Suppose I have sample of 40 data points (annual values of hydrologic variable). I have some variables which influence outcome of data points. What should I do?
Should I go for regression analysis for forecasting or should I use this timeseries sample only to come up with forecasting model.
Also can you suggest literature where minimum no of data points in sample is mentioned for using timeseries analysis for forecasting.
There is no general rule. Forcasting is always tricky and forecasts have to be taken with care. Much mor important than the sample size is the model: is it sensible? Are all important predictors included? Are ineffective/suspicious predictors exlcuded? The model gives you prediction intervals and confidence intervals. The smaller the sample size, the larger the intervals will be. A reasonable way to decide what sample size is required is to define the desired interval width. You may need preleminary data and simulations to find this out.
Pragmatic solution: you do have 40 points. This is the data at hand. If you have a sensible, reasonable model just fit it to the data you have. This gives you the best estimates for forecasts you can have. This might or might not be good enough for the task, but this is all you can do with the data you have.
Note: Even with lots of data and narrow confidence intervals forecast can be drastically wrong. The further away the forecasts are from the actual data, the higher the risk to get starkly wrong forecasts. It also depends on the quality of the model and this is to be judged outside of the data.
Rules of the thumb have been suggested but they vary from field to field. As an example, when dealing with time series analyses of fluctuating populations of insect herbivores, the rule of the thumb is to have at least three cycles and a minimum of 30 generations. Although this is easy to get with an insect that has a short cycle (e.g., the balsam fir sawfly – one generation per year, population cycles of 10 years), it is often impossible to get with insects that have long cycles (e.g., the spruce budworm – one generation per year, population cycles of 35 years). I surely would not apply the rule of 3 cycles to hydrological data.
http://robjhyndman.com/papers/shortseasonal.pdf
'"how much data do I need?” is probably the most common question our business clients ask us'
[from article:]
"whatever approach is taken, if m is the number of months or quarters in a year, then m parameters are required. a regression usually also has another parameter for the time trend. so the total number of parameters in the model is m+1. consequently, m+2 observations is the theoretical minimum number for estimation; that is, 6 observations for quarterly data and 14 observations for monthly data. but this will be sufficient only when there is almost no randomness. for most realistic problems, substantially more data are required"
40 is adequate because 30 is the usual recommendation :)
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