Financial time series modelling in frequency domain

Abstract

In financial time series modelling, one problem is to identify a small number of potentially important factors and incorporate them into a multi-factor model in order to explain the variable in consideration. In this thesis, we propose a new factor search methodology in frequency domain, and select factors based on frequency peak patterns to obtain the final model. This ensures the key patterns in dependent variable be found and suitable factors be selected based on the peaks in common. It performs well even when the number of factors is greater than the sample size. In addition, the frequency domain provides flexibility in dealing with independent variables with different timeframes, and this could be valuable in finance and economic when traditional models usually can handle data in single sampling frequency only. Using the proposed method, we study three different types of applications. The first is to identify the constituents of an index or a mutual fund. We demonstrate that our method can identify most of the constituents based on the frequency fingerprints (key patterns) in the variables. The second is to develop multi-factor models based on macroeconomic factors for economic and financial indices. We show that it is important to include factors with different timeframes to achieve better fit. Finally, we study the influential technical analysis indicators that investors might be using in their trading decisions as reflected in the transacted volume, and compared the indicators selected for the same company traded in Hong Kong and Mainland stock exchange markets.