David Mayer-Foulkes’ Download Page

The program U-Stat can be downloaded here

The PAHO report on investment in health can be downloaded here


New home page   |   Español











The research project "Health, Growth and Income Distribution in Latin America and the Caribbean: A Study of Determinants and regional and Local Behavior " was the winner of the 1997 Regional Research Competition on Investment in Health and Economic Growth of the Pan American Health Organization. To download the report in English or in Spanish, written by Mayer, D.; Mora, H. Cermeño, R. and Duryea, S, use one of the links below.

PAHO Health and Growth.pdf

OPS Crecimiento y Salud.pdf



To download the article Mayer, D., "A generalized fast algorithm for BDS-type Statistics", Studies in Nonlinear Dynamics and Econometrics, Volume 4, Number 1, April, 2000 visit the web page of the electronic journal at Studies in Nonlinear Dynamics and Econometrics, Volume 4.

The program U-Stat can be downloaded here



U-Stat is a Windows program to calculate several statistics based on the multi-dimensional distance histogram C(m,e). These include the following statistics:

  • The Correlation Dimension (Grassberger and Procaccia, 1983)
  • The BDS statistic (Brock, 1986a, 1986b; Brock, Dechert, Sheinkman and LeBaron, 1996)
  • The Simple Non-parametric Test (Mizrach, 1991, 1992, 1994)
  • The Statistical Correlation Dimension or Correlation Dimension Ratio (Mayer, 1995; Mayer and Feliz 1996)
  • Homogenized Integral U-Statistics (Mayer, 1998)
  • Further applications to vector series (Mayer, to be reported)

All confidence intervals are determined by using Brock’s (1986a, 1986b) reshuffling test.

We classify the statistics into orders 1 and 2, according to whether C(m,e) is a histogram of distances between all pairs in a set of vectors (order 2) or between all vectors in the set and a fixed point (order 1, as in the Simple Non-parametric Test). The order 2 histogram requires for its full calculation a number of operations of order N2 (if N is the number of vectors in the set). Thus several authors have devoted much care to the algorithms used for its calculation. U-Stat uses three, which have been verified to produce identical results.

  • The generalized fast algorithm (Mayer, 2000)
  • An algorithm generalizing LeBaron’s (1997) fast algorithm using sorting which is of order N when the calculation is restricted to small values of e (Mayer, to be reported)
  • An algorithm implementing Grassberger’s (1990) box-assisted algorithm (including the calculation of C(1, e) and the use of tao) which is also of order N when the calculation is restricted to small values of e (Mayer, to be reported)

The author thanks CONACYT for the funding received for the development of this program through the research project "Estadísticos U para Pruebas de Independencia No Lineales" (project number 3416P-S9607).



Several additions to U-Stat are presently being written. Thus if you mail me at david.mayer@cide.edu. I will notify you as soon as any changes are implemented.

The program may be freely distributed, so long as its use is cited and acknowledged in full and the terms of the license detailed in the program are kept (all rights reserved).

Please report on any problems, so that the program may be improved. At this stage the program has not been run on many machines so some problems may crop up. Any suggestions and bug reports are welcome.


Once you download the file ustat.zip, decompress it in a directory c:\ustat and follow these instructions.

1)   Copy the files VCF132.OCX, OC30.DLL, MFCANS32.DLL, MSVCRT20.DLL to the directory c:/Windows/System. If your system has more recent versions of some of these files, do not substitute them!

2)   Using the option Run in the Start menu, execute the command Regsvr32.exe Vcf132.ocx. If this command returns a success message, the program will be ready to run by double clicking on ustat.exe.


Brock, W. A. (1986a), "Distinguishing Random and Deterministic Systems: Abridged Version", Journal of Economic Theory 40 168-195.

Brock, W. A. (1986b), "Theorems on Distinguishing Deterministic from Random Systems", Dynamic Econometric Modeling, Proceedings of the third International Symposium in Economic Theory and Econometrics (Edited by W. A. Barnett, E. R. Berndt and H. White), 247-265, Cambridge University Press, New York.

Brock, W. A.; Dechert, W. D.; Sheinkman, J.A. and LeBaron, B. (1996), "A Test for Independence Based on the Correlation Dimension", Econometric Reviews 15(3): 197-235.

Dahlquist, G., and Björck, A. (1974), Numerical Methods, Prentice Hall, Inc., New Jersey, U.S.A.

Grassberger, Peter and Itamar Procaccia (1983), "Measuring the strangeness of strange attractors", Physica 9D, 189-208.

Grassberger, Peter (1990), "An optimized box-assisted algorithm for fractal dimensions'', Physics Letters A 148, 63-68.

LeBaron, Blake (1997) "A Fast Algorithm for the BDS Statistic'', Studies in Nonlinear Dynamics and Econometrics, July, 1997, 2(2): 53-59.

Mayer-Foulkes, D. (2000), "A generalized fast algorithm for BDS-type Statistics", forthcoming in Studies in Nonlinear Dynamics and Econometrics, Volume 4, Number 1, April.

Mayer-Foulkes, D. (1998), "Homogenized Integral U-Statistics for Test of Non-Linearity", Documento de Trabajo del CIDE, División de Economía, No. 118.

Mayer-Foulkes, D. (1995), "A statistical correlation dimension", Journal of Empirical Finance 2 277-293.

Mayer-Foulkes, D., and Raúl Anibal Feliz (1996), "Nonlinear dynamics in the stock exchange", Revista de Análisis Económico Vol. 11, No 1, pp 3-21.

Mizrach, B. (1991). "A simple Nonparametric test for independence." Working paper, Department of Finance, the Wharton School.

Mizrach, B. (1992). "Multivariate nearest-neighbour Forecasts of EMS Exchange Rates." Journal of Applied Econometrics 7; Supplement, S151-63.

Mizrach, B. (1994). "Using U-statistics to detect business cycle non-linearities." Chapter 14 in Willi Semmler (ed) Business Cycles: Theory and Empirical Investigation, Boston, Kluwer Press, 107-29.