Estimation for first-order autoregressive processes with positive or bounded innovations

Consistent estimation and order selection for non-stationary autoregressive processes with stable innovations

A possibly non-stationary autoregressive process, of unknown finite order, with possibly infinite-variance innovations is studied. The Ordinary Least Squares autoregressive parameter estimates are shown to be consistent, and their rate of convergence, which depends on the index of stability, α, is established. We also establish consistency of lag-order selection criteria in the non-stationary c...

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...

Autoregressive Gaussian Random Vectors of First Order

Conditional Maximum Likelihood Estimation of the First-Order Spatial Integer-Valued Autoregressive (SINAR(1,1)) Model

‎Recently a first-order Spatial Integer-valued Autoregressive‎ ‎SINAR(1,1) model was introduced to model spatial data that comes‎ ‎in counts citep{ghodsi2012}‎. ‎Some properties of this model‎ ‎have been established and the Yule-Walker estimator has been‎ ‎proposed for this model‎. ‎In this paper‎, ‎we introduce the...

Innnite Order Cointegrated Vector Autoregressive Processes: Estimation and Inference

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992). The asymptotic properties of the estimated coeecients of the autoregressive ECM (error correction model) and the pure VAR (vector autoregressive) representations are derived under the assumption that the autoregressive order goes to innnity with the sample size. Thes...