Hostname: page-component-89b8bd64d-46n74 Total loading time: 0 Render date: 2026-05-11T09:36:25.538Z Has data issue: false hasContentIssue false
  • English
  • Français

The History of Continuous-Time Econometric Models

Published online by Cambridge University Press:  18 October 2010

A. R. Bergstrom
A. R. Bergstrom*
Affiliation:
University of Essex
Get access Rights & Permissions [Opens in a new window]

Extract

Although it is only during the last decade that continuous-time models have been extensively used in applied econometric work, the development of statistical methods applicable to such models commenced over 40 years ago. The first significant contribution to the problem of estimating the parameters of continuous-time stochastic models from discrete data was made by the British statistician Bartlett [1946] only three years after the pioneering contribution of Haavelmo [1943] on simultaneous equations models. Moreover, by this time the fundamental mathematical theory of continuous-time stochastic models was already well developed, major contributions having been made by some of the leading mathematicians of the twentieth century, including Einstein, Weiner, and Kolmogorov.

Information

Type
Research Article
Information
Econometric Theory , Volume 4 , Issue 3 , December 1988 , pp. 365 - 383
Copyright
Copyright © Cambridge University Press 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Abel, B. (1983). Optimal investment under uncertainty. American Economie Review 73: 228–233.Google Scholar
Abel, B. (1985). A stochastic model of investment marginal q and the market value of the firm. International Economic Review 26: 305–322.Google Scholar
Agbeyegbe, T.D. (1984). The exact discrete analog to a closed linear mixed-order system. Journal of Economic Dynamics and Control 7: 363–375.Google Scholar
Agbeyegbe, T.D. (1987). The exact discrete analog to a closed linear first-order continuous system with mixed sample. Econometric Theory 3: 143–149.Google Scholar
Armington, P. & Wolford, C. (1983). PAC-MOD: An econometric model of U.S. and global indicators. World Bank (Global Modeling and Projections Division), Division Working Paper No. 1983–3.Google Scholar
Armington, P. & Wolford, C. (1984). Exchange rate dynamics and economic policy. Arming-ton Wolford Associates.Google Scholar
Bachelier, L. (1900). Théorie de la Speculation. Annales des Sciences de l'Ecole Normale Supérieure 3: 21–86.Google Scholar
Bartlett, M.S. (1946). On the theoretical specification and sampling properties of autocorrelated time-series. Journal of the Royal Statistical Society Supplement 8: 27–41.10.2307/2983611Google Scholar
Bentzel, R. & Hansen, B. (1954). On recursiveness and interdependency in economic models. Review of Economic Studies 22: 153–168.10.2307/2295873Google Scholar
Bentzel, R. & Wold, H. (1946). On statistical demand analysis from the viewpoint of simultaneous equations. Skandinavisk Actuarietidscrift 29: 95–114.Google Scholar
Bergstrom, A.R. (1966). Nonrecursive models as discrete approximations to systems of stochastic differential equations. Econometrica 34: 173–182.Google Scholar
Bergstrom, A.R. (1967). The construction and use of economic models. London: English Universities Press.Google Scholar
Bergstrom, A.R. (1976). Statistical inference in continuous-time economic models. Amsterdam: North Holland.Google Scholar
Bergstrom, A.R. (1978). Monetary policy in a model of the United Kingdom. In Bergstrom, A.R., Catt, A.J.L., Peston, M.H. & Silverstone, B.D.J. (eds.), Stability and Inflation, Chapter 6, pp. 89–102. New York: Wiley.Google Scholar
Bergstrom, A.R. (1983). Gaussian estimation of structural parameters in higher-order continuous-time dynamic models. Econometrica 51: 117–152.Google Scholar
Bergstrom, A.R. (1984 a). Continuous-time stochastic models and issues of aggregation over time. In Griliches, A. & Intriligator, M.D. (eds.), Handbook of Econometrics, Chapter 20 and pp. 1146–1212. Amsterdam: North Holland.Google Scholar
Bergstrom, A.R. (1984 b). Monetary fiscal and exchange rate policy in a continuous-time model of the United Kingdom. In Malgrange, P. & Muet, P. (eds.), Contemporary Macroeconomic Modelling, Chapter 8 and pp. 183–206. Oxford: Blackwell.Google Scholar
Bergstrom, A.R. (1985). The estimation of parameters in nonstationary higher-order continuous-time dynamic models. Econometric Theory 1: 369–385.Google Scholar
Bergstrom, A.R. (1986). The estimation of open higher-order continuous-time dynamic models with mixed stock and flow data. Econometric Theory 2: 350–373.Google Scholar
Bergstrom, A.R. & Wymer, C.R. (1976). A model of disequilibrium neoclassical growth and its application to the United Kingdom. In Bergstrom, A.R. (ed.), Statistical Inference in Continuous-Time Economic Models, Chapter 10 and pp. 267–328. Amsterdam: North-Holland.Google Scholar
Brennan, M. J. & Schwartz, E.S. (1979). A continuous-time approach to the pricing of bonds. Journal of Banking and Finance 3: 133–155.10.1016/0378-4266(79)90011-6Google Scholar
Chow, G.C. (1981). Econometric analysis by control methods. New York: Wiley.Google Scholar
Doob, J.L. (1953). Stochastic processes. New York: Wiley.Google Scholar
Drollas, L.P. & Greenman, J.V. (1987). The price of energy and factor substitution in the U.S. economy. Energy Economics 6: 159–166.Google Scholar
Durbin, J. (1961). Efficient fitting of linear models for continuous stationary time series from discrete data. Bulletin of the International Statistical Institute 38: 273–282.Google Scholar
Edwards, D.A. & Moyal, J.E. (1955). Stochastic differential equations. Proceedings of the Cambridge Philosophical Society 51: 663–676.Google Scholar
Einstein, A. (1906). Zur theorie der Brownschen bewegung. Annalen der Physik 19: 371–381.Google Scholar
Friedman, A. (1975). Stochastic differential equations and applications. New York: Academic Press.Google Scholar
Gandolfo, G. (1981). Quantitative analysis and econometric estimation of continuous-time dynamic models. Amsterdam: North Holland.Google Scholar
Gandolfo, G. & Padoan, P.C. (1982). Policy simulations with a continuous-time macrodynamic model of the Italian economy: a preliminary analysis. Journal of Economic Dynamics and Control 4: 205–224.10.1016/0165-1889(82)90013-6Google Scholar
Gandolfo, G. & Padoan, P.C. (1984). A disequilibrium model of continuous-time macroecono-metric model of the Italian economy. C.N.R. Progetto Finalizzato Struttura ed Evoluzione dell'Economia Italiana, Working Paper, November 1986, No. 6.Google Scholar
Gandolfo, G. & Padoan, P.C. (1987). The Mark V version of the Italian continuous-time model. Instituto di Economia della Facolta di Scienze Economiche e Bancarie, Siena.Google Scholar
Geweke, J. (1978). Temporary aggregation in the multiple regression model. Econometrica 46: 643–662.Google Scholar
Girshick, M.A. & Haavelmo, T. (1947). Statistical analysis of the demand for food: examples of simultaneous estimation of structural equations. Econometrica 15: 79–110.10.2307/1907066Google Scholar
Grenander, U. (1950). Stochastic processes and statistical inference. Arkiv für Matematkik 1: 195–277.Google Scholar
Haavelmo, T. (1943). The statistical implications of a system of simultaneous equations. Econometrica 11: 1–12.Google Scholar
Haavelmo, T. (1944). The probability approach in econometrics. Econometrica Supplement 12: 1–118.Google Scholar
Haavelmo, T. (1947). Methods of measuring the marginal propensity to consume. Journal of the American Statistical Association 42: 105–122.Google Scholar
Hansen, L. & Sargent, T.J. (1981). Identification of continuous-time rational expectations models from discrete data. Unpublished manuscript.Google Scholar
Hansen, L. & Sargent, T. J. (1983). The dimensionality of the aliasing problem. Econometrica 51: 377–388.10.2307/1911996Google Scholar
Harvey, A.C. & Stock, J.H. (1985). The estimation of higher-order continuous-time autoregressive models. Econometric Theory 1: 97–117.Google Scholar
Harvey, A.C. & Stock, J.H. (1986 a). Estimating integrated higher-order continuous-time autoregressions. LSE Econometrics Projects Discussion Paper No. H.2.Google Scholar
Harvey, A.C. & Stock, J.H. (1986 b). Estimation of multivariate continuous-time autoregressive models with common stochastic trends. LSE Econometrics Projects Discussion Paper No. H. 3.Google Scholar
Houthakker, H.S. & Taylor, L.D. (1966). Consumer demand in the United States 1929–1970: analysis and projections. Cambridge, Massachusetts: Harvard University Press.Google Scholar
Ito, K. (1946). On a stochastic integral equation. Proceedings of the Japanese Academy 1: 32–35.Google Scholar
Ito, K. (1951). On stochastic differential equations. Memoir of the American Mathematical Society 4: 51.Google Scholar
Jones, R.H. (1981). Fitting a continuous-time autoregression to discrete data. In Findley, D.F. (ed.), Applied Time Series Analysis, pp. 651–674. New York: Academic Press.Google Scholar
Jonson, P.D. & Trevor, R.G. (1981). Monetary rules: a preliminary analysis. Economic Record 57: 150–167.Google Scholar
Jonson, P.D., McKibbin, W.J. & Trevor, R.G. (1982). Exchange rates and capital flows. Canadian Journal of Economic 15: 669–692.10.2307/134921Google Scholar
Jonson, P.D., Moses, E.R. & Wyraer, C.R. (1977). The RBA 76 Model of the Australian economy. In Conference in Applied Economic Research, Reserve bank of Australia, pp. 9–36.Google Scholar
Kirkpatrick, G. (1987). Employment growth and economic policy: an econometric model of Germany. Tübingen: J.C.B. Mohr (Paul Siebeck).Google Scholar
Khintchine, A. (1934). Korrelationstheorie der stationäire stochastischen prozesse. Mathematische Annalen 109: 604–615.Google Scholar
Knight, M.D. and Wymer, C.R. (1978). A macroeconomic model of the United Kingdom. IMF Staff Papers 25: 742–778.Google Scholar
Kolmogorov, A. (1931). Über die analytischen methoden in der Wahrscheinlichkeitsrechnung. Mathematische Annalen 104: 415–458.10.1007/BF01457949Google Scholar
Koopmans, T.C. (1950 a). Statistical inference in dynamic economic models. York: Wiley.Google Scholar
Koopmans, T.C. (1950 b). Models involving a continuous-time variable. In Koopmans, T.C. (ed.), Statistical Inference in Dynamic Economic Models, Chapter 16 and pp. 384–392. New York: Wiley.Google Scholar
Koopmans, T.C., Rubin, H. & Leipnik, R.B. (1950). Measuring the equation systems of dynamic economics. In Koopmans, T.C. (ed.), Statistical Inference in Dynamic Economic Models, Chapter 2 and pp. 53–237. New York: Wiley.Google Scholar
Levich, R.M. (1983). Currency forecasters lose their way. Euromoney August 1983.Google Scholar
Malinvaud, E. (1980). Statistical methods of econometrics. Amsterdam: North Holland.Google Scholar
Mann, H.B. & Wald, A. (1943). On the statistical treatment of linear stochastic difference equations. Econometrica 11: 173–220.Google Scholar
Merton, R.C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. Review of Economics and Statistics 51: 247–257.Google Scholar
Merton, R.C. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3: 373–413.Google Scholar
Merton, R.C. (1973). An intertemporal capital asset pricing model. Econometrica 41: 867–887.Google Scholar
Phillips, A.W. (1954). Stabilization policy in a closed economy. Economic Journal 64: 290–323.Google Scholar
Phillips, A.W. (1959). The estimation of parameters in systems of stochastic differential equations. Biometrika 46: 67–76.Google Scholar
Phillips, P.C.B. (1972). The structural estimation of a stochastic differential-equation system. Econometrica 40; 1021–1041.10.2307/1913853Google Scholar
Phillips, P.C.B. (1973). The problem of identification in finite parameter continuous-time models. Journal of Econometrics 1: 351–362.Google Scholar
Phillips, P.C.B. (1974). The estimation of some continuous-time models. Econometrica 42: 803–824.Google Scholar
Phillips, P.C.B. (1976). The estimation of linear stochastic differential equations with exogenous variables. In Bergstrom, A.R. (ed.) Statistical Inference in Continuous-Time Economic Models, Chapter 7 and pp. 135–174. Amsterdam: North Holland.Google Scholar
Phillips, P.C.B. (1978). The treatment of flow data in the estimation of continuous-time systems. In Bergstrom, A.R., Catt, A.J.L., Peston, M.H. & Silverstone, B.D.J. (eds.), Stability and Inflation, Chapter 15 and pp. 251–21 A. New York: Wiley.Google Scholar
Phillips, P.C.B. (1987 a) Time series regression with a unit root. Econometrica 55: 277–302.Google Scholar
Phillips, P.C.B. (1987 b). Asymptotic expansions in nonstationary vector autoregressions. Econometric Theory 3: 45–68.Google Scholar
Richard, D.M. (1978). A dynamic model of the world copper industry. IMF Staff Papers 25: 779–833.Google Scholar
Robinson, P.M. (1976 a). Fourier estimation of continuous-time models. In Bergstrom, A.R. (ed.), Statistical Inference in Continuous-Time Economic Models, Chapter 9 and pp. 215–226. Amsterdam: North Holland.Google Scholar
Robinson, P.M. (1976 b). The estimation of linear differential equations with constant coefficients. Econometrica 44: 751–764.10.2307/1913441Google Scholar
Robinson, P.M. (1976 c). Instrumental variables estimation of differential equations. Econometrica 44: 765–776.Google Scholar
Robinson, P.M. (1977). The construction and estimation of continuous-time models and discrete approximations in econometrics. Journal of Econometrics 6: 173–198.Google Scholar
Robinson, P.M. (1980 a). Continuous model fitting from discrete data. In Brillinger, D.R. & Tiao, G.C. (eds.), Directions in Time Series, pp. 263–278. East Lansing, Michigan: Institute of Mathematical Statistics.Google Scholar
Robinson, P.M. (1980 b). The efficient estimation of a rational spectral density. In Kunt, M. & de Coulon, F. (eds.), Signal Processing: Theories and Applications, 701–704. Amsterdam: North Holland.Google Scholar
Sargan, J.D. (1974). Some discrete approximations to continuous-time stochastic models. Journal of the Royal Statistical Society, Series B, 36: 74–90.Google Scholar
Sargan, J.D. (1976). Some discrete approximations to continuous-time stochastic models. In Bergstrom, A.R. (ed.), Statistical Inference in Continuous-Time Economic Models, Chapter 3 and pp. 27–80. Amsterdam: North Holland.Google Scholar
Sassanpour, C. & Sheen, J. (1984). An empirical analysis of the effect of monetary disequilibrium in open economies. Journal of Monetary Economics 13: 127–163.Google Scholar
Sims, C.A. (1971). Discrete approximations to continuous-time distributed lag models in econometrics. Econometrica 39: 545–563.Google Scholar
Sims, C.A. (1980). Macroeconomics and reality. Econometrica 48: 1–48.Google Scholar
Stefansson, S.B. (1981). Inflation and economic policy in a small open economy: Ireland in the postwar period. Ph.D. Thesis, University of Essex, Colchester.Google Scholar
Strotz, R.H. (1960). Interdependence as a specification error. Econometrica 28: 428–442.Google Scholar
Strotz, R.H. & Wold, H. (1960). Recursive vs nonrecursive systems. Econometrica 28: 417–427.Google Scholar
Telser, L.G. (1967). Discrete samples and moving sums in stationary stochastic processes. Journal of the American Statistical Association 62: 484–499.10.1080/01621459.1967.10482922Google Scholar
Theil, H. (1954). Linear aggregation of economic relations. Amsterdam: North Holland.Google Scholar
Tullio, G. (1981). Demand management and exchange rate policy: the Italian experience. IMF Staff Papers 28: 80–117.Google Scholar
Tustin, A. (1953). The mechanisms of economic systems. London: Heinemann.Google Scholar
Whittle, P. (1951). Hypothesis testing in time-series analysis. Stockholm: Almqvist and Wicksell.Google Scholar
Whittle, P. (1953). The analysis of multiple stationary time series. Journal of the Royal Statistical Society, Series B 15: 125–139.Google Scholar
Wiener, N. (1923). Differential space. Journal of Mathematical Physics 2: 131–174.Google Scholar
Wold, H.O.A. (1952). Demand analysis. Stockholm: Almqvist and Wicksell.Google Scholar
Wold, H.O.A. (1954). Causality and econometrics. Econometrica 22: 162–177.Google Scholar
Wold, H.O.A. (1956). Causal inference from observational data: a review of ends and means. Journal of the Royal Statistical Society, Series A 119: 28–50.10.2307/2342961Google Scholar
Wold, H.O.A. (1960). A generalization of causal chain models. Econometrica 28: 442–463.Google Scholar
Wymer, C.R. (1972). Econometric estimation of stochastic differential-equation systems. Econometrica 40: 565–577.Google Scholar
Wymer, C.R. (1973). A continuous disequilibrium adjustment model of the United Kingdom financial market. In Powell, A.A. & Williams, R.A. (eds.), Econometric Studies of Macro and Monetary Relations, pp. 301–304. Amsterdam: North Holland.Google Scholar
Wymer, C.R. (1978). Computer programs. International Monetary Fund.Google Scholar
Zadrozny, P.A. (1988). Gaussian likelihood of continuous-time ARMX models when data are stocks and flows at different frequencies. Econometric Theory 4: 108–124.Google Scholar