machine learning model vs time series model?

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A general question about machine learning models vs classical time series model in prediction tasks? When to use machine learning models, when to use time series models? What is the advantage and disadvantage of them?

My first thought is time series models are more widely used when there is 1 predictor. However, there are multivariate time series models so this argument doesn't really stand.

Another thought is about the assumption of the model. For example, many machine learning model assumes independence of data while time series model does not. But what else? when should we use machine learning models for prediction task instead of time series models?

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Check out this paper on arXiv. It expounds on the following:

We demonstrate how by applying deep learning techniques to forecasting, one can overcome many of the challenges faced by widely-used classical approaches to the problem.

I think you're right in terms of the one or several time series being predicted: at least Amazon Web Services claims the following for the above arXiv-presented model:

When your dataset contains hundreds of feature time series, the DeepAR+ algorithm outperforms the standard ARIMA and ETS methods

I hope that this gives you some (at least close to) cutting edge work done on machine learning for time series. After all, if "classical" time series models e.g. ARIMA didn't have room for improvement, there would be no comparison to make!