Bayesian analysis of contaminated quarter plane moving average models

• Published in: Journal of statistical computation and simulation 2006-02, Vol.76 (2), p.131-147
• Main Authors: Vallejos, Ronny O., García-Donato, Gonzalo
• Format: Article
• Language: English
• Subjects: Additive outlier; CMA model; Correlation function; Exact sciences and technology; MA model; Mathematics; Multivariate analysis; Nonparametric inference; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Posterior sensitivity; Probability and statistics; Sciences and techniques of general use; Statistics
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949650412331321133

This article deals with Bayesian analysis of quarter plane moving average (MA) models observed on a rectangular part of a lattice. We present some properties concerning the autocorrelation function of MA models. These properties relate correlation parameters with the original model parameters providing much more understandable interpretation of results concerning the model. Simulation experiment is developed to explore the sensitivity of the posterior distribution when the process is contaminated with innovation and additive contamination. We show by simulation that the correlation structure of the model is seriously affected when the process contains additive contamination. We then propose a more general class of MA models which automatically deals with the contamination phenomenon [contaminated MA (CMA) model]. Also, we establish theoretical properties of the correlation function analogous with those in the previous model. Finally, we consider two applications of the CMA model. The results obtained in numerical examples show the goodness of the CMA model under contaminated data.