Determining the impact of different forms of stationarity on financial time series analysis

Abstract

Since most time series data are non–stationary, the econometrician and financial analyst are re–quired to make the data stationary before embarking on any econometric analysis in order to avoid spurious results. Although there are several different ways to render a non–stationary time series stationary, few econometricians and financial analysts look past the first differencing and log–differencing methods. Due to this "difference first, ask questions later" approach, this study aims to determine the impact of different forms of stationarity on financial time series analysis. Further–more, this study aims to determine whether it is of any significance to consider one of the other methods of rendering a time series stationary rather than simply first differencing. As a starting point, the literature on the different forms of stationarity as well as the tests for sta–tionarity is reported. After an extensive review of the literature, it was found that there are at least five different forms of stationarity, each characterised by specific statistical properties of the particu–lar time series. The literature also revealed that the most popular tests of stationarity are the DF–GLS, ADF and KPSS tests. Furthermore, the manner in which the fractional differencing parameter or fractional integration parameter of a time series is determined was reviewed. The methods used to determine the fractional differencing parameter, which were reported in this work, are that of the MRS and GPH methods. Incorporating all the tests and the GPH method, a novel process to deter–mine the correct form of stationarity for a specific time series was introduced. The process was then applied to different types of time series data, which included stock prices, a stock index, consumer price index and an exchange rate. After finding that the time series do differ statistically and have different forms of stationarity, ARFIMA and OLS were employed. ARFIMA and OLS allowed each time series (in its own form of stationarity suggested by the relevant process) to be compared to the al–ternative form. For example, if a time series was found to be fractional difference stationary, its forecasting performance would be tested against its first differenced form. Results indicated that the form of stationarity found in a time series, after employing the relevant process, outperformed its alternative in every instance tested. The results confirmed that it is indeed reckless to "difference first, and ask questions later". First dif–ferencing is not the only method that should be used to render a time series stationary, and it is im–perative that econometricians and financial analysts begin exploring properties of the data and cease blindly following processes suggested for different datasets in the literature. The data should lead the analyst to the method that should be used to truly render a particular non–stationary time series stationary.