Estimating Fourier ARDL cointegration model

[theking]

When applying the Fourier (Bootstrap) ARDL approach, the usual procedure is to incorporate Fourier terms into the model. However, I have observed that EViews generates the residuals used to obtain the error correction term (ECT) and the short-run coefficients from the long-run model without Fourier terms, rather than from the long-run model with Fourier terms. The fact that EViews, or researchers following this approach, use residuals from the long-run model that excludes Fourier terms when calculating the ECT and short-run coefficients raises the question of whether this practice reflects a methodological requirement or merely a software-specific limitation. I also acknowledge the possibility that my interpretation may be incorrect.