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ARMA–GARCH 模型误差零中位数检验AI 解读

Because the ARMA–GARCH model can generate data with some important properties such as skewness, heavy tails, and volatility persistence, it has become a benchmark model in analyzing financial and economic data. The commonly employed quasi maximum likelihood estimation (QMLE) requires a finite fourth moment for both errors and the sequence itself to ensure a normal limit. The self-weighted quasi maximum exponential likelihood estimation (SWQMELE) reduces the moment…

重尾 G-GARCH(1,1) 噪声下自回归模型的 LAD 推断AI 解读

This paper explores the least absolute deviation (LAD) estimator of the autoregressive model with heavy-tailed G-GARCH(1, 1) noise. When the tail index α∈(1,2], it is shown that the LAD estimator asymptotically converges to a linear function of a series of α-stable random vectors with a rate of convergence n1−1/α. The result is significantly different from that of the corresponding least square estimator which is not consistent, and partially solves the problem on the…

门限双重自回归模型的检验与估计AI 解读

This article first proposes a score-based test for a double autoregressive model against a threshold double autoregressive (AR) model. It is an asymptotically distribution-free test and is easy to implement in practice. The article further studies the quasi-maximum likelihood estimation of a threshold double autoregressive model. It is shown that the estimated threshold is n-consistent and converges weakly to a functional of a two-sided compound Poisson process and the…

含厚尾 G-GARCH 噪声的自回归模型渐近推断AI 解读

It is well known that the least squares estimator (LSE) of an AR( p ) model with i.i.d. (independent and identically distributed) noises is n 1/ α L ( n )-consistent when the tail index α of the noise is within (0,2) and is n 1/2 -consistent when α ≥ 2, where L ( n ) is a slowly varying function. When the noises are not i.i.d., however, the case is far from clear. This paper studies the LSE of AR( p ) models with heavy-tailed G-GARCH(1,1) noises. When the tail index α of…