This paper demonstrates how parsimonious models of sinusoidal functions can be used to ﬁt spatially variant time series in which there is considerable variation of a periodic type. A typical shortcoming of such tools relates to the diﬀiculty in capturing idiosyncratic variation in periodic models. The strategy developed here addresses this deﬁciency. While previous work has sought to overcome the shortcoming by augmenting sinusoids with other techniques, the present approach employs station-speciﬁc sinusoids to supplement a common regional component, which succeeds in capturing local idiosyncratic behavior in a parsimonious manner. The experiments conducted herein reveal that a semi-parametric approach enables such models to ﬁt spatially varying time series with periodic behavior in a remarkably tight fashion. The methods are applied to a panel data set consisting of hourly air pollution measurements. The augmented sinusoidal models produce an excellent ﬁt to these data at three diﬀerent levels of spatial detail.
Muller, Nicholas Z. and Phillips, Peter C.B., "Sinusoidal Modeling Applied to Spatially Variant Tropospheric Ozone Air Pollution" (2006). Cowles Foundation Discussion Papers. 1836.