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I would like some opinions on my current situation.

I have a set of time series data that I want to forecast. The data however is not very long (around 500 rows) so I was looking into generating many synthetic datasets that mimic my current one's statistical characteristics.

I have seen online, methods that can generate time series data based on your own dataset for example TimeGAN, DoppleGANger which are a neural-networks. It is well known that neural-networks need a lot of data to perform well and prevent things like overfitting.

You can probably see my problem here, that I don't have enough data to ensure GAN models that are meant to generate me more data work effectively. Or do you think I can just go for it and it wont really matter?

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  • $\begingroup$ Is it one time-series of 500 time-points, or 500 different time-series (of N time-points) ? $\endgroup$
    – Jon Nordby
    Commented Nov 15, 2022 at 18:09
  • $\begingroup$ One time series of 500 consecutive time points (daily) $\endgroup$
    – codinator
    Commented Nov 15, 2022 at 20:05

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Data sparsity should result in uncertainty about the model - it's functional form, presence of outliers, periodicity, etc. 500 rows of data can reliably estimate some stable series; and functions can be arbitrarily complicated so that not even 50,000 could estimate the series. At the end of the day, we make assumptions: the initial assumptions about the level of complexity and desired estimation precision should have dictated the necessary sample size for the analysis. We don't post hoc analyze data without such a consideration, it's a waste of science and of data.

Synthetic data analyses exist, and the analyses are valid when the assumptions are correct. They can improve power or precision by 20% or 30% or more depending the level of risk you're willing to take. These data analyses use external data that have been thoroughly vetted - in terms of cost, they don't always beat the cost of just getting more data yourself. An AI algo is certainly part of generating such data, but an expert in this area could speak volumes more about what's done to prepare and share synthetic data.

Your specific problem is two-fold: a. This wasn't a planned analysis, you collected the data and now you feel apprehensive about the number of observations or quality of the data. b. Using an algorithm internally to generate synthetic data for your own purposes has no limit or scope - you could generate an infinite amount of data for free and, the net result would be that you precisely estimate the AI algorithm that generated the data for you rather than the data you collected which was your initial goal.

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  • $\begingroup$ Could you elaborate on what you mean by 'level of risk willing to take' $\endgroup$
    – codinator
    Commented Nov 15, 2022 at 17:40
  • $\begingroup$ One could, for instance, add 100,000 artificial observations according to $y=sin(t)$ and say "There! look how precisely I estimated the trend, these other data are outliers". This is, of course, insane. But the boundary between sane and instance data integration methods are not as clear as one might suppose. $\endgroup$
    – AdamO
    Commented Nov 15, 2022 at 18:41
  • $\begingroup$ "They can improve power or precision by 20% or 30% or more depending the level of risk you're willing to take." can you please provide some references on this? I am curious to look into this further. $\endgroup$
    – usεr11852
    Commented Dec 21, 2022 at 10:56
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Generating extra data can sometimes help you train a neural net. (Adding noise layers is equivalent to generating extra data, since it fuzzes the existing data.) But you still need to have enough data to train, and to make an independent test. And in your case, you don't.

In your case, with such a small dataset, really your only option is to use Bayesian methods. Have you any reasonable hypotheses about the process? e.g. is it likely to have a components with daily/weekly/annual periodicity? If so, you can make a reasonable prior distribution.

If you have only 500 datapoints and no prior knowledge at all, then there isn't really any way forward.

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