Parsimonious Periodic Time Series Modeling

Abstract

This paper studies techniques for fitting parsimonious periodic time series models to periodic data. Large sample standard errors for the parameter estimates in a periodic autoregressive moving-average time series model under parametric constraints are derived. Likelihood ratio statistics for hypothesis testing are examined. The techniques are applied in modeling daily temperatures at Griffin, Georgia, USA.

Space–time modeling of 20 years of daily air temperature in the Chicago metropolitan region

“…Huerta et al (2004) use a dynamic linear modeling framework to interpolate hourly ozone and air temperature in the Mexico City area. Lund et al (2006) study daily temperatures at Griffin, Georgia, USA between 1931 and 1997 using a parsimonious periodic time-series method. This work has no spatial component.…”

Nonparametric Trend Estimation for Periodic Autoregressive Time Series

“…Periodically, stationary time series are often modeled by periodic autoregressive (PAR) models. See, for instance, Lund et al (2006), for fitting a PAR model to a periodically stationary time series.…”

A prediction‐residual approach for identifying rare events in periodic time series

“…There, the seasonal mean and variance cycles are visually apparent. It turns out that the sample lag‐one autocorrelations are also periodic [see Lund et al. (2005) for justification], with higher correlations occurring during the Fall when long runs of clear sunny days are common; lower correlations occur during late winter when cold front passages are more frequent and serve to break runs of similar weather.…”

“…Before proceeding, we remark that the Griffin series was parsimoniously modelled in Lund et al. (2005).…”