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Trend Stationary


Definition: A time series process is trend stationary if after trends were removed it would be stationary.

Following Phillips and Xiao (1998): iff a time series process yt can be decomposed into the sum of other time series as below, it is trend stationary:

yt = gxt + st

where g is a k-vector of constants, xt is a vector of deterministic trends, and st is a stationary time series.

Phillips and Xiao (1998), p. 2, say that xt may be "more complex than a simple time polynomial. For example, time polynomials with sinusoidal factors and piecewise time polynomials may be used. The latter corresponds to a class of models with structural breaks in the deterministic trend."

Whether all researchers would include statistical models with structural breaks in the class of those that are trend stationary, as Phillips and Xiao do, is not known to this writer.

Note that this definition is designed to discuss the question of whether a statistical model is trend stationary. To decide if one should think of a particular time series sample as trend stationary requires imposing a statistical model first.


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