Theory & Methods: Non‐Gaussian Conditional Linear AR(1) Models

By Gary K. Grunwald, Rob J Hyndman, L. Tedesco, Richard L. Tweedie. 2000

159 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/47f560380eeb72b4d32b845e8f24b99b184bd417

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Citations in the corpus

Count Time Series Models (2012, background): “The CLAR(1) class includes many of the non-Gaussian AR(1) models proposed in the literature and allows various generalizations of previous results; see Grunwald et al. (2000).”
Generalized Autoregressive Moving Average Models (2003, result): “Some of these results are generalizations of results for rst-order autoregressive models given by Grunwald et al. (2000). In Section 4.”
25 Years of IIF Time Series Forecasting: A Selective Review (2005, background): “Grunwald et al. (2000) surveyed many of the stochastic models for count time series, using simple first-order autoregression as a unifying framework for the various approaches.”
Poisson QMLE of Count Time Series Models (2016, methodology): “With this model, we have (1) (Grunwald et al., 2000) with t D !”
25 years of time series forecasting (2006, background): “Grunwald et al. (2000) surveyed many of the stochastic models for count time series, using simple first-order autoregression as a unifying framework for the various approaches.”
Absolute regularity and ergodicity of Poisson count processes (2011, background): “Actually, Grunwald, Hyndman, Tedesco and Tweedie [19], Case II of Proposition 3, Streett [27] and Davis, Dunsmuir and Streett [8] proved ergodicity in special cases.”
Partial Likelihood Inference For Time Series Following Generalized Linear Models (2004, background): “These models have been studied by several authors including Li (1994), Shephard (1995), Zeger and Qaqish (1988), and more recently Benjamin et al. (1998), Davis et al. (1999) and Grunwald et al. (2000).”
Non-Gaussian bifurcating models and quasi-likelihood estimation (2004, background): “Set Yt-j == X Lt /2j j for j == 0, 1, 2, ... , and apply the results of Grunwald et al. (2000) to establish ergodicity.”
Estimation in conditional first order autoregression with discrete support (2005, background): “ Grunwald et al. (2000) show that under very mild conditions (2) is implied by the CLAR(1) structure, but the converse is not true in general.”
Binomial thinning models for integer time series (2006, background): “The INAR(1) process is a member of the wide class of conditional linear first order autoregressive (CLAR(1)) models introduced by Grunwald et al. (2000).”
An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion (2017, unknown): “In particular, the new BerG-INAR(1)BiNB model belongs to the class of CLAR(1) models (conditional linear autoregressive) as defined by Grunwald et al. (2000).”
Stochastic models underlying Croston ’ s method for intermittent demand forecasting 2 February 2005 (2005, methodology): “Potential stationary models are Poisson autoregressive models (see Grunwald et al. 2000) and other time series models for counts 2 February 2005 16 Stochastic models underlying Croston’s method for intermittent demand forecasting (e.g. Cameron & Trivedi 1998, Winkelmann 2000).”
Autoregressive Gamma Processes (2006, background): “innovations as in the general class of models considered by Grunwald et al. (2000).”
Practical drift conditions for subgeometric rates of convergence (2004, background): “Polynomial rates of convergence Polynomial rates of convergence have been widely studied recently under various conditions (see Veretennikov (1997, 1999), Tanikawa (2001), Jarner and Roberts (2002), Fort and Moulines (2002)).”
Bayesian predictions of low count time series (2005, background): “m=l P [B m = l]PMk(εt−1 = m) # ×PMk(εt = yt − s− l), (16)”