Statistics, Economics, Computing, and other research

Please send comments or questions to: michaeldgodfrey@gmail.com.

This page provides information on work that I have been involved in mainly in statistics, economics, and computing.

It also includes two plays written by a good friend, Ed Hartwick. Look in Section G, below.

A. Statistics: Publications and Unpublished Notes

"Modern Techniques of Power Spectrum Estimation."
"An Exploratory Study of the Bi-Spectrum of Economic Time Series."
"Prediction for Non-Stationary Stochastic Processes."
"A Spectrum Analysis of Seasonal Adjustment."
"A Non-linear Analysis of Seasonal Variation."
"Berechnung und Ausschaltung von Saisonschwankung," by A. Wald.
"Extrapolation of 12-Month Moving Averages, by A. Wald.
"The tanh Transformation."
"An Algorithm for Least-Squares Polynomial Approximation."

B. Economics

"Prolegomena to a Theory of Organization," by O. Morgenstern.
On the Accuracy of Economic Observations, by O. Morgenstern.
The problem of Summation in Economic Science, by G. Nyblén.
"Why Economists Cannot Predict the Past."
"Certain Problems in the Application of Mathematical Economics."
An Incremental Cost Model of Message Toll Telephone Services.

C. Computers and Computing

The slides for a talk at Google in August 2012: ''Unreliable Systems built from Reliable Parts.''

The slides for a talk "Computer History" which is made up of items that I learned about computers and computing from about 1958.

D. von Neumann's Contributions to Computing and the EDVAC Computer Design

"Lectures on Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components," by John von Neumann. Notes Prepared by R. S. Pierce at Caltech.
1. "First Draft Report on the EDVAC," by John von Neumann, as published in the IEEE Annals of the History of Computing, vol. 15, no. 4, 1993, pp. 27-43.

F. Machine Independent Organic Software Tools

G. Literary Works by Edward Hartwick

A. Publications and Unpublished Notes

A paper on the foundations of statistical spectrum estimation and complex demodulation: C. Bingham, M. D. Godfrey, and J. W. Tukey, "Modern Techniques of Power Spectrum Estimation," IEEE Transactions on Audio and Electroacoustics, Volume AU-15, Number 2, June 1967, pp. 56-66.
A paper which describes computational techniques for bi-spectrum estimation: M. D. Godfrey, "An Exploratory Study of the Bi-Spectrum of Economic Time Series," Applied Statistics, Volume 14, Issue 1 (1965), pp. 48-69.
A paper "Prediction for Non-Stationary Stochastic Processes," published in Spectral Analysis of Time Series, Proceedings of an Advanced Seminar, Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, ed. Bernard Harris, John Wiley & Sons, 1967, pp. 259-269, which describes a complex-demodulation based method for extrapolation of time series from certain kinds of non-stationary stochastic processes. A sequel to the paper, "Prediction for Non-Stationary Stochastic Processes_2017_v2" dated 2017, presents a clarified derivation of the computational procedure, recomputed results, and computations on additional data. The program which was used in the paper, converted to Octave (Matlab), is available in gziped tar format. There is a short README file and an example data file organized in a form ready for processing. This file contains the complex-demodulation routines which, of course, can be used separately.
A paper which analyses seasonal adjustment methods, previous versions of which appeared in Chapter 24 of Essays in Honor of Oskar Morgenstern, ed. M. Shubik, Princeton University Press, pp. 367-421, and RM-64 of the Econometrics Research Program at Princeton. The paper, "A Spectrum Analysis of Seasonal Adjustment," written with H. Karreman is an analysis, using artificial data to simulate economic times series, of several seasonal adjustment methods. Included is an analysis of a new method which extends the Wald Method and makes use of more modern filtering and extrapolation techniques. This new method also has the property that it only requires the most recent data in order to generate the next values for each year. This avoids the problem of other methods which recompute the entire series and therefore produce new seasonally adjusted values for the entire history. The programs for this new method and some sample data, as described in Appendix C of the paper, are available in a tar file for download.
A proposed non-linear method for seasonal adjustment of economic time series: M. D. Godfrey, "A Non-linear Analysis of Seasonal Variation," in Proc. American Statistical Association, Business and Economic Statistics Section, 1964, pp. 196-199.
A monograph, "Berechnung und Ausschaltung von Saisonschwankungen," by A. Wald which develops a technique for seasonal adjustment of a time-series based on the assumption that the seasonal pattern changes slowly with time. The paper above, "A Non-linear Analysis of Seasonal Variation," made use of the ideas in this monograph. Published in Vienna in 1936. (In German.) Note that the size of this PDF is about 17MB.
A paper, "Extrapolation of 12-Month Moving Averages," by Abraham Wald which introduces a formal statistical method of extrapolating a time-series which contains a changing seasonal pattern. This paper was published in Vienna in 1937. (In German.)
A paper titled "The tanh Transformation" which describes some useful properties of the tanh function.
A short note, "An Algorithm for Least-Squares Polynomial Approximation," on a numerically stable method for polynomial fitting.

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B. Economics

I worked with Oskar Morgenstern for many years. Morgenstern made many contributions, most prominently his collaboration with John von Neumann on The Theory of Games and Economic Behavior. Morgenstern mentioned a RAND report that he had written, "Prolegomena to a Theory of Organization." I read the report and asked him if it would ever be published. He said he hoped to extend it to a fuller and more complete treatment, but he would not oppose its publication in its current form. The opportunity to expand the work never arose. I obtained permission from RAND to look for a publisher and tried several without success. So, this seems an appropriate place to make a thoughtful and important work more widely available. Anyone with an interest in how things are, are not, or might be, organized will enjoy and benefit from this report.
Oskar Morgenstern published his study, On the Accuracy of Economic Observations, first in 1950 and then, in revised form, in 1963. This remains the definitive empirical study of the fundamental inaccuracies of economic data. Present data suggest that, particularly in the U.S., accuracies have not improved since this work was published. This book has long been out of print. Used copies are available on the Web.
1. In 1951, Göran Nyblén published a remarkable book titled The Problem of Summation in Economic Science. The book explores the theoretical and practical problems which derive from the use of summation to arrive at the various aggregate variables (such as National Income, Consumption, Investment, etc.) which form the basis of macroeconomics. Only a few reviews appeared at the time of publication. Oskar Morgenstern frequently referred to the book. But, the ideas have not been pursued and the book is out of print, and at present no copies are available on the Web. Nyblén died in 1954.
2. In order to make this text more accessible, I OCR-converted the original and converted the result to TeX format, and then generated the PDF. For anyone who wants to read the book, use of this edited PDF copy may be more convenient. There may still be some typos due to the OCR and my editing. These can be checked against the original scanned text. (Note that the original is a scanned document converted to PDF which requires Adobe Reader 9 or above.)
3. On February 14, 2010 I completed a further proof reading and updated the edited PDF. Numerous minor typographical errors were corrected, and a few misprints in the equations were found and corrected. This version is, I hope, quite accurate. Of course, I would appreciate hearing about any errors that are found. For reference, this file size is: 5773663.
4. With only modest simplification, one can say that the three texts required for an understanding of Economics are: 1) von Neumann and Morgenstern, The Theory of Games and Economic Behavior, 2) Morgenstern, On the Accuracy of Economic Observations, and 3) Nyblén, The Problem of Summation in Economic Science. The simplification is substantially addressed by reading Keynes, and by following the references in Nyblén.
On September 28, 2007, I gave a talk at Martin Perl's seminar series. The subject was the present state of economics and economic data. The talk is titled "Why Economists Cannot Predict the Past." It argues that not only are economic data generally inadequate, but that the pervasive view that economies obey the laws of Newtonian physics is not a suitable theoretical basis. Both Morgenstern and Nyblén understood this. Unfortunately, their work is unknown in current economic teaching, theory, and practice.
Certain Problems in the Application of Mathematical Economics, is a 1965 paper that I wrote pointing out that classical mechanics equations and classical statistical methods are not appropriate in Economics.
In the early 1970's (before the divestiture) AT&T developed an analytic model of the long run incremental costs of message toll telephone service. Previously, the FCC rate determination process had been carried out through negotiation based on informal impressions of the effects of proposed rate plans. After the model became operational it provided an objective basis for rate determination. The FCC accepted the validity of the model results with respect to the regulatory constraints, and the allowed rate of return on the rate base. In fact, the FCC established their own analysis group which operated a copy of the model system using a duplicate of the computer system in use at AT&T. This basis for rate determination has continued to be used after the Corporate divestiture. This work (in scanned PDF of size 3.6MB and requires Adobe Reader 8 or above) was written for publication by R. L. Breedlove and myself with the title An Incremental Cost Model of Message Toll Telephone Services, American Telephone and Telegraph Company, 195 Broadway, New York City, New York, 1975. However, before publication it was decided that the information should remain Company Confidential. The printing of the book went ahead and it was used as a part of the documentation of the MTS Analysis System. A more readable PDF version which I converted to TeX is available here: Updated MTS Book .
I have a few copies of the printed book. Anyone with a very particular interest in this subject should contact me.

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C. Computers and Computing

The slides for a talk a "Unreliable Systems Built from Reliable Parts". In this talk I discuss the fact that most modern computing systems are unsafe in the sense that data are silently corrupted. Thus, digital information is being stored as if written on papyrus. It will, over time, decay to dust. In addition, hardware failures are not precisely detected and controlled recovery is almost never possible. Finally, an outline specification which can solve this problem was presented. This talk was first given at the Google SciFoo meeting in August 2012.
This talk was put together to record a number of items of technical interest which I learned over an extended period. The talk is "Computer History".

D. von Neumann's Contributions to Computing and to the EDVAC Computer Design

The original Caltech Notes: "Lectures on Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components," J. von Neumann, Notes Prepared by R. S. Pierce at Caltech. This version has been converted to TeX, but the original, scanned, Figures have been used.
A corrected version of the "First Draft Report on the EDVAC," by John von Neumann, as published in the IEEE Annals of the History of Computing, vol. 15, no. 4, 1993, pp. 27-43.
October 5, 2004: David Hemmendinger pointed out that the correct interpretation of von Neumann's logic diagrams, particularly Figure 2, depends on remembering the phrase at the beginning of Sec. 6.4: "All inhibitory stimuli, on the other hand, are absolute." If this is not noted, there is a temptation to treat the inhibitory stimulus like an inverter.
February 12, 2010: Paul Dlugosch pointed out that Figure 8 is incorrect in the sense that it does not match the textual description nor does it function as a discriminator. It is also true that the description is incomplete. The key correction is that the output node of the leftmost element should be connected to the middle element. The text at the beginning of the description should make clear that s and t must be asserted, not just t. When I did the editing I decided to leave all the Figures as drawn in the original, but I should have pointed out this oversight.
For those with a special interest in the history of computing, the original "First Draft Report on the EDVAC," is available. This is a scanned copy of the draft from the University of Pennsylvania Moore School Library. It is interesting to notice the last page which shows the date of each time the Report was checked out from the library.
A paper by me and David Hendry "The EDVAC as von Neumann Planned it" about the von Neumann Report, also published in the IEEE Annals of the History of Computing, vol. 15, no. 1, 1993, pp. 11-21.

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E. The Feynman Nobel Lecture

Feynman's Nobel Lecture, The Development of the Space-Time View of Quantum Electrodynamics, was derived from a version which Feynman gave as a talk at Caltech. The recording of this talk was transcribed and then provided to the Nobel Foundation and also for publication elsewhere. The version here was edited by Michael A. Gottlieb and me in order to correct a substantial number of substantive errors. The Nobel Foundation has accepted this version for use on their web site. It was expected that it will appear on their web site in due course. But, as of February 2012 this has not happened, so it seems unlikely that they will get around to it. In the meantime it is available at the URL above or here.

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F. Machine Independent Organic Software Tools

Starting in the the early 1970's, David Hendry, then at the University of London Institute for Computer Science, developed a language named SNIBBOL. In the period up to 1980 Hans Hermans, Robbie Hessenberg, and I contributed to and used the language. In 1980 we changed the name to MINT and published the book Machine Independent Organic Software Tools. This was published in several editions up to 1985. The software versions were MINT and MINT-2. Starting in 1991 we began work on MINT-3 and in 2001 completed the documentation in TeX and PDF as a new text Machine Independent Organic Software Tools. The complete MINT 3.0 system, with source code, documentation, examples, etc., is available as a tar file.

A number of problems have been identified since the initial version 3.0. These are:

Until January 8, 2002, there was an error in the VM source code due to mishandling of the CR/LF and ^Z sequences in DOS-like files. The error showed up if you tried to recompile the compiler, due to CR/LF sequences and a ^Z character at the end of several of the compiler source files. In any case, everything worked if you did not read files with CR/LF and ^Z in them. The ^Z's have been removed and the compiler now discards ^Z and CR. Barrie Stott reported this error. He has also reported a number of errors or omissions in the book.
As of February 22, 2002, essentially all outstanding corrections have been applied. The highlights are: TRAP was correctly implemented in the Virtual Machine and TRAP-dependent code was also corrected. A substantial number of typographical corrections and clarifications were made in the book. The cover page of the book now includes an Update History. I found a few problems on my own, but the vast majority of the errors were reported by Barrie Stott. The current version of the book (29 March, 2002) includes, I hope, all of Barrie's recommended corrections.
On 26 December, 2002, a correction was introduced to clarify operation on "little-ended" systems such as PowerPC Macs. A few other minor corrections were also added.
On 25 May, 2003, the reference VM (VM-C) was changed to use the GNU "readline" library. This makes interactive use much more convenient. The readline library is available for most systems, but it can be removed if necessary.
On 16 January 2004, two changes were introduced: (1) the VM was changed to provide operand stack expansion and (2) an omission in GETSTR was corrected. The error in GETSTR was that the length check was not correctly implemented and therefore input lines longer than 132 characters would cause failures.
Very minor updates were applied on 14 July, 2004. The changes to the book were all obvious typos. The change to the compiler was to tidy-up the pagination of output which is controlled by the TITLE directive. The VM error dump and trace output was made easier to read.
On 15 August, 2004 the VM was corrected to handle addresses above 31 bits. In a few places unsigned had not been used. Handling of segmentation fault was implemented, and the dump formats were further improved. Very minor changes were made to the book.
On 20 January, 2006, the VM code was modified to provide correct compilation on x64 architecture systems. Only very minor changes were needed since the stacks and VSTORE word sizes were left at 32 bits. Full compatibility exists for Portable Format and PDUMP format files from previous versions. (Actually, the object module as compiled on a Linux i386 system will execute on most Linux x64 systems. However, since RedHat has decided that its Enterprise customers do not deserve the compatible readline library, it will not run on RHEL4 x64. (The RedHat support organization recommends that Fedora should be used instead!)
On 5 April 2010 I converted the MINT book to use PDFTeX. This eliminated use of PostScript files and DVI. This was mainly a technical change, but I also implemented additional links for convenience. Generally, PDFTeX handles links and PDF graphics better than previous systems. (MetaPost is used to generate the Figures.) I updated the tar and zip files, but the only file changed in these is mint.pdf.

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G. Literary Works of Edward Hartwick

Edward Hartwick was born and educated in Germany, emigrated to the United States with his mother in the late 1930's, served in the US Army, earned his Ph.D. in Economics at Chicago, became a successful banker in Los Angeles, and then retired to Bend, Oregon. While a student he was a very active participant in the literary and cultural life of Berlin. In his retirement he took up writing and produced two remarkable works. He died in 2005.

In the mid 1990's my wife and I met Ed and we became close friends. He showed us the typescript of his play and mentioned that he had hoped to have it produced. I read, and much enjoyed, the play. In order to make it more readable and to improve its chances of gaining recognition, I offered to scan in the typescript and convert it to TeX and PDF format. The result is available through the link below. Ed sent this copy to several playhouses. Some were evidently quite interested. But, it quickly became apparent that the large number of characters in the play meant that the cost of production would be high. To date, no one has staged the play.

Ed had also mentioned his translation of Schiller's Don Carlos. At first he could not locate the typescript, but finally he did. I offered to convert this using the same techniques as for the play. Ed would have liked to see this published, but he did not take any serious steps toward this goal. People who have read his translation describe it as very much superior to other published translations. I am sure that this is accurate.

I mentioned the idea of putting these works on the web. While Ed had heard, mainly from me, about the web, he was not in favor of this idea. It seemed to him that this would result in his loss of control over his works. I left it as "just an idea." At this time he also mentioned his intent to assign the rights to his works to me. Since I heard nothing from his executors after his death, I assume that he did not carry out this intent. The works below show that he holds the copyright and my putting them on the web is covered by fair use. Any commercial use of these works would require permission from his estate.

Below are links to these two works:

The Thirteenth Madonna is set in the 1960's. It explores the development of an international political crisis. This was particularly topical in the 1960's, but the prospect of such crises continues to cloud our future.
This is his translation of Schiller's Don Carlos, Crown Prince of Spain. Other English translations have been published, but they do not approach this translation in retaining the sense of the original. Ed was a serious student of Schiller and had often seen his works performed in Berlin.

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As time permits we will add more material to this page, and provide more links to reports and publications.