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An analogue model of phase-averaging procedures

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Author Info
Julia Campos
Neil R. Ericsson
David F. Hendry

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Abstract

This paper considers the statistical and econometric effect that fixed n-period phase-averaging has on time series generated by some simple dynamic processes. We focus on the variance and autocorrelation of the data series and of the disturbance term for levels and difference equations involving the phase-average data. Further, we examine the effect of phase-averaging on the erogeneity of variables in those equations and the implications phase-averaging has for conducting statistical inference. ; To illustrate our analytical results, we investigate claims by Friedman and Schwartz in their 1982 book Monetary Trends in the United States and the United Kingdom about what the properties of phase-average data and the relationships between those data ought to be. We present certain features of the observed series on velocity, examine how well our analytical model captures them, and contrast them with Friedman and Schwartz's predictions. While our model is an extremely simplified characterization of the phase-averaging adopted by Friedman and Schwartz, it does offer several insights into the likely consequences of their approach.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 303.

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Date of creation: 1987
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Related research
Keywords: Business cycles ; Time-series analysis;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hendry, David F. & Pagan, Adrian R. & Sargan, J.Denis, 1984. "Dynamic specification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 18, pages 1023-1100 Elsevier. [Downloadable!] (restricted)
  2. Hendry, David F, 1986. "Econometric Modelling with Cointegrated Variables: An Overview," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 201-12, August.
  3. Nicholls, D F & Pagan, A R, 1983. "Heteroscedasticity in Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 51(4), pages 1233-42, July. [Downloadable!] (restricted)
  4. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-77, August.
  5. Falk, Barry, 1986. "Further Evidence on the Asymmetric Behavior of Economic Time Series over the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1096-1109, October. [Downloadable!] (restricted)
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  6. Hendry, David F & Mizon, Grayham E, 1978. "Serial Correlation as a Convenient Simplification, not a Nuisance: A Comment on a Study of the Demand for Money by the Bank of England," Economic Journal, Royal Economic Society, vol. 88(351), pages 549-63, September. [Downloadable!] (restricted)
  7. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-28, August.
  8. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January. [Downloadable!] (restricted)
  9. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May. [Downloadable!] (restricted)
  10. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June. [Downloadable!] (restricted)
  11. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-28, April. [Downloadable!] (restricted)
  12. Allais, Maurice, 1972. "Forgetfulness and Interest," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 4(1), pages 40-73, Part I Fe. [Downloadable!] (restricted)
  13. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February. [Downloadable!] (restricted)
  14. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September. [Downloadable!] (restricted)
  15. Gould, John P & Nelson, Charles R, 1974. "The Stochastic Structure of the Velocity of Money," American Economic Review, American Economic Association, vol. 64(3), pages 405-18, June. [Downloadable!] (restricted)
  16. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1992. "Stochastic Trends and Economic Fluctuations," NBER Working Papers 2229, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  17. David F. Hendry & Neil R. Ericsson, 1985. "Assertion without empirical basis : an econometric appraisal of monetary trends in ... the United Kingdom, by Milton Friedman and Anna J. Schwartz," International Finance Discussion Papers 270, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  18. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Blackwell Publishing, vol. 53(3), pages 369-84, July. [Downloadable!] (restricted)
  19. Lucas, Robert E., 1977. "Understanding business cycles," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 5(1), pages 7-29, January. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Rajaguru GULASEKARAN & Tilak ABEYSINGHE, 2002. "The Distortionary Effects Of Temporal Aggregation On Granger Causality," Departmental Working Papers wp0204, National University of Singapore, Department of Economics. [Downloadable!]
  2. Michael D. Bordo & Lars Jonung & Pierre Siklos, 1993. "The Common Development of Institutional Change as Measured by Income Velocity: A Century of Evidence from Industrialized Countries," NBER Working Papers 4379, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Neil R. Ericsson & John S. Irons & Ralph W. Tryon, 2000. "Output and inflation in the long run," International Finance Discussion Papers 687, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
    Other versions:
  4. David F. Hendry & Neil R. Ericsson, 1989. "An econometric analysis of UK money demand in MONETARY TRENDS IN THE UNITED STATES AND THE UNITED KINGDOM by Milton Friedman and Anna J. Schwartz," International Finance Discussion Papers 355, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  5. Neil R. Ericsson & David F. Hendry & Hong-Anh Tran, 1993. "Cointegration, seasonality, encompassing, and the demand for money in the United Kingdom," International Finance Discussion Papers 457, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  6. Neil R. Ericsson, David F. Hendry & Kevin M. Prestiwch, . "The UK Demand for Broad Money over the Long run," Economics Papers W29, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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