Recursive ARIMA

Question

I am trying to implement recursive ARIMA that would just update the parameters with new data point, rather than re-estimate them from scratch, without taking into account the previous model. What I have in mind was proposed in:

A. K. Rao, Y. -. Huang and S. Dasgupta, "ARMA parameter estimation using a novel recursive estimation algorithm with selective updating," in IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 3, pp. 447-457, March 1990, doi: 10.1109/29.106863

However, I have difficulties finding in the recent papers that anyone is using a similar approach and how is it performed. I would be grateful to hear from someone who might have tried something like that or some reference. With increase of the data by adding new data points, execution of reestimation on the whole set increases. That is the main reason why I would aim for parameters update, rather than reestimation.

Answer 1

I have managed to implement this through Kalman filter, with the help from GitHub:

SARIMAX: incremental Kalman filter (question)

Basically, with initial parameters and covariance of the initial model:

        mod_test = ARIMA(X[t:t+1],order=best_cfg,exog=Xtemp[t:t+1])
        mod_test.ssm.initialize_known(model_fit.predicted_state[..., -1],
                                      model_fit.predicted_state_cov[..., -1])
        model_fit = mod_test.filter(params_training)
        params_training = model_fit.params

There is also extend function, however, I am not sure if it works the same. My results of forecast MSE for rolling window validation of 1300+ records show the negligible difference:

model_fit = model_fit.extend(X[t:t+1])