Between and beyond: irregular series, interpolation, variograms and smoothing

Time series (and similar one-dimensional series) are more often irregularly spaced than many methods texts or courses admit. Even with a plan of regular measurements, gaps can arise for many human or inhuman reasons, while some series are naturally irregular. Interpolation of values between known values is a centuries-old need, but one neglected by official Stata, which offers only linear interpolation and cubic spline interpolation (in Mata). I review additional user-written commands for interpolation, including those for cubic, nearest neighbour and piecewise cubic Hermite methods available from SSC. Beyond interpolation of irregular series lie the questions of characterising the structure of such series and smoothing in various ways. One useful tool standard in spatial statistics is the variogram, which relates dissimilarity as squared differences between values to their separation in time or distance in space. Diggle and others have shown uses for variograms in time series and longitudinal data analysis. I discuss user-written Stata commands for variogram calculation, plotting and use in relation to exploratory data analysis on the one hand and smoothing on the other.