An approximate maximum likelihood estimation for non-Gaussian non-minimum phase moving average processes

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...

Exact Maximum Likelihood Estimation for Non-Gaussian Non-invertible Moving Averages

A procedure for solving exact maximum likelihood estimation (MLE) is proposed for non-invertible non-Gaussian MA processes. By augmenting certain latent variables, the exact likelihood of all relevant innovations can be expressed explicitly according to a set of recursions (Breidt and Hsu, 2005). Then, the exact MLE is solved numerically by EM algorithm. Two alternative estimators are proposed ...

Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models

Minimum Distance Estimation of Possibly Non-Invertible Moving Average Models

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 in...

Empirical Likelihood Approach for Non-Gaussian Vector Stationary Processes and Its Application to Minimum Contrast Estimation

A. For a class of vector-valued non-Gaussian stationary processes with unknown parameters, we develop the empirical likelihood approach. In time series analysis it is known that Whittle likelihood is one of the most fundamental tools to get a good estimator of unknown parameters, and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we apply the emp...