Diligence in determining the appropriate form of stationarity

Abstract

Orientation: One of the most vexing problems of modelling time series data is determining the appropriate form of stationarity, as it can have a significant influence on the model’s explanatory properties, which makes interpreting the results problematic.

Research purpose: This article challenged the assumption that most financial time series are first differenced stationary. The common difference first, ask questions later approach was revisited by taking a more systematic approach when analysing the statistical properties of financial time series data.

Motivation for the study: Since Nelson and Plosser’s (1982) argued that many macroeconomic time series are difference stationary, many econometricians simply differenced data in order to achieve stationarity. However, the inherent properties of time series data have changed over the past 30 years. This necessitates a proper evaluation of the properties of data before deciding on the appropriate course of action, in order to avoid over-differencing which causes variables to lose their explanatory ability that leads to spurious results.

Research approach, design and method: This article introduced a rigorous process that enables econometricians to determine the most appropriate form of stationarity, which is led by the underlying statistical properties of several financial and economic variables.

Main findings: The results highlighted the importance of consulting the d parameter to makea more informed decision, rather than only assuming that the data are I(1). Evidence also suggested that the appropriate form of stationarity can vary, but emphasises the importance to consider a series to be fractionally differenced.

Practical/managerial implications: Only when data are correctly classified and transformed accordingly will the data be neither under- nor over-differenced, thus enhancing the validity of the results generated by statistical models.

Contribution/value-add: By utilising this rigorous process, econometricians will be able to generate more accurate out-of-sample forecasts, as already proven by Van Greunen, Heymans,Van Heerden and Van Vuuren (2014).