On interpolation in periodic autoregressive processes

On periodic autoregressive processes estimation

We consider the autoregressive estimation for periodically correlated processes, using the parameterization given by the partial autocorrelation function. We propose an estimation of these parameters by extending the sample partial autocorrelation method to this situation. The comparison with other methods is made. Relationships with the stationary multivariate case are discussed.

Testing for Seasonal Unit Roots in Periodic Integrated Autoregressive Processes

The Consequences of Seasonal Adjustment for Periodic Autoregressive Processes

This paper examines the effect of X-11 seasonal adjustment on periodic autoregressive processes, using both analytic techniques and simulation. Analytical results show that adjustment reduces (but does not eliminate) periodicity in the coefficients of a stationary PAR(1) process, and it generally moves the coefficients towards unity. A nonstationary periodically integrated process is converted ...

Karhunen-Loeve Representation of Periodic Second-Order Autoregressive Processes

In dynamic data driven applications modeling accurately the uncertainty of various inputs is a key step of the process. In this paper, we first review the basics of the Karhunen-Loève decomposition as a means for representing stochastic inputs. Then, we derive explicit expressions of one-dimensional covariance kernels associated with periodic spatial second-order autoregressive processes. We al...

On the existence of Hilbert valued periodically correlated‎ autoregressive processes

‎In this paper we provide sufficient condition for existence of a‎ ‎unique Hilbert valued ($mathbb{H}$-valued) periodically‎ ‎correlated solution to the first order autoregressive model‎ ‎$X_{n}=rho _{n}X_{n-1}+Z_{n}$‎, ‎for $nin mathbb{Z}$‎, ‎and‎ ‎formulate the existing solution and its autocovariance operator‎. ‎Also we specially investigate equivalent condition for the‎ ‎coordinate process...