What is the minimum historical data/sample data required for a time series forecasting analysis?

Question

Are there any statistical power analysis/sample size deteminations methods for time series data analysis/forecasting?

For example if I have time series of 30 data points, how can I with confidence use a particular statistical methods like exponential smoothing or arima for predict the future ?

I have seen in some textbooks that have a cursary mention on historical data points required for ARIMA would be 50 or 60. But I have not encountered a formal approach on how much history is required for a a particular time series forecasting method.

I did a thorough search on major time series textbooks and the internet, I'm unable to find any literature on this topic. Any guidance would be helpful.

Answer 1

No, there is no power test. The 60 data points suggested by Box-Jenkins and the 36 by Makradakis are arbitrary and are more from the mind set of a "best fit" modeling approach.

I am of the belief that any time series can be modeled. The signal to noise ratio determines how well you can identify a pattern that would be more complicated than a mean model with some outliers, for example.

Answer 2

I have been teaching Ops management in NTU singapore. This is a standard question my students ask me. To be honest there is no definite answer to the number of historical data points. It depends on what you are forecasting. Assuming stable past data with out trends,even 10 data points can return a reasonable forecast compared to 30 or 60 data points. The smoothing factor is the key. with the right alpha Value you can reduce the number of data points. here is an example below. if you choose alpha value closer to 0.1, the forecasts are very different. I would conclude that for short term forecasting with reasonably stable past, 10 to to 20 points is good, but we must select the right Alpha value with lowest MSE .