The trend superimposed with the seasonal effect constitute the mean of the process. The issue of mean stationarity is usually the first step for further statistical inference. In this talk, we present a theory of testing and estimation for a monotonic trend and the identification of seasonal effects.
Testing is cast as a generic change-point problem, or probabilistic diagnostics.
The change-point problem has been one of the central issues of statistical inference for several decades. It includes, for example, testing for changes in weather patterns and disease rates. We are mainly concerned with a posteriori testing, using spectral analysis to determine periodic components and isotonic regression to estimate the trend.