The econometric analysis of seasonal time series: Applications on some macroeconomic variables

In this paper, it has been mainly aimed to treat the scope of the seasonality - which is an important component of time series - in all its bearings by making analyses on some macroeconomic time series (such as inflation, growth, unemployment, consumption, gdp, exports etc.) to evaluate the structural properties of these series under seasonality. The conducted analyses include Seasonal Autoregressive Integrated Moving Average (SARIMA) modelling, seasonal integration tests based on the study of Ilmakunnas (1990), seasonal unit root tests for quarterly and monthly data under the various auxiliary regression models, deterministic and stochastic seasonality tests and seasonal cointegration. The analyses of seasonal unit roots have been conducted fundamentally with the most popular approach developed by Hylleberg, Engle, Granger and Yoo called HEGY apart from the OCSB, DHF tests. There are some important implications of the results obtained for these applications: firstly, if a series has unit roots at which frequencies, filters corresponding to those frequencies should be applied to the series in interest in order to make it stationary. On the other hand, monthly HEGY seasonal unit root applications have revealed that even though the data are available on monthly basis, they may not include any seasonal unit roots at seasonal frequencies. In addition, it is not certain to say that all Turkish macroeconomic series display only one type of seasonal behaviour. Thus, they can have both a deterministic and stochastic structure. Keywords: HEGY procedure, seasonal unit roots, deterministic-stochastic seasonality, seasonal integration, seasonal cointegration