Correlation Testing in Time Series, SpatialandCross-Sectional Data

We provide a general class of tests for correlation in time series, spatial, spatiotemporaland cross-sectional data. We motivate our focus by reviewing howcomputational and theoretical difficulties of point estimation mount as one movesfrom regularly-spaced time series data, through forms of irregular spacing, and tospatial data of various kinds. A broad class of computationally simple tests isjustified. These specialize to Lagrange multiplier tests against parametric departuresof various kinds. Their forms are illustrated in case of several models for describingcorrelation in various kinds of data. The initial focus assumes homoscedasticity, butwe also robustify the tests to nonparametric heteroscedasticity.