This paper 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...

Assume that S_{t} is a stock price process and Bt is a bond price process with a constant continuously compounded risk-free interest rate, where both are defined on an appropriate probability space P. Let y_{t} = log(S_{t}/S_{t-1}). y_{t} can be generally decomposed into a conditional mean plus...

This paper develops a systematic procedure of statistical inference for the ARMA model with unspecified and heavy-tailed heteroscedastic noises. We first investigate the least absolute deviation estimator (LADE) and the self-weighted LADE for the model. Both estimators are shown to be strongly...

This paper investigates a quasi-likelihood ratio (LR) test for the thresholds in buffered autoregressive processes. Under the null hypothesis of no threshold, the LR test statistic converges to a function of a centered Gaussian process. Under local alternatives, this LR test has nontrivial...

This paper proposes a Cramer-von Mises (CM) test statistic to check the adequacy of weak ARMA models. Without posing a martingale difference assumption on the error terms, the asymptotic null distribution of the CM test is obtained by using the Hillbert space approach. Moreover, this CM test is...

This paper introduces a new model called the buffered autoregressive model with generalized autoregressive conditional heteroskedasticity (BAR-GARCH). The proposed model, as an extension of the BAR model in Li et al. (2013), can capture the buffering phenomenon of time series in both conditional...

This paper 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 the heavy-tailed but also the skewed...

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...

Testing causality-in-mean and causality-in-variance has been largely studied. However, none of the tests can detect causality-in-mean and causality-in-variance simultaneously. In this article, we introduce a factor double autoregressive (FDAR) model. Based on this model, a score test is proposed...

This article proposes Cramer-von Mises (CM) and Kolmogrove-Smirnov (KS) test statistics based on the signs of a time series to test the null hypothesis that the series is a martingale difference sequence (MDS) with conditional heteroscedasity. Both of test statistics allowing for...