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M. Borkovec and C. Klüppelberg, “The Tail of the Stationary Distribution of an Autoregressive Process with ARCH(1) Errors,” Annals of Applied Probability, Vol. 11, No. 4, 1998, pp. 1220-1241.

has been cited by the following article:

• TITLE: Asymptotic Inference for the Weak Stationary Double AR(1) Model

  AUTHORS: Fang Chang, Augustine C. M. Wong, Yanyan Wu

  KEYWORDS: Canonical Parameter; Double Autoregressive Model; p-Value Function; Signed Log-Likelihood Ratio Statistic

  JOURNAL NAME: Open Journal of Statistics, Vol.2 No.2, April 23, 2012

  ABSTRACT: An AR(1) model with ARCH(1) error structure is known as the first-order double autoregressive (DAR(1)) model. In this paper, a conditional likelihood based method is proposed to obtain inference for the two scalar parameters of interest of the DAR(1) model. Theoretically, the proposed method has rate of convergence O(n-3/2). Applying the proposed method to a real-life data set shows that the results obtained by the proposed method can be quite different from the results obtained by the existing methods. Results from Monte Carlo simulation studies illustrate the supreme accuracy of the proposed method even when the sample size is small.