Environmental Economics and Sustainability

2 DETECTING VOLCANIC ERUPTIONS IN TEMPERATURE RECONSTRUCTIONS BY DESIGNED BREAK-INDICATOR SATURATION

Felix Pretis

University of Oxford

Lea Schneider

Johannes Gutenberg University

Jason E. Smerdon

Lamont-Doherty Earth Observatory, Columbia University

David F. Hendry

University of Oxford

1. Introduction

Breaks in time series come in many shapes and may occur at any point in time – distorting inference in-sample and leading to forecast failure out-of-sample if not appropriately modelled. Often an approximate shape of a break can be postulated a priori, either from previous observations or theory. For example, smooth transitions are common in economic time series following recessions or policy interventions, while sudden drops followed by smooth reversions to the mean are typical in climate time series such as temperature records after a large volcanic eruption (e.g. Kelly and Sear, 1984). While the approximate form of a break may be known, the timings and magnitudes of breaks are often unknown. Here, we propose an econometric approach for detecting breaks of any specified shape in regression models using an indicator saturation procedure. Our approach is based on recent developments in variable selection within regression models that involve more variables than observations (Castle et al., 2011). By selecting over a complete set of designed break indicators, our approach produces estimates of the break magnitude and timing without imposing limits on the number of breaks that may ...