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I am looking for resources on the techniques for time series forecasting. It seems that there are three approaches, listed below in the order of their machine learning-ness (and correspondingly their greediness for data):

  • ARIMA and GARCH models
  • Hidden Markov Models (HMMs)
  • Neural networks: RNNs, LSTMs, GRUs

In terms of sources ARIMA/GARCH do not pose problems - there is wealth of books, notes, tutorials, etc. HMMs are well covered as well, but I haven't seen yet anything where they would be applied to time series. Finally, the resources on RNN/LSTM/GRU seem to be scarce, perhaps due to relative novelty of this domain.

I will appreciate books/articles recommendations regarding these techniques and their application to time series. If you want to post your own overview of the subject, it will be greatly appreciated as well.

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    $\begingroup$ I would guess one of the most common statistical ways it is done is exponential smoothing models, which are also one of the more accurate ways according to the M contest. State space models, of which ESM is one case, and transfer function models are also used although I have limited knowledge of these. $\endgroup$
    – user54285
    Commented Jul 23, 2020 at 21:34

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There are a couple of good review papers on the topic of deep learning for forecasting:

A word of warning though: I am a very big fan of LSTM based forecasting and I advocate for it alot in my various roles. But I would be the first to tell you to tread very, very carefully: The number of use cases where LSTM provide an advantage over traditional statistical models is very limited, and Deep Learning is very far from being an established theoretical topic, the way ARIMA or State Space Models are.

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The "classical" methods comprise much more than ARIMA and GARCH (which address different questions, and at least ARIMA is not very useful for forecasting), e.g., decomposition, Exponential Smoothing etc. I recommend this very good free online textbook by Athanasopoulos & Hyndman.

I agree that there is very little in terms of textbooks on HMMs or NNs as used for forecasting, and I would be interested in any pointers.

Looking at book reviews in the International Journal of Forecasting may be helpful (even though the list of search results is admittedly not).

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  • $\begingroup$ I had a strange experience with HMM for forecasting: I came across them in a single source (could have been a post here, or a blog) and subsequently spent several weeks looking for formal references, either textbooks or research papers. In almost all cases HMMs were being used for forecasting discrete binary events (i.e. i.e. future facing binary classification, not regression) and not a single serious source mentioned them for regression type time series forecasting. I think that the few people that cite them for forecasting are just abusing the language. $\endgroup$
    – Skander H.
    Commented Jul 23, 2020 at 17:13
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The combination of differential equations (e.g. ODE of SIR models) and HMM are often used in epidemiology. The hidden states are models as ODEs and the observation process are modeled as HMM. One example is pomp. The model is trained on existing data and produces forecasting on the future. Another goal of this kind of model is to understand epidemiology related parameters. More examples can be found in here and this book

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