On Tests of Trend in a Weakly Stationary Time Series

SYNOPTIC ABSTRACT

Analysis of a Time Series represented by an error model frequently leads to familiar procedures in regression analysis. The statistical models we consider are applicable if the underlying population which generates the data has a substantial change in trend at some point. We are interested in testing hypotheses if this change is significant. Two test statistics are introduced and their distributions are derived under the assumption of weak stationarity. It is proved that these tests are unbiased and their power functions are monotonic. With correlated residuals, the linear test statistic does not give a UMP test. It is shown that a certain quadratic test statistic gives a more powerful test.

KEY WORDS:

• trend
• weak stationarity
• quadratic forms
• power