Forecasting one-step predictions from an ARMA model with continuously added data

I want to forecast one-step predictions of stock returns using MATLAB where new data is continuously added for the data points I am forecasting. For example, after having predicted the january 2010 return, I wish to enter the actual return of january 2010 before trying to predict the february 2010 return. The forecast function in MATLAB does this (https://se.mathworks.com/help/ident/ref/forecast.html), however it seems that when applied to ARIMA models it does not (https://se.mathworks.com/help/econ/arima.forecast.html). I realize that it could be done by using estimate on my data to get the suitable ARMA model, use forecast to get the the one-step prediction, then add the new data point to my data and use estimate again to get the new suitable model and use that model to forecast the next months value but it does not seem like the optimal way to do it. Anyone got any ideas?

Thanks

Answer 1

[Anoop Somashekar]

The current workflow that you have mentioned is correct. To make it more efficient, you could rewrite the model in the state-space form, the new observations would be absorbed sequentially by the Kalman filter i.e. the Kalman filter first makes a one-step forecast, and then use the incoming observation to update the state distribution. The second observation is added in the same manner.

Attached is a simple example of incorporating new observations to ARIMA model for forecasting one-step predictions.