In statsmodels, for the SARIMAX or ARIMA model, I would like to use more than one additional external variable (exogenous variables). E.g. I want to predict yield at time t using AR of lag 3 for the yield time series and AR of lag 4 with weather temperature time series and another variable of market price with AR of lag 3. It doesn't appear possible? Any examples or explanation of how this can be done?
1 Answer
First of all you have to define your exogenous input as an array-type structure with dimensions nobsxk where nobs is the number of your endogenous observations (i.e. supposing that you have a time series, the length of your time series) and k the number of your additional exogenous variables. Supposing that you use a ndarray for this purpose you may begin with something like
exog = np.empty([nobs, k]) and then fill it with the values of your exogenous variables. Then, you define your model as in the following example:
model = sm.tsa.SARIMAX(endog=series, exog=exog, order=order, seasonal_order=seasonal_order).fit(start_params=[0, 0, 0, 0, 0, 1]) where series is your original time series, exog the exogenous input, order a (p,d,q) tuple and seasonal_order a (P,D,Q,s) tuple. You should pay attention to the start_params list which I found essential for successfully building the sarimax model in my case.
When I did not use any exogenous input, the start_params list was start_params = [0, 0, 0, 1] for (p,d,q) = (1,0,0) and (P,D,Q,s) = (1,0,0,37).
When I added 3 new exogenous inputs, I set the start_params list to start_params = [0, 0, 0, 0, 1, 1] which if you notice has 2 additional elements.
I suppose (I do not know for sure neither checked it thoroughly) that if you add k exogenous inputs in your model you have to add k - 1 additional elements in your start_params list in order to build the sarimax model successfully.
Hope it helps. Cheers.
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