Spectral Analysis of New York Stock Market Prices

Clive W. J. Granger and Oskar Morgenstern’s 1962 research memorandum examines New York stock-market prices through spectral analysis. Its central finding distinguishes time scales: short-run movements closely fit a random walk, while long-run components carry more weight than that model predicts. This qualification does not establish reliable investment cycles. Seasonal movements are negligible, the conventional business-cycle component is weak, and prices show little association with trading volume.

The authors introduce their investigation directly:

New York stock price series are analyzed by a new statistical technique.

The methodological novelty is to examine how different frequency bands contribute to observed variation, rather than identify cycles visually. Cross-spectral analysis extends the inquiry to relationships between series: coherence measures association at corresponding frequencies, while phase diagrams estimate frequency-specific leads and lags. Long-run relationships can thus be distinguished from short-run ones.

The memorandum situates this approach within an uneven literature:

While strictly theoretical studies are rare, the stock market having been largely neglected in the development of price theory, there exist, of course, descriptive works, too numerous to mention.

Against this background, the random-walk hypothesis supplies a parsimonious benchmark. The authors define it through uncorrelated price increments, but question whether apparently successful tests capture all relevant features of price behavior:

We shall show that, although the random walk model does appear to fit the data very well, there are certain prominent long-run features of the variables which are not explained by this model.

The crucial distinction is between randomness in first differences and the structure of price levels. Differencing attenuates low-frequency components: substantial long-run oscillations may coexist with increments that appear nearly indistinguishable from white noise. A flat spectrum of price changes therefore does not establish that long-run price movements conform to the model.

The exposition proceeds from an accessible account of spectral methods to empirical findings, with technical treatment and an inventory of series in the appendices. The evidence includes weekly Securities and Exchange Commission indices, monthly prices for six companies, longer Standard and Poor and Dow-Jones indices, and weekly price-and-volume observations for General Electric and Idaho Power. Historical coverage is especially important because slow movements require several repetitions before their amplitude can be estimated reliably. Moving-average detrending reduces leakage from power near zero frequency into neighboring bands. The authors also acknowledge that economic series rarely meet strict stationarity requirements.

First differences of the SEC indices produce nearly flat spectra. Detrended price levels, however, reveal excess low-frequency power, particularly for components lasting approximately two years or longer. Longer monthly indices allow closer examination of the conventional forty-month business cycle. Its peak is not statistically significant and accounts for less than ten percent of variance remaining after detrending; components lasting five years or more are substantially more important.

Seasonal findings similarly weaken familiar market expectations. No significant twelve-month component appears, and small monthly or seasonal-harmonic peaks contribute too little variance to support persuasive investment rules. Cross-spectral results complicate the idea of a uniformly integrated market: some sectoral indices are closely related, utilities are relatively disconnected, and no consistent leading stock-price index emerges.

The low coherence between prices and trading volume applies to ordinary oscillations, not necessarily exceptional movements or trends. Results attributed to M. Hatanaka likewise qualify the usefulness of stock prices as business-cycle indicators: modest estimated leads over industrial production and bank clearings accompany low coherence, limiting their predictive significance.

The memorandum’s contribution is a frequency-specific assessment of market behavior that separates long-run structure from exploitable predictability. Its results support short-run randomness while identifying additional long-run variation, without vindicating cyclical investment strategies. The investigation remains preliminary, and its technical discussion acknowledges that the methods do not uniquely distinguish the exact random-walk parameter from nearby alternatives. The resulting argument is deliberately discriminating: a model can fit much of the evidence while leaving consequential features unexplained.