Abstract

TIME SERIES WITH INTERDEPENDENT LEVEL AND SECOND MOMENT: STATISTICAL TESTING AND APPLICATIONS WITH GREEK EXTERNAL TRADE AND SIMULATED DATA

Alexandros E. Milionis

Bank of Greece and University of the Aegean

Nikolaos G. Galanopoulos

University of Athens

ABSTRACT

This work aims to fill an existing gap in the literature regarding the statistical testing for the existence and the identification of the character of time-varying second moment in its dependence on a non-constant mean level in time series. To this end a new statistical testing procedure is introduced with some considerable advantages over the existing ones. Amongst others it is argued that the existing statistical tests are insufficient and sometimes lead to biased results. Further the effect of the application of this methodology on some crucial elements of time series modelling such as outlier detection and seasonal adjustment is examined, through case studies conducted on a comparative basis using both the new methodology and an established one. The severe consequences of the improper treatment of the type of time-varying second moment dealt with in this work are evidenced and emphasized. The data set comprises time series on monthly external trade statistics for Greece. Overall, the resulting empirical evidence favours the new approach. Further supporting evidence is provided by the application of the new methodology to simulated data.

JEL Classification: C150, C220, C510, F140

Keywords: time series transformations, applied time series analysis, seasonal adjustment, detection of outliers, Greek external trade time series.

Acknowledgements: The authors are grateful to H. Gibson and the referee for helpful comments. The views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Greece.

Correspondence:

Alexandros E. Milionis

Bank of Greece,

Department of Statistics

21 E. Venizelos Avenue,

Athens GR 102 50