This chapter is concerned with forecasting univariate seasonal time series data using periodic autoregressive models We show how one should account for unit roots and deterministic terms when generating out of sample forecasts We illus trate the models for various quarterly UK consumption series This is the rst version July of a chapter that is to be prepared for potential inclusion in the Comp...

Seasonal and periodic vector autoregressions are two common approaches to modeling vector time series exhibiting cyclical variations. The total number of parameters in these models increases rapidly with the dimension and order of the model, making it difficult to interpret the model and questioning the stability of the parameter estimates. To address these and other issues, two methodologies f...

Periodically correlated autoregressive nonstationary processes of finite order are considered. The corresponding Yule-Walker equations are applied to derive the generating functions of the covariance functions, what are called here the periodic covariance generating functions. We also provide closed formulas for the spectral densities by using the periodic covariance generating functions, which...

A new approach to the problem of modelling and predicting respiration motion has been implemented. This is a dual-component model, which describes the respiration motion as a non-periodic time series superimposed onto a periodic waveform. A periodic autoregressive moving average algorithm has been used to define a mathematical model of the periodic and non-periodic components of the respiration...

Periodic autoregressive moving average (PARMA) models are indicated for time series whose mean, variance and covariance function vary with the season. In this study, we develop and implement forecasting procedures for PARMA models. Forecasts are developed using the innovations algorithm, along with an idea of Ansley. A formula for the asymptotic error variance is provided, so that Gaussian pred...

The long-term hydrothermal scheduling (LTHS) problem seeks to obtain an operational policy that optimizes water resource management. most employed strategy such a is stochastic dual dynamic programming (SDDP). primary source of uncertainty in predominant hydropower systems the reservoirs inflow, usually linear time series model (TSM) based on order-p periodic autoregressive [PAR(p)] model. Alth...