Smoothing methods

Abstract

Regression methods are often used to explore the dependence of the timing of natural events on the weather. These methods are generally reasonable straightforward to apply, being available in numerous software packages. Weather data are commonly aggregated to monthly means, so, for example, the date on which a particular species flowers each year might be regressed on the monthly mean temperatures during the period preceding flowering. This aggregation has the benefit of reducing problems due to multicollinearity; temperatures between successive days and weeks tend to be highly correlated. In this chapter, we describe regression methodology that can be applied to correlated predictor variables, such as daily temperature records, avoiding difficulties due to multicollinearity. This method, called penalised signal regression, is based on the observation that the regression coefficients for successive days should be similar in size. Differences in coefficients between neighbouring days are penalised. This results in a smooth curve of regression coefficients that is easily interpretable. We describe several alternative methods that employ this idea and explain how to apply penalised signal regression in practice.