A method of jointly estimating the time-dependent variance of daily commodity price changes and their distribution is presented. The data are copper spot prices (1966-74) and sugar futures prices (1961-73), for London contracts. Much of the leptokurtosis observed in the price change distributions is shown to result from the mixinq of non-normal distributions whose variances differ substantially. There are important consequences for conventional autocorrelation tests, which falsely assume a constant variance. The usefulness of the logarithmic transformation of prices is assessed statistically and it is found that the transformation does help to equalise the variance of price changes.
Anderson, T.W. and A.M. Walker, 1964, “On the Asymptotic Distribution of the Autocorrelations of a Sample from a Linear Stochastic Process”, Annals of Mathematical Statistics35, 1296–1303.
2.
Bachelier, L., 1900, “Theory of Speculation”, reprinted in: P. Cootner, ed., 1964, The Random Character of Stock-market Prices (MIT Press, Boston).
3.
Blattberg, R.C. and N.J. Gonedes, 1974, “A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices”, Journal of Business47, 244–80.
4.
Box, G.E.P. and D.R. Cox, 1964, “An Analysis of Transformations”, Journal of the Royal Statistical Society, Series B, 26, 211–52.
5.
Cargill, T.F. and G.C. Rausser, 1975, “Temporal Price Behavior in Commodity Futures Markets”, Journal of Finance30, 1043–53.
6.
Clark, P.K., 1973, “A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices”, Econometrica41, 135–55.
7.
Fama, E.F., 1965, “The Behavior of Stock Market Prices”, Journal of Business38, 34–105.
8.
Fama, E.F. and R. Roll, 1968, “Some Properties of Symmetric Stable Distributions”, Journal of the American Statistical Association63, 817–36.
9.
Fielitz, B.D., 1971, “Stationarity of Random Data: Some Implications for the Distribution of Stock Price Changes”, Journal of Financial and Quantitative Analysis6, 1025–34.
10.
Granger, C.W.J., 1975, “A Survey of Empirical Studies in Capital Markets”, in: E.J. Elton and M.J. Gruber, eds., International Capital Markets (North-Holland/Elsevier, Amsterdam).
11.
Granger, C.W.J. and O. Morgenstern, 1970, Predictability of Stock Market Prices (Heath Lexington, Massachusetts).
12.
Granger, C.W.J, and P. Newbold, 1976, “Forecasting Transformed Series”, Journal of the Royal Statistical Society, Series B, 38, 189–203.
13.
Hagerman, R.L., 1978, “More Evidence on the Distribution of Security Returns”, Journal of Finance33, 1213–21.
14.
Hsu, D.A., R.B. Miller and D.W. Wichern, 1974, “On the Stable Paretian Behavior of Stock Market Prices”, Journal of the American Statistical Association69, 108–13.
15.
Kendall, H.G. and A. Stuart, 1973, “The Advanced Theory of Statistics”, Volume 2 (third edition, Charles Griffin, London).
16.
Mandelbrot, B., 1963, “The Variation of Certain Speculative Prices”, Journal of Business36, 394–419.
17.
Nelson, H.L. and C.W.J. Granger, 1979, “Experience with Using the Box-Cox Transformation when Forecasting Economic Time Series”, Journal of Econometrics10, 57–70.
18.
Osborne, M.F.M., 1959, “Brownian Motion in the Stock Market”, Operations Research10, 145–73.
19.
Paulson, A.S., E.W. Holcomb and R.A. Leitch, 1975, “The Estimation of the Parameters of the Stable Laws”, Biometrika62, 163–70.
20.
Praetz, P.D., 1969, “Australian Stock Prices and the Random Walk Hypothesis”, Australian Journal of Statistics11, 123–39.
21.
Praetz, P.D., 1972, “The Distribution of Share Price Changes”, Journal of Business45, 49–55.
22.
Praetz, P.D. and E.J.G. Wilson, 1978, “The Distribution of Stock Market Returns: 1958-1973”, Australian Journal of Management, 3, 79–90.
23.
Rocca, L.H., 1969, Time Series Analysis of Commodity Futures Prices, doctoral thesis, University of California, Berkeley.
24.
Taylor, S.J., 1979a, “Price-trends in Capital Markets - a Survey of Models, Autocorrelation Tests, Forecasts, Purchasing and Speculation”, unpublished paper presented at the sixth annual meeting of the European Finance Association.
25.
Taylor, S.J., 1979b, “Empirical Evidence for Trends in Capital Markets”, Economics Letters, forthcoming.
26.
Taylor, S.J. and B.G. Kingsman, 1977, “Comment: an Autoregressive Forecast of the World Sugar Future Option Market”, Journal of Financial and Quantitative Analysis12, 883–90.
27.
Taylor, S.J. and B.G. Kingsman, 1978, “Non-stationarity in Sugar Prices”, Journal of the Operational Research Society29, 971–80.
28.
Taylor, S.J. and B.G. Kingsman, 1979, “Price-trends in Commodity Markets: Models and Empirical Evidence”, unpublished manuscript, Department of Operational Research, University of Lancaster, Lancaster.
29.
Westerfield, R., 1977, “The Distribution of Common Stock Price Changes: an Application of Transactions Time and Subordinated Stochastic Models”, Journal of Financial and Quantitative Analysis12, 743–65.
30.
Wichern, D.W., R.B. Miller and D.A. Hsu, 1976, “Changes of Variance in First-order Autoregressive Time Series Models - with an Application”, Applied Statistics25, 248–56.
