Testing the Significance of the Linear Regression Coefficients: Exploring Some Estimators for the Autocorrelation Function

This work addresses the problem of testing the significance of the slope of a linear trend with and without an eventual seasonal effect. It is assumed that the error term follows an AR(1), and that the autoregressive parameter is unknown. The autoregressive parameter is obtained through some competing estimators, namely, a parametric version, a modified Kendall’s correlation coefficient, and another non-parametric counter part developed earlier in the context of the state space models. The accuracy of the estimation of this parameter is also analyzed. The performance of the tests considering the three estimators simultaneously is compared through a Monte Carlo simulation study under different assumptions. The study is extended in order to compare the slopes of two or more periods in the same time series