# Cycles -1

I’d like  to focus on cycles in business and economic forecasting for the next posts.

“Cycles” – in connection with business and economic time series – evoke the so-called business cycle.

Immediately after World War II, Burns and Mitchell offered the following characterization –

Business cycles are a type of fluctuation found in the aggregate economic activity of nations that organize their work mainly in business enterprises: a cycle consists of expansions occurring at about the same time in many economic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle

Earlier, several types of business and economic cycles were hypothesized, based on their average duration. These included the 3 to 4 year Kitchin inventory investment cycle, a 7 to 11 year Juglar cycle associated with investment in machines, the 15 to 25 year Kuznets cycle, and the controversial Kondratieff cycle of from 48 to 60 years.

Industry Cycles

I have looked at industry cycles relating to movements of sales and prices in semiconductor and computer markets. While patterns may be changing, there is clear evidence of semi-regular pulses of activity in semiconductors and related markets. These stochastic cycles probably are connected with Moore’s Law and the continuing thrust of innovation and new product development.

Methods

Spectral analysis, VAR modeling, and standard autoregressive analysis are tools for developing evidence for time series cycles. STAMP, now part of the Oxmetrics suite of software, fits cycles with time-varying parameters.

Sometimes one hears of estimations in the time domain moving into the frequency domain. Time series, as normally graphed with time on the horizontal axis, are in the “time domain.” This is where VAR and autoregressive models operate. The frequency domain is where we get indications of the periodicity of cycles and semi-cycles in a time series.

Cycles as Artifacts

There is something roughly analogous to spurious correlation in regression analysis in the identification of cyclical phenomena in time series. Eugen Slutsky, a Russian mathematical economist and statistician, wrote a famous “unknown” paper on how moving averages of random numbers can create the illusion of cycles. Thus, if we add or average together elements of a time series in a moving window, it is easy to generate apparently cyclical phenomena. This can be demonstrated with the digits in the irrational number π, for example, since the sequence of digits 1 through 9 in its expansion is roughly random.

Significances

Cycles in business have sort of reassuring effect, it seems to me. And, of course, we are all very used to any number of periodic phenomena, ranging from the alternation of night and day, the phases of the moon, the tides, and the myriad of biological cycles.

As a paradigm, however, they probably used to be more important in business and economic circles, than they are today. There is perhaps one exception, and that is in rapidly changing high tech fields of which IT (information technology) is still in many respects a subcategory.

I’m looking forward to exploring some estimations, putting together some quantitative materials on this.