  A Poisson autoregressive (PAR) model accounting for discreteness and
autocorrelation of count time series data is typically estimated in the
state-space modelling framework through extended Kalman filter. However,
because of the complex dependencies in count time series, estimation becomes
more challenging. PAR is viewed as an additive model and estimated using a
hybrid of cubic smoothing splines and maximum likelihood estimation (MLE) in
the backfitting framework. Simulation studies show that this estimation method
is comparable or better than PAR estimated in the state-space context,
especially with larger count values. However, as [2] formulated PAR for
stationary counts, both estimation procedures underestimate parameters in
nearly nonstationary models. The flexibility of the additive model has two
benefits though: robust estimation in the presence of temporary structural
change, and; viability to integrate PAR model into a more complex model
structure. We further generalized the PAR(p) model into multiple time series of
counts and illustrated with indicators in the financial markets.
