PRACTITIONERS CORNER: A Note on the Empirical Power of Unit Root Tests under Threshold Processes^†

Commodity futures indexes and related exchange traded notes: Linear and nonlinear adjustment

“…This may indicate that most of the market value series do not exhibit a common trend over time. However, a number of authors have mentioned that if a series displays nonlinearity, the linear unit root tests are largely mis-specified (Kapetanios et al, 2003;Pippenger and Goering, 1993). It is therefore instructive to test these series for possible presence of nonlinearity in their data-generating process before one can make conclusions about the long-run relationship between prices of ETN and their underlying values.…”

“…Other than the widely cited poor power problem of the ADF type test, equation (2) assumes that the long adjustment process is linear and symmetric. If the actual series is nonlinear in nature, any test of long-run convergence based on equation (2) will be mis-specified (Pippenger and Goering, 1993). A natural departure from the above specification must start with a formal investigation if theû t series is associated with the existence of nonlinearity.…”

Are Real Interest Rates of EU Accession Countries Characterized by Non-Linear Convergence?

“…For example, early work by Cavaglia (1992) notes the changing patterns in the behaviour of real interest differentials over time by utilising Kalman filtering techniques, while Fountas and Wu (1999) work within a cointegration approach that allows for structural breaks in the series and find evidence in favour of RIP in EU member countries. Pippenger and Goering (1993) and others argue that the presence of threshold nonlinearities reduces the power of standard unit root and cointegration tests. Indeed, Michael et al (1997) show that cointegration or unit root tests may be biased when the linear alternative neglects nonlinearity of smooth transition autoregressive (STAR) type models.…”

Non-linearities in the dynamics of oil prices

“…Recently, however, there has been an increasing interest in examining non-linear adjustment in key economic variables, such as interest rates, inflation and real exchange rates, because if non-linearity is present but ignored and linear models, such as the Augmented-Dickey Fuller (ADF) unit root test, are used, this may result in a misleading conclusion about the time-series properties of the variables. For example, Pippenger and Goering (1993), Balke and Fomby (1997), Enders and Granger (1998), and Caner and Hansen (2001) show that linear unit root tests and cointegration tests have low power in the presence of nonlinearity. In particular, Pippenger and Goering argue that many economic relationships involve economic variables that have implicit transaction costs or arbitrage boundaries where arbitrage is too expensive and, thus, does not take place.…”