CODEWITHSUNDEEP
pythonstatsmodelsarima
randomwalker
randomwalker

Reputation: 303

ARIMA: forecasting next steps without updating model

I would like to forecast a time series as in this example, with an ARIMA of order p=2.

from statsmodels.tsa.arima.model import ARIMA
model = ARIMA(series, order=(2,0,0))
fit = model.fit()

forecast = fit.forecast()[0]

This code fit.forecast()[0] gives the forecast for the next one step, given the last two steps in the series series . If I use fit.forecast()[0:n] it will give the forecast for the next n steps. We have a series from time 0 to time t and the function forecast the next n steps (t+1, t+2...t+n). Since this is an ARIMA with p=2, every step is forecasted by using the last 2 steps as predictors. With this method, however, the last 2 step are actually the past forecasted values...

I would like to do a different thing. I would like to forecast each step (t+1, t+2...t+n) given the past actual values, not forecasted values. And more importantly, I don't want to update the model at every step, i.e. the regression coefficient should be always the same (the ones found by fitting in the range 0 to t)

Upvotes: 2

Views: 1497

Answers (1)

cfulton
cfulton

Reputation: 3195

You are probably looking for details on how to perform an expanding window cross-validation exercise. Details can be found in the notebook https://www.statsmodels.org/devel/examples/notebooks/generated/statespace_forecasting.html and in particular in the "Cross Validation" section.

In brief, you want to do something like:

from statsmodels.tsa.arima.model import ARIMA

# Split data into test and training
nobs = len(series)
n_train = ...
series_train = series.iloc[:n_train]

# Fit the model using the training dataset
model = ARIMA(series_train, order=(2,0,0))
fit = model.fit()

# Compute the first forecast based only on the training dataset
forecasts = []
res = fit
forecasts.append(res.forecast())

# Now step through the test observations:
# (a) add the new observation without refitting the model
# (b) produce a new forecast
for t in range(n_train, nobs):
    # Update the results by appending the next observation
    res = res.append(series.iloc[t:t + 1], refit=False)
    
    # Produce a forecast for t+1 based on data through t
    forecasts.append(res.forecast())

Upvotes: 3

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