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I have 90 markets with quarterly results, with data from 2014 Q1 to 2016 Q2. I'd like to predict 2016 Q4 results. With a time-series in R, as I understand, you need a single observation over multiple time-periods, but I have 90 observations.

One option I considered was to calculate the mean of the 90 observations, and predict a mean result. The problem is that the distribution of the results tends to change from the beginning of the year (tightly packed) to the end of the year (wide, with a long tail of higher results).

I don't necessarily need an accurate prediction of the individual observations, but I do need a good distribution to work with, as I will be creating reward grids based on quartiles.

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  • $\begingroup$ What exactly are you trying to predict? Values for all 90 series? $\endgroup$ – Kontorus Jun 28 '16 at 15:54
  • $\begingroup$ Either a value for all 90, or the general distribution in Q4 (p25, p50, p75 should be sufficient). I am now thinking I could skip the time-series and use a linear model where Q4 ~ year + q1 + q2? $\endgroup$ – pedram Jun 28 '16 at 16:06
  • $\begingroup$ You could use the linear model, but time series seems to be a better idea, just because financial data tends to work better with it $\endgroup$ – Kontorus Jun 28 '16 at 16:45
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For each point in time, you don't have a single observation, but an entire curve or function, namely, the distribution function of your quarterly results over the 90 markets. This is a case of . Thus, I'd recommend you look for "functional data forecasting" or something similar.

For instance, Rob Hyndman has a working paper on forecasting functional time series. It's on age-specific mortality over time, but the ideas might well be applicable to your case.

That said, just ten observations (ten quarters between 2014Q1 and 2016Q2) is very little data. I don't know how well any method will perform here. Stick with something simple.

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The description of your information (90 markets, 10 quarters) sounds like it could be fit with a panel data model. There are many advantages to this approach including increased degrees of freedom, ability to isolate the effects of specific actions or treatments as well as more reliable estimates. The econometric literature on this very flexible class of models is rich and extensive. Among the key texts is Wooldridge's Econometric Analysis of Cross Section and Panel Data. Another good one is Baltagi's Econometric Analysis of Panel Data.

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