Tests for Trend: A Simulation Study

Abstract

In this study, we use the wavelet analysis to construct a test statistic to test for the existence of a trend in the series. We also propose a new approach for testing the presence of trend based on the periodogram of the data. Since we are also interested in the presence of a long-memory process among the data, we study the properties of our test statistics under different degrees of dependency. We compare the results when using the band periodogram test and the wavelet test with results obtained by applying the ordinary least squares (OLS) method under the same conditions.

Keywords:

• Band periodogram
• Discrete wavelet transform
• Fractional difference processes

Mathematics Subject Classification:

• 62J99
• 62G09