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Continuous Time Modelling Based on an Exact Discrete Time Representation

Listed author(s):
  • Chambers, MJ
  • McCrorie, JR
  • Thornton, MA

This chapter provides a survey of methods of continuous time modelling based on an exact discrete time representation. It begins by highlighting the techniques involved with the derivation of an exact discrete time representation of an underlying continuous time model,providing specificc details for a second-order linear system of stochastic differential equations. Issues of parameter identification, Granger causality, nonstationarity, and mixed frequency data are addressed, all being important considerations in applications in economics and other disciplines. Although the focus is on Gaussian estimation of the exact discrete time model, alternative time domain (state space) and frequency domain approaches are also discussed. Computational issues are explored and two new empirical applications are included along with a discussion of applications in the field of macroeconometric modelling.

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Paper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 20497.

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Date of creation: Oct 2017
Handle: RePEc:esx:essedp:20497
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  1. Chambers, Marcus J., 2009. "Discrete Time Representations Of Cointegrated Continuous Time Models With Mixed Sample Data," Econometric Theory, Cambridge University Press, vol. 25(04), pages 1030-1049, August.
  2. Hamilton, James D., 1996. "This is what happened to the oil price-macroeconomy relationship," Journal of Monetary Economics, Elsevier, vol. 38(2), pages 215-220, October.
  3. McCrorie, J. Roderick, 2009. "Estimating Continuous-Time Models On The Basis Of Discrete Data Via An Exact Discrete Analog," Econometric Theory, Cambridge University Press, vol. 25(04), pages 1120-1137, August.
  4. Yu, Jun, 2014. "Econometric Analysis Of Continuous Time Models: A Survey Of Peter Phillips’S Work And Some New Results," Econometric Theory, Cambridge University Press, vol. 30(04), pages 737-774, August.
  5. Jewitt, Giles & Roderick McCrorie, J., 2005. "Computing estimates of continuous time macroeconometric models on the basis of discrete data," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 397-416, April.
  6. Harvey, A. C. & Stock, James H., 1989. "Estimating integrated higher-order continuous time autoregressions with an application to money-income causality," Journal of Econometrics, Elsevier, vol. 42(3), pages 319-336, November.
  7. Harvey, A. C. & Stock, James H., 1988. "Continuous time autoregressive models with common stochastic trends," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 365-384.
  8. Antonio Diez de los Rios & Enrique Sentana, 2011. "Testing Uncovered Interest Parity: A Continuous‐Time Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(4), pages 1215-1251, November.
  9. repec:eee:dyncon:v:79:y:2017:i:c:p:48-65 is not listed on IDEAS
  10. Bergstrom, A. R., 1986. "The Estimation of Open Higher-Order Continuous Time Dynamic Models with Mixed Stock and Flow Data," Econometric Theory, Cambridge University Press, vol. 2(03), pages 350-373, December.
  11. McCrorie, J. Roderick & Chambers, Marcus J., 2006. "Granger causality and the sampling of economic processes," Journal of Econometrics, Elsevier, vol. 132(2), pages 311-336, June.
  12. Bergstrom, A.R., 1997. "Gaussian Estimation of Mixed-Order Continuous-Time Dynamic Models with Unobservable Stochastic Trends from Mixed Stock and Flow Data," Econometric Theory, Cambridge University Press, vol. 13(04), pages 467-505, August.
  13. Marcus J. Chambers, 2011. "Cointegration and sampling frequency," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 156-185, July.
  14. Renault, Eric & Sekkat, Khalid & Szafarz, Ariane, 1998. "Testing for spurious causality in exchange rates," Journal of Empirical Finance, Elsevier, vol. 5(1), pages 47-66, January.
  15. Gandolfo, Giancarlo & Padoan, Pietro Carlo, 1990. "The Italian continuous time model : Theory and empirical results," Economic Modelling, Elsevier, vol. 7(2), pages 91-132, April.
  16. Chambers, Marcus J., 2016. "The estimation of continuous time models with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 390-404.
  17. Campbell, John Y. & Chacko, George & Rodriguez, Jorge & Viceira, Luis M., 2004. "Strategic asset allocation in a continuous-time VAR model," Journal of Economic Dynamics and Control, Elsevier, vol. 28(11), pages 2195-2214, October.
  18. Chambers, Marcus J. & Thornton, Michael A., 2012. "Discrete Time Representation Of Continuous Time Arma Processes," Econometric Theory, Cambridge University Press, vol. 28(01), pages 219-238, February.
  19. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
  20. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  21. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-577, May.
  22. Wymer, Clifford R., 1997. "Structural Nonlinear Continuous-Time Models In Econometrics," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 518-548, June.
  23. Chambers, Marcus J., 2001. "Temporal Aggregation And The Finite Sample Performance Of Spectral Regression Estimators In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 17(03), pages 591-607, June.
  24. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
  25. Hansen, Lars Peter & Sargent, Thomas J, 1983. "The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities," Econometrica, Econometric Society, vol. 51(2), pages 377-387, March.
  26. Wang, Xiaohu & Phillips, Peter C.B. & Yu, Jun, 2011. "Bias in estimating multivariate and univariate diffusions," Journal of Econometrics, Elsevier, vol. 161(2), pages 228-245, April.
  27. Bergstrom,Albert Rex & Nowman,Khalid Ben, 2012. "A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends," Cambridge Books, Cambridge University Press, number 9781107411234.
  28. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
  29. Chambers, Marcus J, 1992. "Estimation of a Continuous-Time Dynamic Demand System," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(1), pages 53-64, Jan.-Marc.
  30. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
  31. repec:cup:etheor:v:33:y:2017:i:03:p:739-754_00 is not listed on IDEAS
  32. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
  33. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
  34. Roderick McCrorie, J., 2001. "Interpolating exogenous variables in continuous time dynamic models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1399-1427, September.
  35. Thornton, Michael A. & Chambers, Marcus J., 2016. "The exact discretisation of CARMA models with applications in finance," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 739-761.
  36. Singer, Hermann, 1995. "Analytical Score Function for Irregularly Sampled Continuous Time Stochastic Processes with Control Variables and Missing Values," Econometric Theory, Cambridge University Press, vol. 11(04), pages 721-735, August.
  37. Chambers, Marcus J. & Roderick McCrorie, J., 2007. "Frequency domain estimation of temporally aggregated Gaussian cointegrated systems," Journal of Econometrics, Elsevier, vol. 136(1), pages 1-29, January.
  38. Nowman, K B, 1997. " Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 52(4), pages 1695-1706, September.
  39. Comte, F. & Renault, E., 1996. "Noncausality in Continuous Time Models," Econometric Theory, Cambridge University Press, vol. 12(02), pages 215-256, June.
  40. Harvey, A. C. & Stock, James H., 1985. "The Estimation of Higher-Order Continuous Time Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 1(01), pages 97-117, April.
  41. Bergstrom, A. R. & Nowman, K. B. & Wymer, C. R., 1992. "Gaussian estimation of a second order continuous time macroeconometric model of the UK," Economic Modelling, Elsevier, vol. 9(4), pages 313-351, October.
  42. Kevin Fergusson & Eckhard Platen, 2015. "Application of Maximum Likelihood Estimation to Stochastic Short Rate Models," Research Paper Series 361, Quantitative Finance Research Centre, University of Technology, Sydney.
  43. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  44. Chambers, Marcus J. & Kyriacou, Maria, 2013. "Jackknife estimation with a unit root," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1677-1682.
  45. Blevins, Jason R., 2017. "Identifying Restrictions For Finite Parameter Continuous Time Models With Discrete Time Data," Econometric Theory, Cambridge University Press, vol. 33(03), pages 739-754, June.
  46. Bergstrom, A. R., 1985. "The Estimation of Parameters in Nonstationary Higher Order Continuous-Time Dynamic Models," Econometric Theory, Cambridge University Press, vol. 1(03), pages 369-385, December.
  47. Phillips, P C B, 1991. "Error Correction and Long-Run Equilibrium in Continuous Time," Econometrica, Econometric Society, vol. 59(4), pages 967-980, July.
  48. Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
  49. McCrorie, J. Roderick, 2000. "Deriving The Exact Discrete Analog Of A Continuous Time System," Econometric Theory, Cambridge University Press, vol. 16(06), pages 998-1015, December.
  50. Marcus J. Chambers & J. Roderick McCrorie, 2006. "Identification And Estimation Of Exchange Rate Models With Unobservable Fundamentals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 573-582, May.
  51. Florens, Jean-Pierre & Fougere, Denis, 1996. "Noncausality in Continuous Time," Econometrica, Econometric Society, vol. 64(5), pages 1195-1212, September.
  52. Marcellino, Massimiliano, 1999. "Some Consequences of Temporal Aggregation in Empirical Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 129-136, January.
  53. Chambers, Marcus J., 1999. "Discrete time representation of stationary and non-stationary continuous time systems," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 619-639, February.
  54. Phillips, P C B, 1972. "The Structural Estimation of a Stochastic Differential Equation System," Econometrica, Econometric Society, vol. 40(6), pages 1021-1041, November.
  55. Barnett,William A. & Gandolfo,Giancarlo & Hillinger,Claude (ed.), 1996. "Dynamic Disequilibrium Modeling: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521462754, November.
  56. Zadrozny, Peter, 1988. "Gaussian Likelihood of Continuous-Time ARMAX Models When Data Are Stocks and Flows at Different Frequencies," Econometric Theory, Cambridge University Press, vol. 4(01), pages 108-124, April.
  57. Thornton, Michael A. & Chambers, Marcus J., 2017. "Continuous time ARMA processes: Discrete time representation and likelihood evaluation," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 48-65.
  58. Bergstrom, Albert Rex, 1983. "Gaussian Estimation of Structural Parameters in Higher Order Continuous Time Dynamic Models," Econometrica, Econometric Society, vol. 51(1), pages 117-152, January.
  59. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
  60. Johan H. L. Oud & Hermann Singer, 2008. "Continuous time modeling of panel data: SEM versus filter techniques," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(1), pages 4-28.
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