PAPER SERIES MODEL SELECTION WHEN THERE ARE MULTIPLE BREAKS

We consider selecting an econometric model when there is unc ertainty over both the choice of variables and the occurrence and timing of multiple locatio n shifts. The theory of general-to-simple (Gets) selection is outlined and its efficacy demonstrated i n a new set of simulation experiments first for a constant model in orthogonal variables, where only one decision is required to select irrespective of the number of regressors (less than the sample size). That generalizes to including an impulse indicator for every observation in the set of candidate regr essors (impulse saturation), as analyzed by Hendry, Johansen and Santos (2008) and Johansen and Niels en (2009). Monte Carlo experiments show its capability of detecting up to 20 shifts in 100 observ ations. JEL classifications:C51, C22. ‘Any sufficiently advanced technology is indistinguishabl e from magic. ’ Arthur C. Clarke, Profiles of The Future , 1961 1 Preface by David Hendry It is a pleasure and privilege to contribute to this volume in ho or of Peter Phillips. Peter’s publications are notable by the power and generality of the ideas, combine d with clear explanations and an incredible span of the entire discipline, setting a standard that few ca n a hieve. His major advances across so many areas are one of the reasons for the rapid progress in our disc ipline. Peter and I first met when Peter was a doctoral student at LSE working with Denis Sargan–Deni s had also been my supervisor and was a major inspiration to both of us. Peter was one of a series of di stinguished New Zealanders to come to the LSE, from his namesake, Bill Phillips (who had taught me), th rough Rex Bergstrom and Cliff Wymer. From the outset, it was clear that Peter had a deep commitment to econometrics, although his actual impact has far exceeded even the LSE faculty’s greatest hope s. P ter has constructed a mighty edifice of invaluable results on the base bequeathed by earlier econ ometricians, resolving one intractable timeseries problem after another. Peter has investigated estim ation, distribution, inference, identification, specification, selection and forecasting, for finite and lar ge samples, in discrete and continuous time, frequency and time domain, stationary and non-stationary p rocesses, linear and non-linear, Bayesian and classical, analytical and computational, advancing the to olkit in too many ways to even list. Peter has also made numerous important professional contributions, including producing an entire generation of doctoral students whose combined output is truly vast; crea ting Econometric Theoryand raising it to a position of pre-eminence; and helping revitalize and recor d the history of our discipline in an invaluable archive of interviews with its pioneers. Quietly spoken, bu t q ick as lightning, he has enlivened many conferences, always moving understanding forward, often m ore than the speaker. Econometrics is in a far stronger state today from the hundreds of ideas and resul ts that Peter has produced directly, and the thousands that have flowed indirectly: we all three wish him c ontinuing high productivity, and cannot imagine him ‘retiring’. ∗Financial support from the ESRC under Research Grant RES-06 2-23-0061 is gratefully acknowledged.