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.
. A significant change point was detected at period 137 suggesting time-varying parameters. The remaining 668 observations suggest a pdq ARIMA Model (3,0,0) with a level.step shift supporting your preliminary conclusions about lag 3. 
. The Actual/Fit/Forecast graph is 
The Residual Plot 
and the acf of the residuals is 
. Since the acf of the residuals shows strong structure at periods 5 and 10 , 
you might further investigate seasonal structure at lag 5. I hope this helps.
Best Answer
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.