Fourier ADL cointegration test to approximate smooth breaks with new evidence from Crude Oil Market

Economic data is typically subject to a number of different forms of structural breaks. Ignoring structural breaks in a model can lead to misspecification issues and false conclusions. This paper proposes a new Autoregressive Distributive Lag (ADL) cointegration test in the presence of nonlinear breaks approximated by a Fourier function. The test offers a simple way to capture smooth structural change in time series data. Exact break dates are not required, and the suggested methodology can accommodate unknown number and form of gradual structural change. The testing procedure circumvents the potential power loss which can result from adding more dummy variables in the testing equation. Simulation results show that our procedure has good size and power properties. We demonstrate our test on the empirical example of real oil prices, oil production, and real economic activity, which are subject to structural breaks. The new test suggests that variables are cointegrated, while a conventional ADL test ignores structural breaks and concludes the opposite. This result casts some doubt on conventional oil price models.