AY2016
program

[Abstract]

This paper proposes a new test for selecting trigonometric terms when the deterministic trend of a univariate time series is periodic.
The problem of unknown frequencies in such a cyclical trend was first investigated by Anderson (1971) under the assumption of serially uncorrelated error term, but we allow for an autoregressive error term without prior knowledge as to whether the error term is stationary or contains an autoregressive unit root. This is achieved by modifying the test statistic proposed by Perron, Shintani and Yabu (2016) which requires the assumption of a known set of frequencies. We show that limiting distribution of our test statistic can be common between the stationary and unit root cases even if frequencies are unknown. Simulation results confirm that our procedure works well with sample size typically available in practice. We illustrate the usefulness of our method via an application to international data on unemployment rate.