Theory and Inference for a Class of Observation-driven Models with Application to Time Series of Counts
By Richard A. Davis, Heng Liu. 2012
66 citations recorded by the source corpus.
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying process that evolves as a function of lagged observations. We employ an iterated random function approach and a special coupling technique to show that, under suitable conditions on the parameter space, the conditional mean process is a geometric moment contracting Markov chain and that the observation process is absolutely regular with geometrically decaying coefficients. Moreover the asymptotic theory of the maximum likelihood estimates of the parameters is established under some mild assumptions. These models are applied to two examples; the first is the number of transactions per minute of Ericsson stock and the second is related to return times of extreme events of Goldman Sachs Group stock.
View Paper: https://www.semanticscholar.org/paper/3e82f3a8e87960532e2f72b8afdd32d13612f617
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Konstantinos Fokianos
- Richard A. Davis
- Christian Francq
- A. Ahmad
- V. Christou
- Jean-Michel Zakoian
- Randal Douc
- Eric Moulines
Citations in the corpus
- MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES (2017, background): “2), or models for time series of counts (Davis and Liu, 2012).”
- QUASI‐LIKELIHOOD INFERENCE FOR NEGATIVE BINOMIAL TIME SERIES MODELS (2013, methodology): “Questions regarding ergodicity and stationarity of negative binomial processes as well as asymptotic maximum likelihood theory have not been addressed in the literature, except by Davis and Liu (2012).”
- Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator (2012, background): “…(2006) or Zhu (2012), Fokianos et al. (2009)), Poisson threshold models (see Henderson et al. (2011)), log-linear Poisson autoregression (see Fokianos and Tjøstheim (2011)); see also Davis et al. (2003), Davis and Liu (2012) and Neumann (2011) for other observation-driven models for Poisson counts.”
- Poisson QMLE of Count Time Series Models (2016, methodology): “Davis and Liu (2015) studied the MLE for a wide class of integer-valued models.”
- Self-Excited Threshold Poisson Autoregression (2013, background): “…on an accompanying intensity process that drives the dynamics of the model; see Davis, Dunsmuir, and Streett (2003), Ferland, Latour, and Oraichi (2006), Fokianos, Rahbek, and Tjøstheim (2009), Fokianos and Tjøstheim (2011), Davis and Liu (2012), and Doukhan, Fokianos, and Tjøstheim (2012).”