Causes of Rank Deficiency when Fitting GARCH models

Question

Danny 2014-9-20

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https://ww2.mathworks.cn/matlabcentral/answers/155575-causes-of-rank-deficiency-when-fitting-garch-models

回答： Yufei Cao 2021-3-26

I am fitting an ARIMA(1,1,1) model with GARCH(P,Q) variance to a time series. I use two for loops to iterate though P = 0:3 and Q = 1:3 (12 total models). A few times I get a warning that the matrix is rank deficient. I was wondering what implications this has for the fitted model that returned this error (is one of the values of P or Q zero?). Also, when comparing the fitted models (using the Bayesian Information Criteria), is a rank deficient model more or less likely to be chosen or will it in some way cause problems with the comparison? TH=he error message is below. Thank you.

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In arch0 at 57 In garch.estimate at 698 In arima.estimate>nLogLike at 1549 In arima.estimate>@(X)nLogLike(X,YData,XData,E,V,Mdl,AR.Lags,MA.Lags,maxPQ,T,isDistributionT,options,userSpecifiedY0,userSpecifiedE0,userSpecifiedV0,trapValue) at 961 In C:\Program Files\MATLAB\R2014a\toolbox\optim\optim\private\evalObjAndConstr.p>evalObjAndConstr at 134 In C:\Program Files\MATLAB\R2014a\toolbox\optim\optim\private\backtrackLineSearch.p>backtrackLineSearch at 74 In C:\Program Files\MATLAB\R2014a\toolbox\optim\optim\sqpLineSearch.p>sqpLineSearch at 305 In fmincon at 828