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矩阵 GARCH 模型：推断与应用AI 解读

Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use…

基于条件分位数变分自编码器的资产定价AI 解读

We propose a new asset pricing model that is applicable to the big panel of return data. The main idea of this model is to learn the conditional distribution of the return, which is approximated by a step distribution function constructed from conditional quantiles of the return. To study conditional quantiles of the return, we propose a new conditional quantile variational autoencoder (CQVAE) network. The CQVAE network specifies a factor structure for conditional quantiles…

广义指数加权移动平均分位数模型及其统计推断AI 解读

The exponentially weighting scheme is a simple and pragmatic approach to compute the value at risk (VaR). However, the existing exponentially weighting methods lack a sound statistical inference procedure. To circumvent this deficiency, this paper proposes a new generalized exponentially weighted moving average (GEWMA) quantile model, which allows a much broader weighting scheme than the benchmark one used in “Risk Metrics” document. For the GEWMA quantile model, a…

非对称幂 GARCH 模型的混合分位数估计AI 解读

Asymmetric power GARCH models have been widely used to study the higher order moments of financial returns, while their quantile estimation has been rarely investigated. This paper introduces a simple monotonic transformation on its conditional quantile function to make the quantile regression tractable. The asymptotic normality of the resulting quantile estimators is established under either stationarity or non-stationarity. Moreover, based on the estimation procedure, new…

半参数 GARCH 模型的自适应推断AI 解读

This paper considers a semiparametric generalized autoregressive conditional heteroskedasticity (S-GARCH) model. For this model, we first estimate the time-varying long run component for unconditional variance by the kernel estimator, and then estimate the non-time-varying parameters in GARCH-type short run component by the quasi maximum likelihood estimator (QMLE). We show that the QMLE is asymptotically normal with the parametric convergence rate. Next, we construct a…

ZD-GARCH 模型：研究异方差的新方法AI 解读

This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH model, the ZD-GARCH(1, 1) model is always non-stationary regardless of the sign of the Lyapunov exponent γ0, but interestingly it is stable with its sample path oscillating randomly between zero and infinity over time when γ0=0. Furthermore, this paper studies the generalized quasi-maximum likelihood…

含条件异方差的缓冲自回归模型：汇率应用AI 解读

This article introduces a new model called the buffered autoregressive model with generalized autoregressive conditional heteroscedasticity (BAR-GARCH). The proposed model, as an extension of the BAR model in Li et al. (2015), can capture the buffering phenomena of time series in both the conditional mean and variance. Thus, it provides us a new way to study the nonlinearity of time series. Compared with the existing AR-GARCH and threshold AR-GARCH models, an application to…

弱 ARMA 模型综合相关性检验的 Bootstrap 方法AI 解读

Summary The paper uses a random-weighting (RW) method to bootstrap the critical values for the Ljung–Box or Monti portmanteau tests and weighted Ljung–Box or Monti portmanteau tests in weak auto-regressive moving average models. Unlike the existing methods, no user-chosen parameter is needed to implement the RW method. As an application, these four tests are used to check the model adequacy in power generalized auto-regressive conditional heteroscedasticity models.…

重尾创新 ARCH 类模型的符号综合诊断检验AI 解读

This paper proposes a sign-based portmanteau test for diagnostic checking of ARCH-type models estimated by the least absolute deviation approach. Under the strict stationarity condition, the asymptotic distribution is obtained. The new test is applicable for very heavy-tailed innovations with only finite fractional moments. Simulations are undertaken to assess the performance of the sign-based test, as well as a comparison with other two portmanteau tests. A real empirical…

条件异方差模型的新型皮尔逊准极大似然估计AI 解读

This article proposes a novel Pearson-type quasi-maximum likelihood estimator (QMLE) of GARCH(p, q) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not just the heavy-tailed but also the skewed innovations. Under strict stationarity and some weak moment conditions, the strong consistency and asymptotic normality of the PQMLE are obtained. With no further efforts, the PQMLE can be…

ARMA–GARCH/IGARCH 模型的全局自加权与局部准最大指数似然估计AI 解读

This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA–GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given…