Minimum Distance Estimation of Possibly Non-Invertible Moving Average Models

32 Pages Posted: 22 Mar 2015

See all articles by Nikolay Gospodinov

Nikolay Gospodinov

Federal Reserve Bank of Atlanta

Serena Ng

Columbia Business School - Economics Department

Date Written: November 2013


This paper considers estimation of moving average (MA) models with non-Gaussian errors. Information in higher-order cumulants allows identification of the parameters without imposing invertibility. By allowing for an unbounded parameter space, the generalized method of moments estimator of the MA(1) model has classical (root-T and asymptotic normal) properties when the moving average root is inside, outside, and on the unit circle. For more general models where the dependence of the cumulants on the model parameters is analytically intractable, we consider simulation-based estimators with two features that distinguish them from the existing work in the literature. First, identification now requires information from the second and higher-order moments of the data. Thus, in addition to an autoregressive model, new auxiliary regressions need to be considered. Second, the errors used to simulate the model are drawn from a flexible functional form to accommodate a large class of distributions with non-Gaussian features. The proposed simulation estimators are also asymptotically normally distributed without imposing the assumption of invertibility. In the application considered, there is overwhelming evidence of non-invertibility in the Fama-French portfolio returns.

Keywords: GMM, simulation-based estimation, non-invertibility, identification, non-Gaussian errors, generalized lambda distribution

JEL Classification: C13, C15, C22

Suggested Citation

Gospodinov, Nikolay and Ng, Serena, Minimum Distance Estimation of Possibly Non-Invertible Moving Average Models (November 2013). FRB Atlanta Working Paper No. 2013-11. Available at SSRN: or

Nikolay Gospodinov (Contact Author)

Federal Reserve Bank of Atlanta ( email )

Atlanta, GA 30309
United States


Serena Ng

Columbia Business School - Economics Department ( email )

420 West 118th Street
New York, NY 10027
United States

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