In the last post I covered a generic overview of some of the issues involved in time series prediction. However there are more basic issues to consider before I start covering some examples. When modeling time series, the two key problems are noise and non-stationarity. The noise is a function of the lack of complete information from the past behaviour of the time series to fully capture the dependency between the future and the past. The noise in the data could lead to a persistent bias towards over-fitting or under-fitting the data. As a consequence the obtained model will have a poor level of performance when applied to new data patterns. The non-stationarity aspect of time series data implies that dynamics can change over time. This will lead to gradual changes in the measured relationship between the input and output variables. This is one of the reasons why academics favor ARCH and GARCH processes to address these issues specifically. That said, in general it is hard for a single prediction model to capture such a dynamic input–output relationship inherent in the data.
One of the key problems facing a single model to learn the data is that there exists inconsistencies in the level of noise in different regions of the dependent variable output. This leads to a situation that penalizes certain regions at the expense of others. This is often a key reason why academics fail to see an effect because the “baby is thrown out with the bathwater”- highly profitable regions are smoothed in the prediction function with regions containing nothing but noise or perhaps even an opposing effect. In the converse situation the distinct regions may be overfitted by a function that does not generalize to the rest of the variable output, and as a consequence the predictions are unstable.
The only way to adequately capture the non-linearities that exist in the data is to: 1) use non-linear functions that are robust 2) use multiple linear, non-linear, or discrete models using historical situational returns in combination such that the underlying data is more accurately represented. The use of “Zones” by CSS was one method of parsing the data to capture non-linearities, other methods include using using multiple “setups” framed in a historical context, neural networks, indicators and systems, and of course linear quadratic programming (ie optimization). Lest one be deluded into thinking that simple data mining is sufficient for extracting relationships, they are sorely mistaken. The path towards the balance between robustness and rigor and creating a model of sufficient complexity that is also time-varying (ie adaptive) is one without a good map. The only way to find your way through the woods of the financial wilderness is with a compass, trial and error, common sense, and an open mind.