Prediction intervals for ARMA.predict

Question

The Summary of an ARMA prediction for time series (print arma_mod.summary()) shows some numbers about the confidence interval. Is it possible to use these numbers as prediction intervals in the plot which shows predicted values?

ax = indexed_df.ix[:].plot(figsize=(12,8))
ax = predict_price.plot(ax=ax, style='rx', label='Dynamic Prediction');
ax.legend(); 

I guess the code:

from statsmodels.sandbox.regression.predstd import wls_prediction_std
prstd, iv_l, iv_u = wls_prediction_std(results)

found here: Confidence intervals for model prediction

...does not apply here as it is made for OLS rather then for ARMA forecasting. I also checked github but did not find any new stuff which might relate to time series prediction.

(Making forecasts requires forecasting intervals i guess, especially when it comes to an out-of sample forecast.)

Help appreciated.

Farhi

Answer 1

I suppose, for out-of-sample ARMA prediction, you can use ARMA.forecast from statsmodels.tsa

It returns three arrays: predicted values, standard error and confidence interval for the prediction.

Example with ARMA(1,1), time series y and prediction 1 step ahead:

import statsmodels as sm
arma_res = sm.tsa.ARMA(y, order=(1,1)).fit()
preds, stderr, ci = arma_res.forecast(1)

Extract

Looks like that method is available for ARIMA models as well. statsmodels.sourceforge.net/devel/generated/… – Redistrict

Does anyone have any resources of how they calculate the confidence interval? Is it simply using the standard deviation of the data? – Redistrict

import statsmodels.api as sm instead of import statsmodels as sm – Shornick