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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

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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Bibliographic Info

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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Handle: RePEc:fip:fedgif:303

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Related research

Keywords: Business cycles ; Time-series analysis;

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  1. 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.
  2. Falk, Barry L., 1986. "Further Evidence on the Asymmetric Behavior of Economic Time Series over the Business Cycle," Staff General Research Papers 11097, Iowa State University, Department of Economics.
  3. 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.
  4. 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.
  5. 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.).
  6. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  7. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
  8. 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.
  9. 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.
  10. 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.
  11. Lucas, Robert E., 1977. "Understanding business cycles," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 5(1), pages 7-29, January.
  12. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
  13. 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.
  14. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  15. Nicholls, D F & Pagan, A R, 1983. "Heteroscedasticity in Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 51(4), pages 1233-42, July.
  16. 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.
  17. Allais, Maurice, 1972. "Forgetfulness and Interest," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 4(1), pages 40-73, Part I Fe.
  18. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September.
  19. Brunner, Karl & Meltzer, Allan H., 1986. "The national bureau method, International capital mobility, and other essays," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 24(1), pages 1-10, January.
  20. Weiss, Andrew A., 1984. "Systematic sampling and temporal aggregation in time series models," Journal of Econometrics, Elsevier, vol. 26(3), pages 271-281, December.
  21. 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.
  22. 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.
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Citations

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Cited by:
  1. 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.).
  2. 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.
  3. 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.
  4. 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.).
  5. Granger, C.W.J. & Siklos, P.L., 1993. "Systematic Sampling, Temporal Aggregation, Seasonal Adjustment, and Cointegration: Theory and Evidence," Working Papers 93001, Wilfrid Laurier University, Department of Economics.
  6. 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.
  7. Edward Nelson, 2012. "The correlation between money and output in the United Kingdom: resolution of a puzzle," Finance and Economics Discussion Series 2012-29, Board of Governors of the Federal Reserve System (U.S.).
  8. Yamin Ahmad & Ivan Paya, 2014. "Temporal Aggregation of Random Walk Processes and Implications for Asset Prices," Working Papers 14-01, UW-Whitewater, Department of Economics.
  9. 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.).

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