Abstract: Barnett-Gallant-Hinich-Jungeilges-Kaplan-Jensen (1997) conducted a blind study of the power of a number of nonlinearity tests. This note questions their findings for the Hinich (1982) test by reanalyzing the data for a range of bandwidths. In contrast to the original findings that were not able to reject linearity for the GARCH, NLMA and ARCH models, our findings show that linearity is significantly rejected. The power of the original Hinich (1982) test and a proposed modification was examined using Monte Carlo methods.

This study employed the Hinich portmanteau bicorrelation test (Hinich and Patterson, 1995; Hinich, 1996) as a diagnostic tool to determine the adequacy of the GARCH model in describing the returns generating process of Malaysia’s stock market, specifically the Kuala Lumpur Stock Exchange Composite Index (KLSE CI). The bicorrelation results demonstrated that, while GARCH model is commonly applied to financial time series, this model cannot provide an adequate characterization for the underlying process of KLSE CI. Further investigation using the windowed test procedure revealed that this was due to the presence of episodic non-stationarity in the data, which could not be captured by any kind of ARCH or GARCH model, even after modifications to the specifications of the GARCH model. Thus, this study points to the need to continue the search for a parsimonious and congruent model capable of capturing the episodic features presence in the returns series of KLSE CI. Keywords: GARCH; Non-linearity; Non-stationarity; Data generating process; Bicorrelation; Malaysian stock market.

We propose a new test based on a Fourier series to approximate the unknown form of a nonlinear time-series model. The test has good size and power properties to detect structural breaks, seasonal parameters and random coefficients. Moreover, it has reasonable power to discriminate between nonlinearity in variables and nonlinearity in parameters. We use the test to show that U.S. inflation is appropriately estimated with a time-varying intercept that jumps in the late 1960’s, peaks in the early 1980’s and then begins to decline. German income and consumption data is used to illustrate the ability of the test to suggest the form of the nonlinearity. Keywords: Time-varying parameters, Fourier-series approximation, Nuisance parameters,