Statistics and Its Interface

Volume 16 (2023)

Number 1

Special issue on recent developments in complex time series analysis – Part I

Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)

On dual-asymmetry linear double AR models

Pages: 3 – 16



Songhua Tan (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China)

Qianqian Zhu (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China)


This paper introduces a dual-asymmetry linear double autoregressive (DA-LDAR) model that can allow for asymmetric effects in both the conditional location and volatility components of time series data. The strict stationarity is discussed for the new model, for which a sufficient condition is established. A self-weighted exponential quasi-maximum likelihood estimator (EQMLE) is proposed for the DALDAR model, and a mixed portmanteau test for goodness-of-fit is constructed based on the self-weighted EQMLE. It is noteworthy that all the asymptotic properties for estimation and testing are established without any moment condition on the data process, which makes the new model and its inference tools applicable for heavy-tailed data. Since all inference tools need to estimate the unknown density function of innovations, we employ a random-weighting bootstrap method to facilitate accurate inference and show its asymptotic validity. Simulation studies provide support for theoretical results, and an empirical application to NASDAQ Composite Index illustrates the usefulness of the new model.


asymmetry effects, bootstrap method, double autoregressive models, exponential QMLE, portmanteau test, strict stationarity

Zhu’s research was supported by an NSFC grant 12001355, Shanghai Pujiang Program 2019PJC051 and Shanghai Chenguang Program 19CG44.

Received 1 March 2021

Accepted 11 July 2021

Published 28 December 2022