1 Detecting and Modeling Nonlinearity in the Gas Furnace Data

The Hinich (1982) bispectrum test for nonlinearity and Gaussianity indicates that the residuals of the Tiao-Box (1981) constrained and unconstrained VAR models for the gas furnace data reject the assumption of Gaussianity and linearity over a grid of bandwidths for estimating the bispectrum. These findings call into question the specification of the linear VAR and VARMA models assumed by Tiao-Box (1981). Utilizing the Hinich (1996) nonlinearity test, the residuals of the VAR model were shown to exhibit episodic nonlinearity. The sensitivity of the results to outliers is investigated by estimating and testing the residuals of L1 and MINIMAX models from 1-6 lags. Building on the linear dynamic specification, a multivariate adaptive regression splines (MARS) model is estimated and shown to remove the nonlinearity in the residuals. Using MARS ANOVA analysis, a parsimonious four variable model was estimated and tested.