Testing for Linear Trend with Application to Relative Primary Commodity Prices

Abstract

Much research has been devoted to assessing the evidence for linear trend in a time series. We discuss the statistical implications of some recent developments, with specific application to 24 time series of relative primary commodities prices.

The long-run behaviour of the terms of trade between primary commodities and manufactures: a panel data approach

“…According to Cuddington and Urzúa (1989), this finding, strictly speaking, does not support the views of PS, because the latter refer to a secular terms of trade deterioration. 7 Third, von Hagen (1989), Cuddington (1992), Newbold and Vougas (1996), Kim et al (2003), Kellard and Wohar (2006), Harvey et al (2010) and Ghoshray (2011) do not find strong support for the PS hypothesis.…”

“…Grilli and Yang (1988) construct a US dollar commodity price index spanning from 1900 to 1986, consisting of 24 internationally traded non-fuel commodities. The Grilli and Yang (GY) dataset has become the most widely used data source in the literature related to the PS hypothesis; see, among others, Cuddington andUrzúa (1989), von Hagen (1989), Perron (1990), Powell (1991), Helg (1991), Ardeni and Wright (1992), Bleaney and Greenaway (1993), Newbold and Vougas (1996), León and Soto (1997), Kim et al (2003), Zanias (2005), Kellard and Wohar (2006) and Ghoshray (2011). However, it is worth mentioning that the work of GY is not only important because they constructed a consistent dataset over a long period of time, but also because it is perhaps the first study that tests whether commodity prices can be viewed as trend-stationary (TS) or difference-stationary (DS) processes, based on the ADF unit root test of Dickey and Fuller (1979).…”

“…However, it is worth mentioning that the work of GY is not only important because they constructed a consistent dataset over a long period of time, but also because it is perhaps the first study that tests whether commodity prices can be viewed as trend-stationary (TS) or difference-stationary (DS) processes, based on the ADF unit root test of Dickey and Fuller (1979). Subsequently, the ADF test has also been employed by Bleaney and Greenaway (1993), Reinhart and Wickham (1994), and Kim et al (2003), who analyse major commodity groupings, and by Cuddington (1992), who uses price data for individual commodities. 4 Further extending the line of work based on unit root tests, Cuddington and Urzua (1989), Perron (1990), Helg (1991), Reinhart and Wickham (1994) and Newbold and Vougas (1996) apply the ADF test allowing for the presence of a known structural break.…”

Evaluation of Linear Trend Tests Using Resampling Techniques

“…This has been shown with Monte Carlo simulations and different estimators for the linear trend (Woodward and Gray, 1993;Sun and Pantula, 1999;Roy et al, 2004;Kim et al, 2003). On the other hand, a deterministic trend may alert the sample autocorrelation used in the statistic of the trend test (Fried and Imhoff, 2003).…”

“…For the latter, the statistic is simply the estimated trend coefficient b standardized with its standard error. When the residuals are short-term correlated, simple corrections in the estimation of the standard error of b are suggested making use of the autocovariance (Grenander, 1954) (Woodward and Gray, 1993;Sun and Pantula, 1999;Roy et al, 2004;Kim et al, 2003). On the other hand, a deterministic trend may alert the sample autocorrelation used in the statistic of the trend test (Fried and Imhoff, 2003).…”