Solved – ARIMA real time predictions

arimaforecastingtime series

I have trained ARIMA model in Python (concretely SARIMAX, as I need seasonal ARIMA). That gives me a model which I can use to forecast one or multiple future values.

What would be the correct procedure to create real time predictions? Should I:

retrain ARIMA model each time a new value occurs and forecast one value
retrain ARIMA model after N moments and predict values for next N moments
something else?

Also, if I retrain model should I:

use all previous values
use last N values

If I should use only last N values how to determine size of N?

I'm familiar with concept that you generate a model periodically (but not too often) and use that model on real time values to predict the dependent variable, but in case of time series it seems that retraining a model is needed more often to get better predictions.

Best Answer

If you need only one-step-ahead forecasts, then calculate these forecasts and retrain each time you see new observations. Use all historical data. There is no reason not to use all data. (Using only the last $N$ observations truncates the distant past, not using the most recent observations truncates the recent past.)

Of course, if you need $h$-step-ahead predictions, your latest prediction will only be based on a model with observations $h$ periods old. You should still refit your model each time you get new data.

Of course, if you are constrained by computing capacity, it makes sense to weigh this advice against the small improvement it gets you, and you might choose only to update every $k$ periods. Similarly, if your forecast consumer is unhappy if the forecast changes appreciably every period, e.g., because different ARIMA models are selected today and yesterday (a change in the order of integration will be most visible). Here, a tradeoff between accuracy and acceptance might mean that you only refit every $k$ periods. Or that you indeed refit the parameters, but only allow the model to be changed every $k$ periods.

If your time series had a structural change in the past, it may make sense to start the history only after that, because ARIMA is not good at dealing with those. Alternatively, you could work with dummy regressors to capture the structural change using ARIMAX or regression with ARIMA errors.

Related Solutions

Solved – Initialize ARIMA simulations with different time-series

You can "fit" the model to different data and then simulate:

m2 <- Arima(z,model=m1)
simulate.Arima(m2,future=TRUE,bootstrap=TRUE)

m2 will have the same parameters as m1 (they are not re-estimated), but the residuals, etc., are computed on the new data.

However, I am concerned with your model. Seasonal models are for when the seasonality is fixed and known. With animal population data, you almost certainly have aperiodic population cycling. This is a well-known phenomenon and can easily be handled with non-seasonal ARIMA models. Look at the literature on the Canadian lynx data for discussion.

By all means, use the square root, but then I would use a non-seasonal ARIMA model. Provided the AR order is greater than 1, it is possible to have cycles. See

You can do all this in one step:

m1 <- auto.arima(y, lambda=0.5)

Then proceed with your simulations as above.

Solved – ARIMA continuous forecasting

ARIMA models are univariate so the only information they use is the history of the series. Essentially, they tell you how the variable will react to previous stochastic variation. When you start forecasting with them you no longer have any 'noise' in them because your model will not add in error terms (and nor should it). So what you'll see is that the forecast will quickly decay to the constant term/trend in your ARIMA model. Re-estimating the model won't help because you're not adding any new information about the underlying process.

Over 180+ forecast periods you'll need to add in more explanatory variables to get anything more than a trend line out of your model. For instance, you might include macroeconomic projections as an input, which would give you some dynamics over a 6 month period.

Update: If you are going for in-sample predictive power then using all the data will give you a better fit, so yes it will improve. The underlying question is what you want to achieve. If you're trying to understand the causative factors explaining the dependent variable then a few extra observations aren't going to overturn your theoretical priors. If you want forecasting power then you want to use as much data as possible to estimate your model. Of course you need to be wary of overfitting, which I guess is why you want to check the estimation against a sub-sampled model. If you're seeing a lot of change in your coefficients as you increase the sample size and they don't stabilise that's indicating your model's mis-specified.

Best Answer

Related Solutions

Solved – Initialize ARIMA simulations with different time-series

Solved – ARIMA continuous forecasting

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