Time Series Analysis Based on Exponential Model Excited by t-Distribution Process and Its Algorithm

Junibakti SANUBARI  Keiichi TOKUDA  Mahoki ONODA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.5   pp.808-819
Publication Date: 1993/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
exponential model,  t-distribution,  M-estimate,  time series analysis,  finite-length cepstrum,  

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In this paper, a new time series analysis method is proposed. The proposed method uses the exponential (EXP) model. The residual signal is assumed to be identically and independently distributed (IID). To achieve accurate and efficient estimates, the parameter of the system model is calculated by maximizing the logarithm of the likelihood of the residual signal which is assumed to be IID t-distribution. The EXP model theoretically assures the stability of the system. This model is appropriate for analyzing signals which have not only poles, but also poles and zeroes. The asymptotic efficiency of the EXP model is addressed. The optimal solution is calculated by the Newton-Raphson iteration method. Simulation results show that only a small number of iterations are necessary to reach stationary points which are always local minimum points. When the method is used to estimate the spectrum of synthetic signals, by using small α we can achieve a more accurate and efficient estimate than that with large α. To reduce the calculation burden an alternative algorithm is also proposed. In this algorithm, the estimated parameter is updated in every sampling instant using an imperfect, short-term, gradient method which is similar to the LMS algorithm.