Friday, November 4, 2016

L1 Trend Filtering

Author and guest post by Eren Ocakverdi.

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.