¹ The Kress Library at the Harvard Business School has a microfilm of the complete series copied from the originals held in the Goldsmith Library at the London School of Economics.

² Notes of Price Indices on Amsterdam Exchange by de Pryscouranten (1708–1788), Kress Library, Harvard University.

³ Mortimer, Thomas, Every Man His Own Broker (5th ed., London, 1762), p. 181Google Scholar: “India Bonds are the most convenient and profitable security can be possessed of, who has a quantity of cash unemployed, but which he knows not how soon he may have occasion for…. There is as little trouble with an India bond as with a Banknote…” This passage is quoted with approval by Ashton, T. S., Economic Fluctuations in England, 1700–1800 (Oxford, 1959), p. 112.Google Scholar

⁴ Box, G. E. P. and Jenkins, C. M., Time Series Analysis: Forecasting and Control (San Francisco, 1970), p. 44.Google Scholar

⁵ Our data consist of monthly observations over a period of 59 years with fully sufficient degrees of freedom for spectral methods. When sub-periods are considered, the number of lags estimated is reduced to take account of the reduction in degrees of freedom.

The spectral power function is the Fourier transform of the autocovariance function and the spectral density function the Fourier transform of the autocorrelation function. In practice we must estimate the autocovariance and autocorrelation functions with discrete data. Thus point estimates of these functions are averaged within a neighborhood of a given lag. Each weighting scheme defines a different estimator of the autocovariance function, and, correspondingly, of the spectral power function. In the selection of a given estimator one encounters the same consideration as with the more familiar estimation problems associated with the linear model. That is, it is a trade-off of bias and variance.

We have selected the Parzen windon (or estimator) for the analysis in this paper. See V. K. Smith and Marcis, R. G., “Applications of Spectral Analysis: Some Further Considerations,” Decision Sciences, 4 (January 1973)Google Scholar; Jenkins, G. M. and Watts, D. G., Spectral Analysis and its Applications (San Francisco, 1969)Google Scholar, and Fishman, G. S., Spectral Methods in Econometrics (Santa Monica: The Rand Corporation, 1968)Google Scholar, R-453PR for a discussion of the properties of alternative estimators.

The variance ratio for the Parzen estimator is given by .539L/N, where L = number of lags, N = number of observations. For the full period we have L = 60; for the sub-periods we use L = 24. The selection is somewhat arbitrary, involving a trade-off between variance and resolution of the estimates.

One additional point should be noted regarding the estimates of the spectral power functions. They are point estimates and have been represented as continuous diagrams for convenience. As point estimates, each value is a random variable. To the extent that we could define a specific null hypothesis then some discussion of the statistical significance of the estimates is warranted. In the absence of such a statement, however, selection of any one model such as random variation is arbitrary. Since our objective is descriptive, we have refrained from testing particular hypotheses with the spectral estimates.

⁶ Since spectral analysis requires that the time series involved be stationary, we detrended all variables using a first order polynomial trend estimate. See Fishman, Spectral Methods in Econometrics, and V. K. Smith and Marcis, R. G., “Applications of Spectral Analysis: Some Further Considerations,” Decision Sciences, 4 (Jan. 1973), for discussion of detrending techniques and their effects.Google Scholar

⁷ Smith, V. K. and Marcis, R. G., “A Time Series Analysis of Post Accord Interest Rates,” Journal of Finance, 27 (June 1972).CrossRefGoogle Scholar

⁸ Coherence may be interpreted as analogous to the R² statistic of regression and correlation analysis. The parallel with an ordinary correlation coefficient can be further exploited in the development of a test statistic for joint association as is done by Jenkins, G. M. and Watts, D. G., Spectral Analysis and its Applications (San Francisco, 1969), pp. 379–380Google Scholar note. The arctanh (), where _xy is the square root of the estimated coherence between X and Y at a given frequency, may be assumed to follow (approximately) a normal distribution. This assumption is used in developing the critical values for our null hypothesis of no association (i.e. K_xy = 0).

⁹ John, A.H., “Insurance Investment and the London Money Market of the 18th Century,” Economica, 20 (May 1953), pp. 137–158.CrossRefGoogle Scholar

¹⁰ Ashton, T. S., Economic Fluctuations in England 1700–1800, Oxford: p. 136.Google Scholar