We have developed a new test for non-linearity in time series data in discrete time. A comparative study has been conducted on Subba Rao, Gabr and Hinich's test, Keenan's test, Petruccelli and Davies' test, and the new test. Both simulated and real data are used in the study. The implication for forecasting is briefly discussed. KEY WORDS Non-linearity tests Threshold autoregression Functional expansion Bilinear models Symmetric distribution CUSUM Non-standard test Nuisance parameter
We may argue that there is a need for developing tests for non-linearity of time-series data. The following, not in any order of preference, represent some of the more obvious reasons.
(i) The tests will throw some light on the incidence rate of non-linearity in real time series.
(ii) The tests will suggest when it might be profitable to use non-linear predictors in preference to linear ones. For example, Tong (1983), Subba Rao and Gabr (1984), Maravall (1983) and Petruccelli and Davies (1986b) have demonstrated the great potential of non-linear prediction in diverse fields, ranging from the natural sciences to business. (iii) Non-linearity is often related to a fundamentally different system of dynamics from a linear one in terms of the underlying biology, physics, chemistry, engineering, etc. For example, the generating mechanism of the population cycles exhibited by the famous Australian blowfly data of A. J. Nicholson is known to be related to the food-limitation imitated in his laboratory experiments and the development time taken for an egg to be hatched into a fly. Many other examples are included in Tong (1983), for instance; A REVIEW OF SOME OF THE TESTS Frequency-domain approach Recently a number of tests have been proposed in the area. Slubba Rao and Gabr (1980) addressed the problem of 'testing for linearity' by bringing to fruition partially the proposal due * Now at the Temple University, U.S.A.