Predict function from system identification toolbox, which algorithm is it?

Hi,

Using System Identification Toolbox I have generated an ARMAX polynomial model. I want to use this to predict a state and compare them to some measurements in order to generate residuals. I found the predict function and it seems like it does what I want.

I have two questions:

Which method does the predict function use to predict?

How do I know that I'm using the correct predict function? I found a lot of others, and they're all called just predict. (I'm coming from python, so this is a bit confusing for me)

Answer 1

[Star Strider]

The documentation does not go into any details as to how it works.

Aniother function that could be worth considreing is the forecast function.

To see how well the estimated system fits the data, use the compare function. I would do that first, to be certain that the identified system is appropriate.

[Julian Jørn]

Thanks. I can't quite understand the difference between the forecast and the predict function. My goal is to predict a state for T time steps into the future using inputs the whole time. This should be done using an ARMAX- model. I also want to use the last measurements before the prediction as initial values for the prediction. Which function best suits this purpose?

[Star Strider]

As always, my pleasure!

The forecast function is different from the predict function.

I would use forecast, because from the documentation:

• yf = forecast(sys,PastData,K) forecasts the output of an identified time series model sys, K steps into the future using past measured data, PastData.
• forecast performs prediction into the future, in a time range beyond the last instant of measured data. In contrast, the predict command predicts the response of an identified model over the time span of measured data. Use predict to determine if the predicted result matches the observed response of an estimated model. If sys is a good prediction model, consider using it with forecast.

The documentation does not go into any detail as to how it works, however Introduction to Forecasting of Dynamic System Response suggests to me that it does exactly what you want.

I’m learning from this as well. While I always use compare to see how the Bode plots of the estimated system fit the data in the frequency domain, the predict function apparently does the same in the time domain. The forecast function extends this into the future beyond the measured data used for the initial identification to additional time-domain results. (This is my impression from reading the documentation. I intend to explore these.)

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[Julian Jørn]

Thanks a lot! So if I understand correctly, both forecast and predict use the input, but predict also utilizes the measurements of the output too?

[Star Strider]

As always, my pleasure!

The way I read it, both do.

The difference is summarised (more or less) in the description of the outputs.

• The predict function (see yp) gives the extrapolated output to new values of the extrapolated input.
• The forecast function (see yf) extrapolates the outputs on the basis of known inputs.

Both return iddata objects.

I wish the documentation specifically discussed the differences, and in more detail.

[Julian Jørn]

Thanks! This has been helpful.

[Star Strider]

As always, my pleasure!

I have requested MathWorks to help clarify the differences between the two funcitons. I will post back if their reply is at variance with what I have written here. I also requested a new documentation page about the differences and in the different applicatioons each would be best to use.

[Julian Jørn]

That's nice!

[Star Strider]

Thank you!

EDIT — (13 Apr 2022 at 19:36)

It turns out that my interpretation is correct.

MathWorks reply (in part):

• However, their main difference can be found on the documentation page itself. In the 'forecast' function documentation page Forecast identified model output - MATLAB forecast (mathworks.com), you can see under the Description: 'forecast performs prediction into the future, in a time range beyond the last instant of measured data. In contrast, the predict command predicts the response of an identified model over the time span of measured data. Use predict to determine if the predicted result matches the observed response of an estimated model. If sys is a good prediction model, consider using it with forecast'. This can be illustrated in the plots from the examples Forecast identified model output - MATLAB forecast (mathworks.com) using 'forecast' function and Predict K-step-ahead model output - MATLAB predict (mathworks.com) using 'predict' function.

So predict is the time-domain equivalent of compare, and forecast extends the model response to future values of the independent variable.