A single-blind controlled competition among tests for nonlinearity and chaos

Abstract

Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a single-blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and nonchaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by e-mail, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos.

A Comparison of the Statistical Properties of Financial Variables in the USA, UK and Germany over the Business Cycle

“…This is a general test against the strict null hypothesis that the disturbance process is independent and identically distributed (i.i.d.). The null hypothesis was strongly rejected for each of our series, but the results are not reported since (as pointed out by Barnett et al, 1998) they are not informative about the type of non-linearity. Potentially more informative tests for non-linearity relating to the conditional mean are the RESET test (of Ramsey, 1974) and the neural net (NN) test (of Lee et al, 1993), results for both of which are included in Table 3.…”

Comparison of Near Neighbour and Neural Network in Travel Forecasting

“…Before forecasting the time series using nonlinear techniques, we should confirm the presence of nonlinearity in data (Barnett et al, 1995(Barnett et al, , 1996(Barnett et al, , 1997Ashley and Patterson, 2000). We propose the use of the BDS test (Brock et al, 1996) and Kaplan test (Kaplan, 1994(Kaplan, , 1995 because of their generality.…”

“…The Kaplan test (Kaplan 1994(Kaplan , 1995 was initially formulated to detect determinism in the underlying dynamics of a time series, though it has been used to detect deterministic or stochastic nonlinearities (see Barnett et al, 1995Barnett et al, , 1996Barnett et al, , 1997. It compares the distances between points in an m-dimensional embedded space with the distances between their images.…”

Tests of non‐linearity using LIFFE futures transactions price data

“…A rejection of the linear null using the bispectrum test, as is the case here, is an important result since it indicates that non-linear dependence of a form in addition to, or instead of (but perhaps having the same properties as), ARCH is present in the data. As Barnett et al (1998) argue, rejection of the i.i.d. null by the Hinich test provides very strong evidence against the null hypothesis since the test is very conservative and can often fail to reject even if the data generating process is truly non-linear.…”

“…Barnett et al (1998) point out that the cumulants are the coe¤cients of the power series expansion of the logarithm of a distribution, rather than of the level, as is the case for the moments.…”