Phase-Plane Plotting the Nondurable Goods Index. Nondurable goods last less than two years: Food, clothing, cigarettes, alcohol, but not personal computers!! The nondurable goods manufacturing index is an indicator of the economics of everyday life.
The nondurable goods manufacturing index is an indicator of the economics of everyday life.
The index has been published monthly by the US Federal Reserve Board since 1919.
It complements the durable goods manufacturing index.
We want to represent the data yj by a smooth curve x(t). The curve should have at least two smooth derivatives. We use spline smoothing, penalizing the size of the 4th derivative.
A function Pspline in S-PLUS is available by ftp from
There are three large loops separated by two small loops or cusps:
The Treasury Board, fearing that the economy was becoming overheated again, clamped down on the money supply. The effect was catastrophic, and nearly wiped out the fall cycle.
This new crash was even more dramatic than that of 1929, but was forgotten because of the outbreak of World War II.
Now look at three pivotal years, 1974 to 1976, when the Vietnam War ended and the OPEC oil crisis happened. Watch the shrinking of the fall cycle.
Over the last ten years the size of all three cycles have become much smaller.
We see by inspection that seasonal trends change systematically over time, and can also change abruptly.
We first estimate the principal components of seasonal variation, using a version of principal components analysis adapted to functional data, and sensitive only to effects periodic over one year.
We can compute scores at each year for these three principal components, sometimes called empirical orthogonal functions.
Plotting the evolution of these scores over the 51 years shows some interesting structural changes in the economics of everyday life.
Ramsay, J. O. and Ramsey, J. B. (2001) Functional data analysis of the dynamics of the monthly index of non‑durable goods production. Journal of Econometrics, 107, 327‑344.