Some Aspects of Statistical Analysis of Financial Time Series Data

Technical analysis is widely adopted by investors in practice. Moving average strategy is the simplest and most popular trading rule. This simple moving average strategy suffers a well-known drawback since its allocation is always either 100% or 0%. This rule is independent of the investor's risk tolerance level which is widely considered as an important factor in any investment activity. We first introduce an investor's specific risk tolerance into the moving average strategy. We then propose a single-asset generalized moving average crossover (SGMA) strategy and a multiple-asset generalized moving average crossover (MGMA) strategy. The SGMA and MGMA strategies allocate wealth among risky-assets and risk-free asset with the risk tolerance specified by the investor. These trading strategies are evaluated on both simulation data and high-frequency exchange-traded fund (ETF) data. It is evident that both the SGMA and MGMA strategies can significantly increase the investor's expected utility of wealth and expected wealth.

Movements of stocks or equity indices are very important information for an investment decision. Empirical studies illustrate that the movements switch among different regimes or states. The Markov regime-switching model has important applications to this type analysis. However, parameters estimated under normality assumption might not be stable and the corresponding change-point detection algorithm might face some challenges when either the empirical distribution is heavy-tailed or observed data contain outliers. We relax the normality assumption and propose a generalized regime-switching (generalized RS) model. We then improve the corresponding change-point detection algorithm by using the generalized RS model. The change-point detection algorithm using the generalized RS model is tested on both simulation data and Hang Seng monthly index data from January 1988 to March 2015. Simulations studies show that the change-point detection algorithm using the generalized RS model can improve the accuracy of identifying change-points when either the empirical distribution is heavy-tailed or observed data contain outliers. It is also evident that the identified change-points on Hang Seng monthly index data match the observed market behavior.