No feasible solution in seasonal ARIMA process

Hello everyone!

I created a seasonal ARIMA process and when I run it, I get the following output/warning. It says no feasible solution can be found... Does anyone know how to get rid of this problem?

.......

__________________________________________________________ End diagnostic information

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in feasible directions, to within the selected value of the function tolerance, and constraints are satisfied to within the selected value of the constraint tolerance.

criteria details

Warning: Nonlinear inequality constraints are active; standard errors may be inaccurate. > In arima.estimate at 1018 In austesten_sarima at 40

    ARIMA(3,1,2) Model Seasonally Integrated with Seasonal AR(3) and MA(2):
    --------------------------------------------------------------------------
    Conditional Probability Distribution: Gaussian

                                  Standard          t     
     Parameter       Value          Error       Statistic 
    -----------   -----------   ------------   -----------
     Constant              0         Fixed          Fixed
        AR{1}       0.863241     0.0692327        12.4687
        AR{2}      -0.171672     0.0765376       -2.24298
        AR{3}       0.115093     0.0421485        2.73065
       SAR{1}       0.857417      0.564547        1.51877
       SAR{2}       0.292977      0.575573       0.509018
       SAR{3}      -0.192652      0.210905      -0.913454
        MA{1}      -0.409755      0.297717       -1.37632
        MA{2}      -0.580543      0.295877       -1.96211
       SMA{1}       -1.35118      0.423402       -3.19126
       SMA{2}       0.351184       0.42345        0.82934
     Variance       0.822403    0.00364983        225.326

__________________________________________________________ Diagnostic Information

Number of variables: 12

Functions Objective: @(X)nLogLike(X,YData,XData,E,V,OBJ,AR.Lags,MA.Lags,maxPQ,T,isDistributionT,options,userSpecifiedY0,userSpecifiedE0,userSpecifiedV0,trapValue) Gradient: finite-differencing Hessian: finite-differencing (or Quasi-Newton) Nonlinear constraints: @(x)nonLinearConstraints(x,LagsAR,LagsSAR,LagsMA,LagsSMA,tolerance) Nonlinear constraints gradient: finite-differencing

Constraints Number of nonlinear inequality constraints: 4 Number of nonlinear equality constraints: 0

Number of linear inequality constraints: 0 Number of linear equality constraints: 1 Number of lower bound constraints: 12 Number of upper bound constraints: 12

Algorithm selected sequential quadratic programming

__________________________________________________________ End diagnostic information

No feasible solution found.

fmincon stopped because the size of the current step is less than the default value of the step size tolerance but constraints are not satisfied to within the selected value of the constraint tolerance.

criteria details

Warning: Nonlinear inequality constraints are active; standard errors may be inaccurate. > In arima.estimate at 1018 In austesten_sarima at 40 Error using arima/validateModel (line 1298) The non-seasonal moving average polynomial is non-invertible.

Error in arima/setLagOp (line 401) OBJ = validateModel(OBJ);

Error in arima/estimate (line 1088) OBJ = setLagOp(OBJ, 'MA' , LagOp([1 coefficients(iMA)' ], 'Lags', [0 LagsMA ]));

Error in austesten_sarima (line 40) [fit,EstParamCov,LogL,info] = estimate(model,Y,'options',options);

Answer 1

[Matt J]

It says in the documentation that the 'MA' parameter must be a "cell vector of nonseasonal moving average coefficients corresponding to an invertible polynomial."

However, one of your error messages says

 In austesten_sarima at 40 Error using arima/validateModel (line 1298) The non-seasonal moving average polynomial is non-invertible.

[MC3105]

I know that this is a problem.. although my question is: How can I solve it? How can I assure that my SMA polynomial is non-invertible.

The funny thing is, that this does not happen at every run-through, but only for certain input data (it's a sliding window prediction).

[Matt J]

Not sure, but it's not really a MATLAB issue. It's an issue in the theory of ARIMA and how you've chosen your model parameters. However, Rule 10 in this document might help,

http://people.duke.edu/~rnau/411arim3.htm