Multivariate Time Series Forecasting with Neural Networks (3) – multivariate signal noise mixtures

In this follow up post we apply the same methods we developed previously to a different dataset. In this third post we mix the previous two datasets.

So, on the one hand, we have noise signals, on the other hand we have innovators and followers.

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Multivariate Time Series Forecasting with Neural Networks (1)

In this post we present the results of a competition between various forecasting techniques applied to multivariate time series. The forecasting techniques we use are some neural networks, and also – as a benchmark – arima.

In particular the neural networks we considered are long short term memory (lstm) networks, and dense networks.

The winner in the setting is lstm, followed by dense neural networks followed by arima.

Of course, arima is actually typically applied to univariate time series, where it works extremely well. For arima we adopt the approach to treat the multivariate time series as a collection of many univariate time series. As stated, arima is not the main focus of this post but used only to demonstrate a benchmark.

To test these forecasting techniques we use random time series. We distinguish between innovator time series and follower time series. Innovator time series are composed of random innovations and can therefore not be forecast. Follower time series are functions of lagged innovator time series and can therefore in principle be forecast.

It turns out that our dense network can only forecast simple functions of innovator time series. For instance the sum of two-legged innovator series can be forecast by our dense network. However a product is already more difficult for a dense network.

In contrast the lstm network deals with products easily and also with more complicated functions.

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