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What techniques can be used to predict a time series (say monthly economic data) with another time series (say a company's sales)?

If you only have about 50 data points of monthly data, and a yearly seasonality for both your predictor and predicted variables. Is the best way to do this simply to remove seasonality (say with a moving average) on both, and then OLS regress one on the other? Is it ARIMA? Is there anything more appropriate? If I try every possible lag for every predictor and then pick the one that fits best, do I not face a cherry-picking problem?

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  • $\begingroup$ Consider a vector autoregressive (VAR) model with seasonal dummies. $\endgroup$ – Richard Hardy Aug 6 '15 at 10:32
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Easiest technique could be multiple regression where you have monthly dummies (actually 12-1).

Other technique could be ARIMAX which means you have time series model with explanatory variables and not only ARIMA.

Of course there are more exotic time series models like state space models which could be used.

Number of observations is quite small but sometimes I have used something like three years of data successfully, but this depends on problem on hand.

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