Observations on the application of chaos theory to the study of Kondratyev waves

Summary form only given. The existence of "long" waves years in economic variables, having a period of about 55, has been a contentious issue in economics since they were first proposed by Nikolai Dmitriyevich Kondratyev in the 1920s. Economic activity, as measured by changes in the rate of growth of GNP, fluctuates on a 25- to 30-year Kuznets cycle. Two of these cycles make up a Kondratyev wave, in which the PPI is seen to fluctuate between inflationary and deflationary episodes on an approximate 55-year period. All analyses of cycles in economic history suffer from a lack of data, and his problem becomes acute when considering long waves, simply because there are fewer possible cycles to observe. Furthermore, it has been known for a long time that windowing of time series data can impose a false periodicity. We use some simple calculations to demonstrate that similar pitfalls can occur when applying chaos theory to analyze time series. What, then, does our analysis suggest is the bottom line? To the question, "Do Kondratyev waves actually exist?" we would respond "Probably." We would be more certain if Berry could have included some more quantitative analysis, most importantly, a trial of his techniques on suitably constructed periodic, chaotic, and random time series. To the question, "Are the long waves endogenous or exogenous?" we would respond that the situation here is much more uncertain. In particular, performing chaos maps with synthetic data could be a crucial test. Finally, to the question, "Do technological innovations really cluster during periods of deflationary growth?" we would respond that, again, we would like to see more quantitative arguments, including cluster analysis.