Arc length tests for equivalent autocovariances

Abstract

This paper presents a new test for discerning whether or not two independent time series have the same dynamics. Several methods in the time and spectral domain have previously been devised to conduct such a test. Here, we explore a new approach to the problem by comparing sample arc lengths (ALs) of the two series. Because sample ALs are derived from first-order differences in the series, the proposed methods work for both stationary autoregressive moving average and non-stationary autoregressive integrated moving average processes. This robustness is advantageous when one is unsure about unit root properties in the underlying series.

Keywords:

• arc length
• autocovariance
• ARMA
• ARIMA

Acknowledgements

The authors would like to give special thanks to Hany Bassily for first suggesting the AL idea.

Notes

Most economists pegged June 2009 as the end of the recession.