Two New Zealand pioneer econometricians

We analyze trend elimination methods and business cycle estimation by data …ltering of the type introduced by Whittaker (1923) and popularized in economics in a particular form by Hodrick and Prescott (1980/1997; HP). A limit theory is developed for the HP …lter for various classes of stochastic trend, trend break, and trend stationary data. Properties of the …ltered series are shown to depend closely on the choice of the smoothing parameter (). For instance, when = O(n 4) where n is the sample size, and the HP …lter is applied to an I(1) process, the …lter does not remove the stochastic trend in the limit as n ! 1. Instead, the …lter produces a smoothed Gaussian limit process that is di¤erentiable to the 4'th order. The residual 'cyclical' process has the random wandering non-di¤erentiable characteristics of Brownian motion, thereby explaining the frequently observed 'spurious cycle' e¤ect of the HP …lter. On the other hand, when = o(n); the …lter reproduces the limit Brownian motion and eliminates the stochastic trend giving a zero 'cyclical'process. Simulations reveal that the = O(n 4) limit theory provides a good approximation to the actual HP …lter for sample sizes common in practical work. When it is used as a trend removal device, the HP …lter therefore typically fails to eliminate stochastic trends, contrary to what is now standard belief in applied macroeconomics. The …ndings are related to recent public debates about the long run e¤ects of the global …nancial crisis.

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“…1 (c.f. Phillips, 2010). In the HP case (m = 2); the limit off is a simple linear trend, as is well known.…”

Section: Algebraic and Operator Solutionsmentioning

confidence: 74%

“…When higher order di¤erences are used in the penalty function, the …lter selects a higher order time polynomial as the trend when ! 1; as shown in Phillips (2010).…”

Section: Introductionmentioning

confidence: 86%

Business Cycles, Trend Elimination, and the HP Filter

Phillips

Jin

2015

SSRN Journal

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“…1 as n ! 1: These are particularly relevant in applied time series work that use trend detection …ltering methods such as the Whittaker …lter (Whittaker, 1923;Phillips, 2010;Phillips and Jin, 2015), the Hodrick Prescott …lter (Leser, 1961;Hodrick and Prescott, 1997), and bandpass …lters (Baxter and King, 1999). Conditions for validity in such cases will be considered in subsequent work.…”

Section: Nonlinear Functionals Of Nonstationary Processesmentioning

confidence: 99%

Latent Variable Nonparametric Cointegrating Regression

2020

Self Cite

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This article studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such models occur in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent or filtered variable as in mixed-data-sampling. The treatment allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable, including correctly specified as well as misspecified systems, and is therefore intermediate between nonlinear nonparametric cointegrating regression and completely spurious nonparametric nonstationary regression. The results relate to recent work on dynamic misspecification in nonparametric nonstationary systems and the limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series. Some implications for forecasting under misspecification are also examined.

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“…A discussion of Aitken's contributions to econometrics and some tales of his eminence as a mental arithmetician are given inPhillips (2010).…”

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confidence: 99%

Unit Roots in Life—a Graduate Student Story

Phillips

2014

Econom. Theory

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On the evening of March 7, 2008, the New Zealand Econometric Study Group Meeting held its Conference Dinner. The venue was the Owen Glenn Building, the spectacular new home of the Auckland Business School and the Department of Economics at the University of Auckland. The meeting was organized by my colleagues, co-authors, and close companions Donggyu Sul and Chirok Han. Chirok did double duty by videotaping the evening, Donggyu coordinated festivities with consummate skill, and we settled in to a memorable evening.Econometricians, old friends, former students, two of my former teachers, faculty, and senior administrators were gathered together to celebrate my 60th birthday. Many had traveled long distances from overseas and navigated busy schedules to come to this event. It was a singular honor. My wife and daughter were with me. Opening speeches from Bas Sharp and John McDermott broke the ice with endearing tales from the past and jokes about some mysterious hole in my vita. I stood at the front table, looked out, and felt a glow of fellowship envelop me. I was fortunate indeed. Life had bestowed many gifts. The warmth of family, friends, and collegiality were at the top of the list. My education and early training in New Zealand were a clear second.What follows is a graduate student story. It draws on the first part of the speech I gave that evening at the NZESG conference dinner. It mixes personal reflections with recollections of the extraordinary New Zealanders who shaped my thinking as a graduate student and beginning researcher—people who have had an enduring impact on my work and career as an econometrician. The story traces out these human initial conditions and unit roots that figure in my early life of teaching and research.

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Two New Zealand pioneer econometricians

Cited by 24 publications

References 29 publications

Business Cycles, Trend Elimination, and the HP Filter

Business Cycles, Trend Elimination, and the HP Filter

Latent Variable Nonparametric Cointegrating Regression

Unit Roots in Life—a Graduate Student Story

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