Dependence structure in financial time series: Applications and evidence from wavelet analysis

Conventional time series theory and spectral analysis have independently achieved significant popularity in mainstream economics and finance research over long periods. However, the fact remains that each is somewhat lacking if the other is absent. To overcome this problem, a new methodology, wavelet analysis, has been developed to capture all the information localized in time and in frequency, which provides us with an ideal tool to study non-stationary time series. This paper aims to explore the application of a variety of wavelet-based methodologies in conjunction with conventional techniques, such as the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and long-memory parameter estimates, in analysing the short and long term dependence structure of financial returns and volatility. Specifically, by studying the long-memory property of these time series we hope to identify the source of their possible predictability. Above all else, we document the indispensable role of trading activities associated with low frequencies in determining the long-run dependence of volatility. It follows that GARCH models incorporating long-memory and asymmetric returns-volatility dynamics can provide reasonably accurate volatility forecasts. Additionally, the persistence parameter of returns, represented by the Hurst index, is observed to be correlated to trading profits obtained from typical technical rules designed to detect and capitalize on existing trending behaviour of stock prices. This implies that the Hurst index can be used as a good indicator of the long-memory characteristic of the market, which in turn drives such trending behaviour.