Estimating non-linear ARMA models using Fourier coefficients

Linear time-series models are often inadequate to capture the presence of asymmetric adjustment and/or conditional volatility. Parametric models of asymmetric adjustment and ARCH-type models necessitate specifying the nature of the non-linear coefficient. If there is little a priori information concerning the actual form of the non-linearity, the estimated model can suffer from a misspecification error. We show that a non-linear time-series can be represented by a deterministic time-dependent coefficient model without first specifying the nature of the non-linearity. The methodology is applied to real GDP and the NYSE Transportation Index.