A semiparametric spatial FARIMA applied in the presence of spatial seasonality

A semiparametric spatial long-memory time series model, called Semi-SFARIMA, in the presence of a seasonality surface and random intraday eects is introduced and dened. Initially, a local polynomial double conditional smoothing (LP-DCS) tech- nique is employed to smooth the seasonal surface in the nonparametric part. Subse- quently, intraday curves are identified using automated local polynomial smoothing in a one-dimensional context. Ultimately, residual series obtained from the preced- ing steps undergo modeling using a (parametric) spatial FARIMA framework. The statistical significance of the estimated spatial FARIMA parameters are assessed through asymptotically valid standard errors. The estimation method is illustrated by in-depth analysis of air temperature from two distinct weather stations, Yuma and Murphy. Since the example series include missing values, an imputation method for univariate time series is considered as a preliminary treatment during the data collection and processing. The proposed ideas prove to be useful in practice when being confronted with spatial time series with two-directional seasonality patterns.