Cycles are a kind of a “vintage topic” in forecasting. Back in the 1920’s, business and industry cycles were a big-time research focus, influencing early work at the National Bureau of Economic Research (NBER) and elsewhere. But, it seems to me, modern time series methods evolved out of a critique of cycles – in the development of autocorrelation analysis by Udny Yule, for example, or in Eugen Slutsky’s observation that rolling sums of random numbers can mimic cyclical behavior.
Cycles and their extraction persist, however, in applied work for production concerns. Sometimes results surface in the academic literature, as with recent publications on cycles in the global semiconductor industry.
The concept of an “industry cycle” suggests dynamics somewhat independent of the ebb and flow of general economic activity. In semiconductors, Moore’s Law creates an underlying dynamic which may or may not coincide with the overall business cycle. Moore’s Law, of course, states that that integrated circuit densities roughly double and unit costs are approximately cut in half every 18 months. Semiconductor fabrication, therefore, involves significant retooling periodically to take advantage of this boost in processing power and reduction in unit costs.
Indeed, Moore’s Law is one reason why the modern electronics industry has been so fast-paced, compared with other manufacturing. Getting more for less is simply a offer you can’t refuse.
Tan and Mathews make an excellent summary of initiatives in the analysis of industry and, specifically, semiconductor cycles in their 2010 article Identification and Analysis of Industry Cycles. The market research vendor IC Insights also can be mentioned, as a leader in the innovative interpretation of semiconductor cycles.
One of the major conclusions of Tan and Mathews’ research is that,
..it seems plausible there are at least three cyclical components underlying the global semiconductor series, with cycle length of 4 years, 2.29 years, and 1.03 years respectively.
The purpose of this post is to suggest that it is, indeed, not terribly difficult to validate these ideas with readily available data and the Fast Fourier Transform.
Global semiconductor shipments are tracked by the Semiconductor Industry Association (SIA) which provides historical data back to the 1970’s, in the form of three month moving averages of global semiconductor billings.
The chart below shows monthly billings from 1978:3 to 2012:8, measured in US dollars. As can be seen, semiconductor sales are highly volatile. Three major events causing significant drops are (1) overcapacity in DRAM memory chips coinciding with the Asian currency crisis after 1995, (2) the deep recession in 2001 in global electronics related to overbuilding communications infrastructure and the aftermath of the Y2K mania, and (3) the more recent recession of 2008-2009.
A chart of year-over-year growth in billings is more suggestive of what we normally consider to be cycles.
There are 414 datapoints in this series.
I mention this detail, because it is relevant in applying and interpreting the Fast Fourier Transform (FFT), which I do with Matlab. The FFT translates from the time domain above to the frequency domain, as in the following graphic.
While the data seem “noisy” if we consider the relative maximum peak amplitudes at frequencies of 9, 16, and somewhat greater than 40, we find confirmation of a 3.83 year cycle, 2.16 year cycle, and some evidence of around a 1 year cycle. In other words, divide these peak frequencies into the total number of observations (414).
Tan and Mathews mention that a four-year cycle is consistent not only with the business cycle as identified by the NBER, but also the Kitchin inventory cycle. The two-year cycle looks to be more consonant with an industry cycle fueled by fab investment, supply-and-demand and pricing in semiconductors, related to Moore’s Law.
I’m experimenting with the Fourier Transform, and sometime will make the reverse movement – from a set of dominant frequencies back to an underlying waveform.