IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v164y2011i2p268-293.html
   My bibliography  Save this article

Generalized spectral testing for multivariate continuous-time models

Author

Listed:
  • Chen, Bin
  • Hong, Yongmiao

Abstract

We develop an omnibus specification test for multivariate continuous-time models using the conditional characteristic function, which often has a convenient closed-form or can be accurately approximated for many multivariate continuous-time models in finance and economics. The proposed test fully exploits the information in the joint conditional distribution of underlying economic processes and hence is expected to have good power in a multivariate context. A class of easy-to-interpret diagnostic procedures is supplemented to gauge possible sources of model misspecification. Our tests are also applicable to discrete-time distribution models. Simulation studies show that the tests provide reliable inference in finite samples.

Suggested Citation

  • Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    • Handle: RePEc:eee:econom:v:164:y:2011:i:2:p:268-293
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440761100114X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Michael S. Johannes & Nicholas G. Polson & Jonathan R. Stroud, 2009. "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2559-2599, July.
    3. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. repec:bla:jfinan:v:58:y:2003:i:2:p:753-778 is not listed on IDEAS
    6. Su, Liangjun & White, Halbert, 2007. "A consistent characteristic function-based test for conditional independence," Journal of Econometrics, Elsevier, vol. 141(2), pages 807-834, December.
    7. Aït-Sahalia, Yacine & Kimmel, Robert L., 2010. "Estimating affine multifactor term structure models using closed-form likelihood expansions," Journal of Financial Economics, Elsevier, vol. 98(1), pages 113-144, October.
    8. 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.
    9. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    10. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    11. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    12. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    13. Brandt, Michael W. & Santa-Clara, Pedro, 2002. "Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets," Journal of Financial Economics, Elsevier, vol. 63(2), pages 161-210, February.
    14. Jiang, George J & Knight, John L, 2002. "Estimation of Continuous-Time Processes via the Empirical Characteristic Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 198-212, April.
    15. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    16. 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.
    17. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    18. 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..
    19. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, November.
    20. Aït-Sahalia, Yacine & Fan, Jianqing & Peng, Heng, 2009. "Nonparametric Transition-Based Tests for Jump Diffusions," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1102-1116.
    21. Li, Fuchun, 2007. "Testing The Parametric Specification Of The Diffusion Function In A Diffusion Process," Econometric Theory, Cambridge University Press, vol. 23(2), pages 221-250, April.
    22. Darrell Duffie & Lasse Heje Pedersen & Kenneth J. Singleton, 2003. "Modeling Sovereign Yield Spreads: A Case Study of Russian Debt," Journal of Finance, American Finance Association, vol. 58(1), pages 119-159, February.
    23. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    24. Fan, Yanqin, 1997. "Goodness-of-Fit Tests for a Multivariate Distribution by the Empirical Characteristic Function," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 36-63, July.
    25. Jarrow, Robert & Li, Haitao & Liu, Sheen & Wu, Chunchi, 2010. "Reduced-form valuation of callable corporate bonds: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 95(2), pages 227-248, February.
    26. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    27. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 211-239, June.
    28. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    29. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    30. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    31. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(6), pages 797-834, December.
    32. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    33. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, November.
    34. Jun Pan & Kenneth J. Singleton, 2008. "Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads," Journal of Finance, American Finance Association, vol. 63(5), pages 2345-2384, October.
    35. Bhardwaj, Geetesh & Corradi, Valentina & Swanson, Norman R., 2008. "A Simulation-Based Specification Test for Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 176-193, April.
    36. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, November.
    37. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    38. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    39. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    40. Gao, Jiti & King, Maxwell, 2004. "Adaptive Testing In Continuous-Time Diffusion Models," Econometric Theory, Cambridge University Press, vol. 20(5), pages 844-882, October.
    41. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    42. Easley, David & O'Hara, Maureen, 1992. "Time and the Process of Security Price Adjustment," Journal of Finance, American Finance Association, vol. 47(2), pages 576-605, June.
    43. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    44. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
    45. Chen, Song Xi & Gao, Jiti & Tang, Chenghong, 2005. "A test for model specification of diffusion processes," MPRA Paper 11976, University Library of Munich, Germany, revised Feb 2007.
    46. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, November.
    47. A. Ronald Gallant & George Tauchen, "undated". "Reproducing Partial Observed Systems with Application to Interest Rate Diffusions," Computing in Economics and Finance 1997 114, Society for Computational Economics.
    48. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
    49. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    50. Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292.
    51. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lazar, Emese & Qi, Shuyuan, 2022. "Model risk in the over-the-counter market," European Journal of Operational Research, Elsevier, vol. 298(2), pages 769-784.
    2. Bin Chen & Jinho Choi & Juan Carlos Escanciano, 2017. "Testing for fundamental vector moving average representations," Quantitative Economics, Econometric Society, vol. 8(1), pages 149-180, March.
    3. Emese Lazar & Shuyuan Qi & Radu Tunaru, 2020. "Measures of Model Risk in Continuous-time Finance Models," Papers 2010.08113, arXiv.org, revised Oct 2020.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:wyi:journl:002142 is not listed on IDEAS
    2. repec:wyi:journl:002117 is not listed on IDEAS
    3. Bin Chen & Yongmiao Hong, 2013. "Characteristic Function-Based Testing for Multifactor Continuous-Time Markov Models via Nonparametri," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    5. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    7. Song, Zhaogang, 2011. "A martingale approach for testing diffusion models based on infinitesimal operator," Journal of Econometrics, Elsevier, vol. 162(2), pages 189-212, June.
    8. repec:wyi:journl:002108 is not listed on IDEAS
    9. Egorov, Alexei V. & Hong, Yongmiao & Li, Haitao, 2006. "Validating forecasts of the joint probability density of bond yields: Can affine models beat random walk?," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 255-284.
    10. Chen, Bin & Hong, Yongmiao, 2012. "Testing For The Markov Property In Time Series," Econometric Theory, Cambridge University Press, vol. 28(1), pages 130-178, February.
    11. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
    13. Carrasco, Marine & Chernov, Mikhaël & Florens, Jean-Pierre & Ghysels, Eric, 2000. "Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions," IDEI Working Papers 116, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2002.
    14. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    15. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(2), pages 541-563, April.
    16. Xiaowei Zhang & Peter W. Glynn, 2018. "Affine Jump-Diffusions: Stochastic Stability and Limit Theorems," Papers 1811.00122, arXiv.org.
    17. Diep Duong & Norman Swanson, 2013. "Density and Conditional Distribution Based Specification Analysis," Departmental Working Papers 201312, Rutgers University, Department of Economics.
    18. Boswijk, H. Peter & Laeven, Roger J.A. & Vladimirov, Evgenii, 2024. "Estimating option pricing models using a characteristic function-based linear state space representation," Journal of Econometrics, Elsevier, vol. 244(1).
    19. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    20. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research.
    21. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
    22. Peng Cheng & Olivier Scaillet, 2002. "Linear-Quadratic Jump-Diffusion Modeling with Application to Stochastic Volatility," FAME Research Paper Series rp67, International Center for Financial Asset Management and Engineering.
    23. Durham, Garland B., 2003. "Likelihood-based specification analysis of continuous-time models of the short-term interest rate," Journal of Financial Economics, Elsevier, vol. 70(3), pages 463-487, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:164:y:2011:i:2:p:268-293. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.