EMPIRICAL CHARACTERISTIC FUNCTION IN TIME SERIES ESTIMATION
EMPIRICAL CHARACTERISTIC FUNCTION IN TIME SERIES ESTIMATION
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DOI：
10.1017/s026646660218306x
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发表时间：
2001-04
影响因子：
0.8
通讯作者：
J. Knight;Jun Yu
中科院分区：
文献类型：
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作者：
J. Knight;Jun Yu
由于经验特征函数（ECF）是经验分布函数的傅里叶变换，它保留了样本中的所有信息，但可以克服似然引起的困难。本文讨论了一种严格平稳过程的ECF估计方法。在一定的正则性条件下，得到的估计量是一致的和渐近正态的。将该方法应用于稳定自回归移动平均（ARMA）模型的估计。对于最大似然方法不可行的一般稳定ARMA模型，蒙特卡洛证据表明，ECF方法对于所有感兴趣的参数都是可行的估计方法。对于高斯ARMA模型和特定稳定ARMA模型，给出了最优权函数和估计方程。蒙特卡罗研究突出了ECF方法相对于精确和条件极大似然方法的有限样本性能。
Because the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. The method is applied to estimate the stable autoregressive moving average (ARMA) models. For the general stable ARMA model for which the maximum likelihood approach is not feasible, Monte Carlo evidence shows that the ECF method is a viable estimation method for all the parameters of interest. For the Gaussian ARMA model, a particular stable ARMA model, the optimal weight functions and estimating equations are given. Monte Carlo studies highlight the finite sample performances of the ECF method relative to the exact and conditional maximum likelihood methods.