Estimation of Poisson autoregressive model for multiple time series - Redondo, Paolo Victor T.; Lansangan, Joseph Ryan G.; Barrios, Erniel B. (2022)
A Poisson autoregressive (PAR) model accounting for discreteness and autocorrelation of count time series data is typically estimated in the state-space modeling framework through an 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 at the least comparable to PAR estimated in the state-space context, especially with larger counts. The flexibility of the additive model has two significant benefits: [1] robust estimation in the presence of temporary structural change and [2] viability to integrate the PAR model into a more complex model structure. We further generalized the PAR(p) model into multiple time series of counts and illustrated it with indicators in the financial markets.
Keywords: Time-series analysis; Mathematical models