Statistical models for time series with discrete time index and discrete state index, i.e. lists of non-negative whole numbers with a causal ordering.
C&c symbolic dynamics, nonlinear time series wizardry,
branching processes and
Galton Watson processes
for some important special cases.
If there is no serial dependence, you might want unadorned
Series monotonic increasing at a decreasing rate?
Perhaps you have a
Finite state Markov chains
Often fit as if non-parametric,
although there exist parametric transition tables if you’d like,
and if you have a large state space you probably would like.
GLMs applied to time series. Fokianos et al.
Non-linear processes, arbitrary interaction dynamics, Turing machines, discretised continuous processes…
Todo: get a handle on Twitter’s
Robust anomaly detection
(Cui and Lund 2009):
This paper proposes a simple new model for stationary
time series of integer counts.
Previous work has focused on thinning methods
and classical time series autoregressive moving-average difference equations;
in contrast, our methods use a renewal process
to generate a correlated sequence of Bernoulli trials.
By superpositioning independent copies of such processes,
stationary series with binomial, Poisson, geometric
or any other discrete marginal distribution
can be readily constructed.
The model class proposed is parsimonious, non-Markov
and readily generates series with either short- or long-memory
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