Statsmodels ARIMA: Constant Value for Each Forecast

Question

I'm trying to use statsmodels' ARIMA to forecast a time series. I'm using sklearn's TimeSeriesSplit to evaluate my models. Unfortunately, when I forecast the next fold of data (which has true value Y_test ), I get a constant prediction:

if is_arima:
      Y_train = Y_train.astype(float)
      # build basic ARIMA model
      arima_model = ARIMA(Y_train, order=(2,0,1))
      # fit it, using exogenous variables
      arima_results = arima_model.fit()
      # predict next len(test) values, using exogenous variables (X_test)
      preds = arima_results.forecast(steps=len(Y_test))[0]
      print(preds)

Which gives me:

115.65096239  120.89113477  121.52020239  121.59572014  121.60478583
  121.60587414  121.60600479  121.60602047  121.60602235  121.60602258
  121.6060226   121.60602261  121.60602261  121.60602261  121.60602261
  121.60602261  121.60602261  121.6060226   121.6060226   121.6060226
  121.6060226   121.6060226   121.6060226   121.6060226   121.6060226
  121.6060226   121.6060226   121.6060226   121.6060226   121.6060226...

This makes me think my ARIMA isn't using the prediction at time t for its prediction at time t+1?

I understand the output isn't perfectly constant but my dataset shows large variation, so this is mildly concerning. Any idea what's going on?

Thanks!

Answer 1

Your using ARIMA(2,0,1), so your prediction is

x(t) = constant + w(t) + a1 * x(t-1) + a2 * x(t-2) + b1 * w(t-1)

So, your prediction depends on 2 factors. You have your autoregressive terms and your moving average term. Your autoregressive terms are just a constant times the prior period's value plus a different constant times the value 2 periods ago. Then you have a moving average term, which is a constant times the error from the prior period's prediction. So your model is probably mostly dominated by the prior 2 periods, and that it probably finds an equilibrium rather quickly.

Try printing out the parameters and then plugging it into excel to see what is happening in the model.

print(arima_model.summary())
print(arima_model.params)

Answer 2

You are making use of recursive strategy to do multi step prediction ie forecasts generated in the prior steps are used for the prediction of next forecasts iteratively. It leads to error accumulation and as a result forecasting converges to a value. Arima does not perform well for very long data series.