My students and I have had some luck with short time series in quality control applications, where we could try the idea that many time series in our area were AR(1) or at least behaved that way if they were short. Our main results, can be found summarized here: https://scholar.google.com/scholar?hl=en&as_sdt=0%2C36&q=Booth+HU+Wright+Outliers+in+Short+times+series&btnG= Wish you the best of luck, David Booth

Hello John Rahilly

For extremely short time series, simper models work much better. Since, there is no way of validating your model with held-out samples due to sample scarcity, you can use AIC as a proxy to select your best simpler models. From your description, it looks like even random-walk or AR(1) process can stand out as good candidate. The R package auto.arima() also selects simpler models for short timeseries. For further reference, you can have a look into this blog by Rob J Hyndman: https://robjhyndman.com/hyndsight/short-time-series/

Wish you best luck!

Let us be realistic. The sample size of 5 is far too small for any meaningful statistical inference. In fact no lesser than a size of 30 is acceptable for any statistical inference.

Your Data set is too small, See our recent paper on statistical model and Time series, FYI

Research Electrical Energy Demand Forecasting Using Time Series Approach

I suggest you use grey prediction models with rolling mechanism technique. These models can be metabolic grey model (MGM(1,1) or nonlinear metabolic grey model (NMGM(1,1)).

Dear John Rahilly

It is definitely possible to do with as less as 5 observations.

To get better forecasting, additional information will be needed.

If it is possible on your part to share further details on your dataset, concise methods can be further discussed.

regards,