Structure of Wavelet Covariance Matrices and Bayesian Wavelet Estimation of Autoregressive Moving Average Model with Long Memory Parameter’s

In the process of exploring and recognizing of statistical communities, the analysis of data obtained from these communities is considered essential. One of appropriate methods for data analysis is the structural study of the function fitting by these data. Wavelet transformation is one of the most powerful tool in analysis of these functions and structure of wavelet coefficients are very important. In this paper, we discuss in detail wavelet transformation and Autoregressive moving average model with long memory. The structure of covariance matrices of wavelet coefficients and Bayesian wavelet estimation of parameters are investigated.  At the end ‎We use R software for simulation in order to perform applications and test validity of this model. It is shown that this estimation has better performance than the others.