Asymptotic inference of the ARMA model with time‐functional variance noises
研究了带时变方差噪声的ARMA模型，证明了最小二乘估计的相合性和渐近正态性，并构建了Wald检验和Portmanteau检验，通过模拟和实例验证了方法。
Abstract This paper studies the autoregressive and moving average (ARMA) model with time‐functional variance (TFV) noises, called the ARMA‐TFV model. We first establish the consistency and asymptotic normality of its least squares estimator (LSE). The Wald tests and portmanteau tests are constructed based on the theory for variable selection and model checking. A simulation study is carried out to assess the performance of our approach in finite samples, and two real examples are given. It should be mentioned that the process generated from the ARMA‐TFV model is not stationary, and the technique in this paper is nonstandard and may provide insights for future research in this area.