Extracting the trend of a time series is an important
analytical task as it simply depicts the underlying movement of the variable of
interest. Had this so-called long term component known in advance, we would
have been able to foresee its future course. In practice, however, there are
several other factors (e.g. cycle, noise) in play that have influence on the
dynamics of a time dependent variable.
Time path of a variable can either be deterministic
(assuming the change in trend is constant) or stochastic (assuming the change
in trend varies randomly around a constant). Estimation of a deterministic
trend is straightforward, yet it often oversimplifies the data generating
process. The assumption of stochastic trend seems to be a better fit to
observed behavior of various time series as they tend to evolve with abrupt
changes. Nevertheless, its estimation is difficult and can have serious
implications due to accumulation of past errors.
