Building Econometric Models

Testing for Non-linearity – The RESET Test

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• The “traditional” tools of time series analysis (acf’s, spectral analysis) may find no evidence that we could use a linear model, but the data may still not be independent.
• Portmanteau tests for non-linear dependence have been developed.
• The simplest is Ramsey’s RESET test, which took the form:
• Here the dependent variable is the residual series and the independent variables are the squares, cubes, …, of the fitted values.

Testing for Non-linearity – The BDS Test

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• Many other non-linearity tests are available - e.g., the BDS and bispectrum test
• BDS is a pure hypothesis test. That is, it has as its null hypothesis that the data are pure noise (completely random)
• It has been argued to have power to detect a variety of departures from randomness – linear or non-linear stochastic processes, deterministic chaos, etc)
• The BDS test follows a standard normal distribution under the null
• The test can also be used as a model diagnostic on the residuals to ‘see what is left’
• If the proposed model is adequate, the standardised residuals should be white noise.

Chaos Theory

• ‘Introductory Econometrics for Finance’ © Chris Brooks 2013

• Chaos theory is a notion taken from the physical sciences
• It suggests that there could be a deterministic, non-linear set of equations underlying the behaviour of financial series or markets
• Such behaviour will appear completely random to the standard statistical tests
• A positive sighting of chaos implies that while, by definition, long-term forecasting would be futile, short-term forecastability and controllability are possible, at least in theory, since there is some deterministic structure underlying the data
• Varying definitions of what actually constitutes chaos can be found in the literature.