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A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models

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  • Januj Amar Juneja

    (San Diego State University)

Abstract

This paper conducts a computational analysis of several specifications of the affine term structure model (ATSM) to explore the tradeoff between estimation when parameter restrictions are imposed and computational burdens are simplified and estimation in the absence of parameter restrictions and the economic implications of the findings are able to be generalized. We measure the effects of this tradeoff using distance measures constructed from histograms containing data corresponding to important components of the state space model formulation for the ATSM generated from simulation analyses. In estimating each specification, we optimize the log-likelihood function for the underlying state space model using the Kalman filter (KF). We find that the introduction of parameter restrictions bolsters the variability in its computation by introducing complex parameter dependencies (e.g., higher order exponents, exponentiation, logarithms, logarithms of higher order exponents) that are difficult to interpret. For conditional moments, the introduction of parameter restrictions reduces the complexity of the parameter dependencies and this reduces the variability in its computation. Finally, we connect these insights obtained from the simulation analyses to the application of the KF using market data and perform consistency tests on each state space model to demonstrate the accuracy of the application of the KF. Suggestions for future research are provided.

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  • Januj Amar Juneja, 2022. "A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 173-220, June.
  • Handle: RePEc:kap:compec:v:60:y:2022:i:1:d:10.1007_s10614-021-10146-1
    DOI: 10.1007/s10614-021-10146-1
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    1. Christopher G. Lamoureux & H. Douglas Witte, 2002. "Empirical Analysis of the Yield Curve: The Information in the Data Viewed through the Window of Cox, Ingersoll, and Ross," Journal of Finance, American Finance Association, vol. 57(3), pages 1479-1520, June.
    2. Francis X. Diebold & Monika Piazzesi & Glenn D. Rudebusch, 2005. "Modeling Bond Yields in Finance and Macroeconomics," American Economic Review, American Economic Association, vol. 95(2), pages 415-420, May.
    3. Jackson, Laura E. & Owyang, Michael T. & Soques, Daniel, 2018. "Nonlinearities, smoothing and countercyclical monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 95(C), pages 136-154.
    4. Hlouskova, Jaroslava & Sögner, Leopold, 2020. "GMM estimation of affine term structure models," Econometrics and Statistics, Elsevier, vol. 13(C), pages 2-15.
    5. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    6. Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2009. "An arbitrage-free generalized Nelson--Siegel term structure model," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 33-64, November.
    7. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    8. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 115-130, March.
    9. Collin-Dufresne, Pierre & Goldstein, Robert S. & Jones, Christopher S., 2009. "Can interest rate volatility be extracted from the cross section of bond yields?," Journal of Financial Economics, Elsevier, vol. 94(1), pages 47-66, October.
    10. Dempster, M.A.H. & Tang, Ke, 2011. "Estimating exponential affine models with correlated measurement errors: Applications to fixed income and commodities," Journal of Banking & Finance, Elsevier, vol. 35(3), pages 639-652, March.
    11. Creal, Drew D. & Wu, Jing Cynthia, 2015. "Estimation of affine term structure models with spanned or unspanned stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 60-81.
    12. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    13. Antonio Diez de Los Rios, 2015. "A New Linear Estimator for Gaussian Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 282-295, April.
    14. Pierre Collin‐Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, August.
    15. Andrew Ang & Sen Dong & Monika Piazzesi, 2005. "No-arbitrage Taylor rules," Proceedings, Federal Reserve Bank of San Francisco.
    16. Date, Paresh & Wang, Chieh, 2009. "Linear Gaussian affine term structure models with unobservable factors: Calibration and yield forecasting," European Journal of Operational Research, Elsevier, vol. 195(1), pages 156-166, May.
    17. Pierre Collin‐Dufresne & Robert S. Goldstein & Christopher S. Jones, 2008. "Identification of Maximal Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 63(2), pages 743-795, April.
    18. Juneja, Januj, 2014. "Term structure estimation in the presence of autocorrelation," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 119-129.
    19. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.
    20. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2013. "Pricing the term structure with linear regressions," Journal of Financial Economics, Elsevier, vol. 110(1), pages 110-138.
    21. Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, vol. 42(6), pages 926-938, June.
    22. Hamilton, James D. & Wu, Jing Cynthia, 2012. "Identification and estimation of Gaussian affine term structure models," Journal of Econometrics, Elsevier, vol. 168(2), pages 315-331.
    23. Martino Grasselli & Claudio Tebaldi, 2008. "Solvable Affine Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 135-153, January.
    24. Malik, Sheheryar & Pitt, Michael K., 2011. "Particle filters for continuous likelihood evaluation and maximisation," Journal of Econometrics, Elsevier, vol. 165(2), pages 190-209.
    25. Januj Juneja, 2013. "A study of the solution to the Riccati equation in term structure modelling," Applied Financial Economics, Taylor & Francis Journals, vol. 23(23), pages 1797-1803, December.
    26. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    27. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    28. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May.
    29. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    30. Chib, Siddhartha & Ergashev, Bakhodir, 2009. "Analysis of Multifactor Affine Yield Curve Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1324-1337.
    31. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 300-314, July.
    32. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    33. Adam Goliński & Peter Spencer, 2021. "Estimating the Term Structure with Linear Regressions: Getting to the Roots of the Problem [Term Structure Persistence]," Journal of Financial Econometrics, Oxford University Press, vol. 19(5), pages 960-984.
    34. Marco Realdon, 2020. "Affine and quadratic models with many factors and few parameters," The European Journal of Finance, Taylor & Francis Journals, vol. 26(11), pages 1019-1046, July.
    35. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    36. David Bolder, 2001. "Affine Term-Structure Models: Theory and Implementation," Staff Working Papers 01-15, Bank of Canada.
    37. Juneja, Januj, 2017. "Invariance, observational equivalence, and identification: Some implications for the empirical performance of affine term structure models," The Quarterly Review of Economics and Finance, Elsevier, vol. 64(C), pages 292-305.
    38. Fernandes, Marcelo & Vieira, Fausto, 2019. "A dynamic Nelson–Siegel model with forward-looking macroeconomic factors for the yield curve in the US," Journal of Economic Dynamics and Control, Elsevier, vol. 106(C), pages 1-1.
    39. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    40. Dai, Qiang & Singleton, Kenneth J., 2002. "Expectation puzzles, time-varying risk premia, and affine models of the term structure," Journal of Financial Economics, Elsevier, vol. 63(3), pages 415-441, March.
    41. Chen, Ren-Raw & Scott, Louis, 2003. "Multi-factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model," The Journal of Real Estate Finance and Economics, Springer, vol. 27(2), pages 143-172, September.
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