# High dimensional time series

I'm not sure what words I should look for. I have an under determined dataset of 8000 correlated variables (sales) over 12 months (ie 12 observations for each variable). And I basically want to predict the future. Where should I start? PCA?

My question is, what are the techniques used to deal with lots of (correlated) variables and few observations in the case of time series.

I'm looking for orientations (but a full solution is of course welcome!).

I'm agnostic, so stats/econometrics/model-based are as fine as machine learning/AI/not-model-based, as long as they yield results that are useful and mean something. Repeatable/standardizable solutions are more than welcome.

• What is the expected horizon for your projections (1 month, 1 quarter)? Will you be using only sales data or some exogenous variables like CPI, PPI with known official forecasts to overcome the Zach's mentioned problem while forecasting either the principal components or some selected leading indicators? – Dmitrij Celov Jan 10 '12 at 13:45
• @DmitrijCelov, those are excellent questions and I must admit I haven't done a good job exploring them before posting. I'd say that as a start I won't include any exogenous variable. The reason I asked this question is that coming from a stats world I'd have some ideas if there were only 2 or 3 variables; with so many variables I naturally thought of more "ML" techniques that deals with tons of features. But my little knowledge of those techniques doesn't include anything specific to time series. – Arthur Jan 11 '12 at 16:46

• (+1) in general I share the same ideas as yours, if not all of the prices are in coincident state, there still is hope to detect some leading indicator or define common and idiosyncratic part. In general the interval forecasts will be quite wide, but who knows. Diffusion index model may be technically applied since $T<<N$, but the uncertainty in time domain will be too high IMHO. – Dmitrij Celov Jan 10 '12 at 13:48