The Tail of the Stationary Distribution of an Autoregressive Process with Arch(1) Errors

By M. Borkovec, Claudia Klüppelberg. 2001

109 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance

View Paper: https://www.semanticscholar.org/paper/7327ffed42335c957ce85b42c70778f7dc4a4eec

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Citations in the corpus

The tail of the stationary distribution of a random coefficient AR(q) model (2004, background): “7) was investigated in [3] by different, purely analytic methods.”
Asymptotic inference for a nonstationary double AR(1) model (2008, background): “The condition for weak stationarity of model (1) is that φ2 + α 1, which was proved by Guégan & Diebolt (1994) for sufficiency and by Borkovec & Klüppelberg (2001) for necessity.”
Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps (2009, methodology): “Now we consider an example described by Borkovec and Klüppelberg in (2).”
Conditional variance estimation in heteroscedastic regression models (2009, background): “2) and σ̃(2) j,(2)(x) = 1 4 (1 + 2) σ̂(2) j ( x + (2−1/2 − 1)γh1 ) + 1 2 σ̂(2) j ( x + 2γh1 ) + 1 4 (1− 2) σ̂(2) j ( x + (2−1/2 + 1)γh1 ) (3.”
Estimation and testing stationarity for double‐autoregressive models (2004, background): “Choose δ ∈ .0, δ̃/ and let g.x/ = 1 + |x|δ, where x ∈ R. Borkovec and Kluppelberg (1998) showed that there is an M that is sufficiently large that sup |x| M [E{g.yt/|yt−1 = x}] < ∞, .”
Statistics of Extremes (2004, background): “Not surprisingly, their extremal properties have been thoroughly investigated (Basrak et al. 2002; Borkovec 2000; Borkovec and Klüppelberg 2003; de Haan et al. 1989; Mikosch and Stărică 2000), even for multivariate versions (Stărică 1999).”
Stability and the Lyapounov exponent of threshold AR-ARCH Models (2004, unknown): “For nonthreshold ARCH and GARCH models, the stationary distribution has been shown to have regularly varying tails [e.g., Borkovec (2000), Borkovec and Klüppelberg (2001) and Basrak, Davis and Mikosch (2002)].”
A Double AR(p) Model: Structure and Estimation (2007, unknown): “When p = 1, it was studied by Guégan and Diebolt (1994), Borkovec (2001) and Borkovec and Kluppelberg (2001).”
GARCH Models (2010, unknown): “See Mikosch and Stărică (2000), Borkovec and Klüppelberg (2001), Basrak, Davis and Mikosch (2002) and Davis and Mikosch (2009).”
Unit root vector autoregression with volatility induced stationarity (2014, methodology): “This contrasts the univariate double autoregressive (DAR) models where a unit-root does not necessarily imply non-stationarity as lagged values of the process enter the conditional variance, see e.g. Borkovec and Klüppelberg (2001) and Ling (2004).”