5,051 research outputs found
Stationary Gaussian Markov Processes as Limits of Stationary Autoregressive Time Series
We consider the class, ℂp, of all zero mean stationary Gaussian processes, {Yt : t ∈ (—∞, ∞)} with p derivatives, for which the vector valued process {(Yt(0) ,...,Yt(p)) : t ≥ 0} is a p + 1-vector Markov process, where Yt(0) = Y(t). We provide a rigorous description and treatment of these stationary Gaussian processes as limits of stationary AR(p) time series
The tail of the stationary distribution of a random coefficient AR(q) model
We investigate a stationary random coefficient autoregressive process.
Using renewal type arguments tailor-made for such processes, we show that the
stationary distribution has a power-law tail. When the model is normal, we show
that the model is in distribution equivalent to an autoregressive process with
ARCH errors. Hence, we obtain the tail behavior of any such model of arbitrary
order
The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains
We introduce the cluster index of a multivariate regularly varying stationary
sequence and characterize the index in terms of the spectral tail process. This
index plays a major role in limit theory for partial sums of regularly varying
sequences. We illustrate the use of the cluster index by characterizing
infinite variance stable limit distributions and precise large deviation
results for sums of multivariate functions acting on a stationary Markov chain
under a drift condition
Iterated limits for aggregation of randomized INAR(1) processes with Poisson innovations
We discuss joint temporal and contemporaneous aggregation of independent
copies of strictly stationary INteger-valued AutoRegressive processes of order
1 (INAR(1)) with random coefficient and with idiosyncratic
Poisson innovations. Assuming that has a density function of the form
, , with , different limits of appropriately centered and scaled
aggregated partial sums are shown to exist for , ,
or , when taking first the limit as
and then the time scale , or vice versa. In fact, we
give a partial solution to an open problem of Pilipauskaite and Surgailis
(2014) by replacing the random-coefficient AR(1) process with a certain
randomized INAR(1) process.Comment: 49 pages. Results on centralization by the empirical mean are adde
Graphical modelling of multivariate time series
We introduce graphical time series models for the analysis of dynamic
relationships among variables in multivariate time series. The modelling
approach is based on the notion of strong Granger causality and can be applied
to time series with non-linear dependencies. The models are derived from
ordinary time series models by imposing constraints that are encoded by mixed
graphs. In these graphs each component series is represented by a single vertex
and directed edges indicate possible Granger-causal relationships between
variables while undirected edges are used to map the contemporaneous dependence
structure. We introduce various notions of Granger-causal Markov properties and
discuss the relationships among them and to other Markov properties that can be
applied in this context.Comment: 33 pages, 7 figures, to appear in Probability Theory and Related
Field
Latent Gaussian Count Time Series Modeling
This paper develops theory and methods for the copula modeling of stationary
count time series. The techniques use a latent Gaussian process and a
distributional transformation to construct stationary series with very flexible
correlation features that can have any pre-specified marginal distribution,
including the classical Poisson, generalized Poisson, negative binomial, and
binomial count structures. A Gaussian pseudo-likelihood estimation paradigm,
based only on the mean and autocovariance function of the count series, is
developed via some new Hermite expansions. Particle filtering methods are
studied to approximate the true likelihood of the count series. Here,
connections to hidden Markov models and other copula likelihood approximations
are made. The efficacy of the approach is demonstrated and the methods are used
to analyze a count series containing the annual number of no-hitter baseball
games pitched in major league baseball since 1893
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