A Nonlinear Time Series Workshop: A Toolkit for Detecting and Identifying Nonlinear Serial Dependence (Dynamic Modeling and Econometrics in Economics and Finance Book 2)

The complex dynamic behavior exhibited by many nonlinear systems - chaos, episodic volatility bursts, stochastic regimes switching - has attracted a good deal of attention in recent years. __A Nonlinear Time Series Workshop__ provides the reader with both the statistical background and the software tools necessary for detecting nonlinear behavior in time series data. The most useful existing detection techniques are described, including Engle's LaGrange Multiplier test for conditional hetero-skedasticity and tests based on the correlation dimension and on the estimated bispectrum. These techniques are illustrated using actual data from fields such as economics, finance, engineering, and geophysics. The analysis ofwhat might be called "dynamic nonlinearity" in time series has its roots in the pioneering work ofBrillinger (1965) - who first pointed out how the bispectrum and higher order polyspectra could, in principle, be used to test for nonlinear serial dependence - and in Subba Rao and Gabr (1980) and Hinich (1982) who each showed how Brillinger's insight could be translated into a statistical test. Hinich's test, because ittakes advantage ofthe large sample statisticalpropertiesofthe bispectral estimates became the first usable statistical test for nonlinear serial dependence. We are forever grateful to Mel Hinich for getting us involved at that time in this fascinating and fruitful endeavor. With help from Mel (sometimes as amentor, sometimes as acollaborator) we developed and applied this bispectral test in the ensuing period. The first application ofthe test was to daily stock returns {Hinich and Patterson (1982, 1985)} yielding the important discovery of substantial nonlinear serial dependence in returns, over and above the weak linear serial dependence that had been previously observed. The original manuscript met with resistance from finance journals, no doubt because finance academics were reluctant to recognize the importance of distinguishing between serial correlation and nonlinear serial dependence. In Ashley, Patterson and Hinich (1986) we examined the power and sizeofthe test in finite samples Front Matter....Pages i-ix Nonlinearity in Stochastic Processes: What it is and Why it Matters....Pages 1-38 Detecting Nonlinear Serial Dependence....Pages 39-49 How to Run the Toolkit Program on a PC....Pages 51-62 Artificially Generated Data: Size Considerations....Pages 63-72 Artificially Generated Data: Power and Model Specification Considerations....Pages 73-93 Analysis of Stock Market Returns....Pages 95-119 Glint Tracking Errors in Radar....Pages 121-136 Seismic Data....Pages 137-159 Analysis of U.S. Real GNP....Pages 161-166 Dynamic Structure of Macroeconomic Technology Shocks....Pages 167-175 Climatological Data....Pages 177-188 Back Matter....Pages 189-201