Challenges of trending time series econometrics

Abstract

We discuss some challenges presented by trending data in time series econometrics. To the empirical economist there is little guidance from theory about the source of trend behavior and even less guidance about practical formulations. Moreover, recent proximity theorems [W. Ploberger, P.C.B. Phillips, Empirical limits for time series econometric models, Econometrica 71 (2003) 627-673] reveal that trends are more elusive to model empirically than stationary processes, with the upshot that optimal forecasts are also harder to estimate when the data involve trends. These limitations are implicitly acknowledged in much practical modeling and forecasting work, where adaptive methods are often used to help keep models on track as trends evolve. The paper discusses these broader issues and limitations of econometrics and offers some thoughts on new practical possibilities for data analysis in the absence of good theory models for trends. In particular, a new concept of coordinate cointegration is introduced and some new econometric methodology is suggested for analyzing trends and co-movement and for producing forecasts in a general way that is agnostic about the specific nature of the trend process. Some simulation exercises are conducted and some long historical series on prices and yields on long securities are used to illustrate the methods.

Economic transition and growth

“…In conducting the regression (18) we may employ either h it computed directly from log y it as in (10) or, as discussed above, use filtered data O h it based on fitted values log y it from a coordinate trend regression (Phillips, 2005) or a smoothing filter that removes business cycles.…”

Statistical inference from atmospheric time series: detecting trends and coherent structures

“…2. As Phillips (2005) noted, "no one understands trends, but everyone sees them in the data", and in spite of observational successes, the problem of describing turbulent flows with CSs remains a formidable theoretical challenge (Tabeling, 2002). In Sect.…”

Modelling trends and cycles in economic time series: historical perspective and future developments

“…For example, if we were examining rainfall records over a hundred years, a slow rise from the beginning of the period to the end would be regarded as a trend; but if we possessed records for two thousand years… the rise over a particular century might appear as a slow oscillatory movement, so that any inference from the 'trend' in a particular century to the effect that the weather was likely to continue becoming wetter might be quite false.'' While Granger et al (1997) consider some very general conditions for the behaviour of trends, Phillips (2001aPhillips ( , 2003Phillips ( , 2005 has discussed the notion of trendlike behaviour in economic time series, suggesting that one of the 'laws' of modern econometrics is that ''no one really understands trends, even though most of us see trends when we look at economic data'' (Phillips 2003, p C35). Phillips' view is that standard trend formulations ''do no more than provide coordinate systems for capturing trend effects'' and that ''we must learn to do inference about trends in settings where the real trend in the data is far more complex than the coordinates we use to describe it'' (Phillips 2001a, p 24).…”