An Estimation of Nonlinear Time Series with ARCH errors using ECLMS algorithm

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  • ECLMSアルゴリズムを用いたARCH誤差項を有する非線形時系列の推定法
  • ECLMS アルゴリズム オ モチイタ ARCH ゴサコウ オ ユウスル ヒセンケイ ジケイレツ ノ スイテイホウ

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Abstract

Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroskedasticity (ARCH) processes were introduced in Engle (1982). This type of model behavior has already proven useful in modeling several different economic phenomena. In those papers, maximum likelihood estimation of the linear regression model with ARCH error was discussed. However, it is well known that there exists the nonlinearity in economic time series by empirical research. Recently, the extended correlation least mean squares (ECLMS) algorithm has been proposed to solve the double-talk problem in the echo canceling system. The characteristic of ECLMS algorithm is to utilize the correlation functions of the input signal instead of the input signal itself, to process and find the parameters of system. Noise signal is separated from observed signal by ECLMS algorithm. Therefore, the estimation performance is considerably improved. Parameters in nonlinear time series are calculated by ECLMS algorithms. We demonstrate that it is feasible to esti-mate second-order Volterra model with ARCH error by ECLMS algorithm and some numerical examples are presented to illustrate that the proposed method can work well for noisy signal using computer simulation.

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