What's the minimum sample size required to do a time series analysis? I'd like to know the minimum number of monthly data points required to do time series analysis with the seasonality effect in forecasting.
I read some articles & they were saying that 50 or 60 data points are sufficient.
Is that the really minimum? Are there any trustful documentation which can be used as literature in this problem?
I'd be grateful if anyone can help. 
Thank you.
 A: Hanke and Wichern, chapter 3, page 80  ( http://www.amazon.com/Business-Forecasting-Edition-John-Hanke/dp/0132301202 ) recommend a minimum 2xs to 6xs depending on the method (where s is the seasonal period, so s=12 for monthly data).  50 data points would be 50/12 = 4 years of data.
But it depends on the regularity of the data.  If the seasonal pattern is quite regular, 3 years is OK.
A: If you are going to perform the standard decomposition method, then it's the question of how many data points make the sample of each seasonal index, calculated as a geometric mean.
So, how many data do you consider sufficient for a reasonable estimate of the mean value? 
On the other hand, if you proceed with the ARIMA, it's the question of how many data points make a reasonable estimate of autocorrelation on the series reduced by a full season.
So think about it in this way. I have been working with time series analyses, 50-60 sounds reasonable to me.
A: I suggest approaching this problem from a slightly different, more pragmatic angle. Rather than considering a general rule of thumb, you could take a strictly empirical approach to consider if your forecasting model is good enough for your specific short-time-series dataset.
"Good enough" should be understood in the same sense of what is a "good" or "useful" time series model. In principle, a good or useful model is one that does a better job forecasting than a naive (default) forecast model. (This is a universal principle for forecasting evaluation, not just for short time series.) Common naive forecast models for non-seasonal data are the last outcome in the series or the mean of the last two to four outcomes. Common naive forecast models for seasonal data are the mean of outcomes for the last season, or slightly more complex, the outcome for the same period from the last season. These naive forecast models tend to provide surprisingly robust forecasts that can be hard to beat by simple forecast models.
So, if any forecast model that you can create on your short series can do better than an appropriate naive forecast model, then it should be considered good enough to go by--it has demonstrated that it is better than the naive model and so you are justified to prefer your forecast model.
The only caveat is that with a short time series, it is very difficult to demonstrate that your forecast model is not better just by chance or that it is not overfitting the past data. For such assurance, you need to validate the performance of your model, and sliding window validation will normally cut the already-small dataset size in at least half, so its results might not be reliable.
In summary: even for a short time series, you can argue that your forecasting model is good or useful by demonstrating its superiority to a naive default forecast, but it might be difficult to demonstrate that such superiority is reliable.
