Title: Indirect pairwise fitting of latent autoregressive and moving average models
Authors: Guido Masarotto - University of Padova (Italy)
Xanthi Pedeli - Ca Foscari University (Italy) [presenting]
Cristiano Varin - Ca Foscari University of Venice (Italy)
Abstract: Several models for non-normal time series are built on a latent autoregressive and moving average component. Although these models have attractive properties and interpretation, the fitting is often difficult because computation of their likelihoods involves high-dimensional integration. To overcome the complexity of the exact likelihood one can rely on the pairwise likelihood of order $m$ using only bivariate densities of observations separated at most by $m$ units. However, a wrong choice of the order of the pairwise likelihood may have a significant impact on the fit of the underlying model. For example, even though the pairwise likelihood of order $p$ is efficient for inference in the autoregressive model of order $p$, it is grossly inefficient for inference in moving average models. Based on the idea of the pairwise likelihood, an indirect fitting of latent autoregressive and moving average models is suggested. The estimation strategy consists of two ingredients. The first ingredient is parameter augmentation to split maximization of the pairwise likelihood in $m$ separate sub-problems, thus reducing the computational cost of the fitting algorithm without affecting the statistical efficiency. The second ingredient is indirect inference to cope with the performance loss of moving average models using a truncated autoregressive representation.