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Consideration of trends in time series. (English) Zbl 1266.62071
Summary: Even though the trend components of economic time series were among the first to be distinguished, even today the trend remains relatively little understood. As P.C.B. Phillips [Math. Comput. Simul. 68, No. 5-6, 401–416 (2005; Zbl 1065.62196)] noted, no one understands trends, but everyone sees them in the data. Economists and econometricians can give plenty of examples of trends, such as straight lines, exponentials or polynomials in time, and also forms of random walks, but these are merely examples. Individuals or groups do have their own personal definitions, but these diverse approaches illustrate the lack of a generally accepted definition of a trend. They also suggest a richness of alternatives to consider, both individually and jointly. We make a variety of observations about trends, and based on these, we offer working definitions of various kinds of trends. We emphasize that these are working definitions, as our purpose here is to invite discussion, not to settle matters once and for all. Our hope is that our discussion here may facilitate the development of increasingly better methods for prediction, estimation and hypothesis testing for non-stationary time-series data, and ultimately may enable decision makers to make more informed decisions.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics
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