unpredictability. The second part of this paper dedicates to analyzing the interaction between A and B share markets. As a contrast to the past literature, the change in trading volume of B share market is found to be a much more sensitive leading indicator to the change in A share market, in the sense of Granger causality with a VAR fashion. This finding may further reveal the unbalanced investor structure in A and B share markets.