Some Basic Issues in Time Series Modelling

Abstract

Modern time series analysis has been primarily concerned with an understanding (description and prediction) of time varying behaviour of economic phenomenon. However, the patterns of time varying behaviour have not remained the same over the years. The reasons for this could be several. Among others, mention may be made of: (i) the changing character of markets in the wake of liberalization of economies and globalization of trade and markets, and (ii) new and alternative ways of looking at time varying behaviour, given the availability of high frequency or longer time series data, computing algorithms and software, and new techniques and tests. In the backdrop of this, addressing the concern of understanding time varying behaviour as accurately as possible, poses a formidable challenge to the time series econometrician. Some clarity on the basic issues of time series modelling however, might provide some relief. Time series modelling may be carried out in time and frequency domains. In time domain, time is the unit of analysis. The dynamic evolution of a phenomenon over time is traced with the help of suitable statistical models designed for this purpose. In the frequency domain, the unit of analysis is frequency component. Under this approach a given time series is decomposed into frequency components and statistical analysis is undertaken to trace the behaviour of components. In both the approaches, what is studied is the inter-temporal dependence (association) among the past, present and future of a time varying phenomenon, from a given set of sample data. The only difference between the two approaches is that in the time domain the temporal properties of a variable are studied on the basis of realizations recorded at a pre-determined frequency, while in the frequency domain, the sample realizations depend not on a single frequency component but on several components. As a result, there is an absence of frequency based information in time domain, and vice versa. But both are equivalent approaches. Depending on the nature of the problem at hand, the choice of domain may be decided (Granger in Econometrica 37(3):424–438, 1969). It would however be more profitable if both time and frequency information are simultaneously available. This is possible in the time–frequency domain, known as wavelet analysis. The present paper highlights some basic issues of concern in time, frequency (spectral) and time–frequency (wavelet analysis) domains, by placing them in a comparative context. The paper is organised into three sections, one each for each of the domains of analysis. The first section deals with the basic issues in time domain, followed by the frequency and time–frequency domains in the next two sections.