Two step ahead autoregressive prediction

Is it possible to use the AR function in Matlab to train models such as:

y(t+2)=a(1)u(t-1)+a(2)u(t-2)+...+a(p)u(t-p)

rather than:

y(t+1)=a(1)u(t-1)+a(2)u(t-2)+...+a(p)u(t-p)

I want to avoid predicting y(t+2) using y(t+1).

Many thanks

[Ganesh]

Hi @Elias Pergantis,

If you would like to predict y(t+2), you can use the Nonconsecutive Lags parameter and tweak the array indices to achieve the result. However, by skipping a term in the middle might stand as a blocker to predict the subsequent terms of the sequence. Kindly ensure that all terms of the sequence are sequentially computed to avoid miscalculations.

Thank you,

Ganesh Saravanan

Answer 1

[Divyam]

Hi @Elias Pergantis, yes, you can utilize the AR functions to train models which have non-consecutive lags between terms using the 'ARLag' parameter of the 'regARIMA' function. Here is a sample code for the same.

% Sample Model Equation: y(t) = 0.25*u(t-3) + 0.1*u(t-4) + 0.05*u(t-5) 

% The 'AR' parameter sets the coefficients of the u(t-k) terms 
Mdl = regARIMA('AR', {0.25, 0.1, 0.05}, 'ARLags', [3,4,5]) 

Mdl = 
  regARIMA with properties:

     Description: "ARMA(5,0) Error Model (Gaussian Distribution)"
      SeriesName: "Y"
    Distribution: Name = "Gaussian"
       Intercept: NaN
            Beta: [1×0]
               P: 5
               Q: 0
              AR: {0.25 0.1 0.05} at lags [3 4 5]
             SAR: {}
              MA: {}
             SMA: {}
        Variance: NaN

% 'ARLag' parameter specifies that nonzero AR coefficients exist at lags t-3, t-4, and t-5  
Mdl.AR 

ans = 1x5 cell array
    {[0]}    {[0]}    {[0.2500]}    {[0.1000]}    {[0.0500]}

For more information regarding how to model AR models with Nonconsecutive Lags, you can refer to this documentation: https://www.mathworks.com/help/econ/specification-for-regression-models-with-ar-errors.html#:~:text=using%20dot%20notation.-,AR%20Error%20Model%20with%20Nonconsecutive%20Lags,-Try%20This%20Example