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.

Again, as previously, we make use of the github hosted package timeseries_utils, and a script, which follows here:

Data

As stated, the main difference to the previous posts is the data.

In this post the data is composed of an innovator, a follower and some mixtures.

Arima

As mentioned, the defineFitPredict needs to be defined for each forecasting technique. In the case of arima we use defineFitPredict_ARIMA, which is  supplied by our package timeseries_utils.

Now we run the script shown above.

The configuration is this:

The result is:

Interpretation : As is evident in the figures and the reported skill scores arima struggles to predict anything meaningful at all, except for mixture1, which contains a signal. The more complicated signal-bearing mixtures muixture2 and mixture3 are not predicted any better than by the benchmark.

 

Dense

As mentioned, the  defineFitPredict needs to be defined for each forecasting technique. In the case of our dense network we usedefineFitPredict_DENSE, which is also supplied by our package timeseries_utils.

Now we run the script shown above.

The model summary is this:

 

The result is:

 

Interpretation : Dense does a pretty good job. Of course it cannot predict the innovator1, however it noticeably fails with the complicated construction of mixture3.

 

LSTM

As mentioned, the  defineFitPredict needs to be defined for each forecasting technique. In the case of our LSTM network we use defineFitPredict_LSTM, which is also supplied by our package timeseries_utils.

Now we run the script shown above.

The model summary is this:

The result is:

Interpretation : LSTM does a pretty good job. Of course it cannot predict the innovator1, in particular it noticeably fails with the complicated construction of mixture3.

 

Method/TimeseriesArimaDenseLSTM
follower1
innovator1
mixture1
mixture2
mixture3

The joint winners are Dense and LSTM.