Modeling Trends

In this chapter we consider the modeling of nonstationary mean time series, or trends, by state space methods. Initially we consider a Gaussian disturbances state space smoothness priors modeling that is appropriate when the trend is a smooth function. An example of the analysis of simulated data illustrates the method of analysis. Secondly we model simulated time series data with local trend and globally stochastic components. A generalization of the latter procedure is shown in the analysis of a collection of 22 years of daily maximum temperatures recorded in Tokyo. Evidence is shown to justify modeling this data with a common trend plus an individual annual AR processes model. The analysis of the Tiao and Tsay (1985, 1989) flour price data, another example of the analysis of multiple time series with common trend and individual AR process is also shown. On the basis of these examples, the common trend individual AR process modeling is offered as a candidate parsimonious model of multiple nonstationary mean time series.