Nonparametric and Semiparametric Approaches in Financial Econometrics FAME/NCCR Doctoral Course

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1 Nonparametric and Semiparametric Approaches in Financial Econometrics FAME/NCCR Doctoral Course Oliver Linton April 28, 2003 Instructor: Oliver B. Linton. web page Time and Location: Monday :00-13:00, 14:00-17:00 College Propédeutique Room201; Tuesday :00-12:00, 13:00-15:00 Main Building Room 4202 Course Description: This course covers nonparametric and semiparametric approaches in Financial Econometrics. We rst review nonparametric and semiparametric methods and techniques. We then look at non and semiparametric models for volatility, nonparametric methods for estimating static yield curves, and estimation of dynamic yield curve models. 1 Econometric Methods Bickel, P. J., Klaassen, C. A. J., Ritov, Y. and J. A. Wellner (1993). E cient and adaptive estimation for semiparametric models. The John Hopkins University Press, Baltimore and London. Bosq, D (1998). Nonparametric Statistics for Stochastic Processes. Estimation and Prediction. Springer, Berlin. Fan, J. (1992). Design-adaptive nonparametric regression. J. Am. Statist Soc. 82, Härdle, W. (1990). Applied Nonparametric Regression. Cambridge University Press. Härdle, W., and O.B. Linton (1994). Applied nonparametric methods. in The Handbook of Econometrics, vol. IV, eds. D.F. McFadden and R.F. Engle III. North Holland. 1

2 Hastie, T. and Tibshirani, R. (1990). Generalized Additive Models. Chapman and Hall, London. Horowitz, J.L. (1998). Semiparametric methods in econometrics. Springer-Verlag: Berlin. Mammen, E., O. Linton, and Nielsen, J. P. (1999). The existence and asymptotic properties of a back tting projection algorithm under weak conditions. Annals of Statistics. Masry, E. (1996). Multivariate local polynomial regression for time series: Uniform strong consistency and rates. J. Time Ser. Anal. 17, Masry, E., and J. Fan (1997). Local Polynomial Estimation of Regression Functions for Mixing Processes. Scandinavian Journal of Statistics 24, Newey, W., and D.F. McFadden (1994). Large Sample Estimation and Hypothesis Testing. in The Handbook of Econometrics, vol. IV, eds. D.F. McFadden and R.F. Engle III. North Holland. Pagan, A and A. Ullah (1999). Nonparametric Econometrics. Cambridge University Press. Powell, J.L. (1994). Estimation of Semiparametric Models. in The Handbook of Econometrics, vol. IV, eds. D.F. McFadden and R.F. Engle III. North Holland. Robinson, P.M. (1983). Nonparametric estimation for time series models, Journal of Time Series Analysis, 4, Stone, C.J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, Teräsvirta, T., D. Tjøstheim, and C.W.J. Granger. (1994) Aspects of Modelling Nonlinear Time Series in The Handbook of Econometrics, vol. IV, eds. D.L. McFadden and R.F. Engle, , Amsterdam: Elsevier. Tong, H. (1990). Nonlinear Time Series Analysis: A dynamic Approach, Oxford University Press, Oxford. 2 Semiparametric ARCH Models Audrino, F., and Bühlmann, P. (2001), Tree-structured GARCH models, Journal of The Royal Statistical Society, 63, Bollerslev, T., R.F. Engle, and D. Nelson (1994). ARCH Models. in The Handbook of Econometrics, vol. IV, eds. D.F. McFadden and R.F. Engle III. North Holland. 2

3 Carrasco, M. and Chen, X. (2002), Mixing and Moment Properties of Various GARCH and Stochastic Volatility Models, Econometric Theory, 18, Drost, F.C., and C.A.J. Klaassen (1997). E cient estimation in semiparametric GARCH models. Journal of Econometrics 81, Drost, F.C.,and T.E. Nijman (1993): Temporal Aggregation of GARCH Processes, Econometrica 61, Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. in ation, Econometrica 50: Engle, R.F. and G. González-Rivera, (1991). Semiparametric ARCH models, Journal of Business and Economic Statistics 9: Engle, R.F. and V.K. Ng (1993). Measuring and Testing the impact of news on volatility. The Journal of Finance XLVIII, Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993), On the Relation Between the Expected Value and the Volatility of the Nominal Excess Returns on Stocks, Journal of Finance, 48, Gouriéroux, C. and A. Monfort (1992). Qualitative threshold ARCH models. Journal of Econometrics 52, Härdle, W. and A.B. Tsybakov, (1997). Locally polynomial estimators of the volatility function. Journal of Econometrics, 81, Lee, S., and Hansen, B. (1994), Asymptotic Theory for the GARCH(1,1) Quasi-Maximum Likelihood Estimator, Econometric Theory, 10, Linton, O. (1993) Adaptive estimation in ARCH models. Econometric Theory 9, Lumsdaine, R. L. (1996), Consistency and Asymptotic Normality of the Quasi-Maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models, Econometrica, 64, Masry, E., and D. Tjøstheim (1995). Nonparametric estimation and identi cation of nonlinear ARCH time series: strong convergence and asymptotic normality. Econometric Theory 11,

4 Nelsen, D. (1990). Conditional heteroskedasticityin asset returns: A new approach. Econometrica 59, Pagan, A.R., and G.W.Schwert (1990): Alternative models for conditionalstock volatility, Journal of Econometrics 45, Static Yield Curves Amihud, Y. and Mendelsohn, H. (1991) Liquidity, Maturity, and the Yields on U.S. Treasury Securities, The Journal of Finance, 46, Anderson, N., F. Breedon, M. Deacon, A. Derry, and G. Murphy (1996). Estimating and Interpreting the Yield Curve. John Wiley Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1997). The econometrics of nancial markets. Princeton University Press. Campbell, J.Y., and Shiller, R.J. (1991). Yield spreads and interest rate movements: A birds eye view. Review of Economic Studies 58, Chambers, D. R., Carleton, W. T. and Waldman, D. W. (1984), A New Approach to Estimation of the Term Structure of Interest Rates, Journal of Financial and Quantitative Analysis, 19, Dahlquist, M., and Svensson, L.E.O. (1996). Estimating the term structure of interest rates for monetary policy analysis. Scandinavian Journal of Economics 98, Eom, Y. H., Subrahmanyam, M., and Uno, J. (1998). Coupon e ects and the pricing of Japanese government bonds: an empirical analysis. Journal of Fixed Income, September, Estrella, A. and Mishkin, F. S. (1998). Predicting U.S. recessions: nancial variables as leading indicators. Review of Economics and Statistics 80, Fisher, M. E., Nychka, D. and Zervos, D. (1995). Fitting the term structure of interest rates with smoothing splines. Federal Reserve Bank Finance and Economics Discussion paper no Frankel, J. A. and Lown, C. S. (1994). An indicator of future in ation extracted from the steepness of the interest rate yield curve along its entire length. Quarterly Journal of Economics 109,

5 Linton, O., E. Mammen, J. Nielsen and C. Tanggaard (2001). Estimating Yield Curves by Kernel Smoothing Methods. Journal of Econometrics 105/ McCulloch, J. H. (1971). Measuring the Term Structure of Interest Rates. Journal of Business 44, McCullough, J. H. (1975). The Tax-Adjusted Yield Curve. The Journal of Finance, 30, Nelson, C.R. and Siegel, A. F. (1987). ParsimoniousModelling of Yield Curves, Journalof Business, 60, Schaefer, S. M. (1981). Measuring a tax-speci c term structure of interest rates in the market for British government securities. The Economic Journal, 91, Shea, G. S. (1984). Pitfalls in Smoothing Interest Rate Term Structure Data: Equilibrium Models and Spline Approximations. Journal of Financial and Quantitative Analysis, 19, Svensson, L. E. O. (1994). Estimating and Interpreting Forward Interest Rates: Sweden , CEPR Discussion Paper Tanggaard, C. (1992). Kernel smoothing of discount functions. Aarhus School of Business Working paper no Tanggaard, C. (1997). Nonparametric smoothing of Yield Curves. Review of Quantitative Finance and Accounting 9, Vasicek, O.A. and Fong, H.G. (1982). Term Structure Modelling using Exponential Splines. The Journal of Finance, 37, Di usions for Interest Rate Dynamics Aït-Sahalia, Y. (1996). Nonparametric Pricing of Interest rate Derivative Securities. Econometrica 64, 3, Aït-Sahalia, Y. (1996). Testing Continuous-TimeModels of the Spot Interest Rate. The Review of Financial Studies 9, Aït-Sahalia, Y. and A.W. Lo (1998). Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices. The Journal of Finance LIII,

6 Bandi, F. and P. Phillips (1998). Econometric Estimation of Di usion models. Unpublished paper, Yale University. Bosq, D. (1999). Nonparametric Statistics for Stochastic Processes. Lecture Notes in Statistics. Springer. Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1997). The econometrics of nancial markets. Princeton University Press. Conley, T.G., L.P. Hansen, E.G.J. Luttmer, and J.A. Scheinkman (1997). Short-Term Interest Rates as Subordinated Di usions. The Review of Financial Studies 10, Cox, J., J. Ingersoll and S. Ross (1985). A Theory of the Term Structure of Interest Rates. Econometrica, 53, Florens-Zmirou (1993). On Estimating the Di usion Coe cient from Discrete Observations. Applied Probability, Heath,D., R. Jarrow, A. Morton (1992). Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation. Econometrica 60, Hull, J. and A. White (1990). Pricing Interest Rate Derivative Securities. Review of Financial Studies 3 (4), Je rey, A. (1995). Single Factor Heath-Jarrow-Morton Term Structure Models based on Markov Spot Interest Rate Dynamics. Journal of Financial and Quantitative Analysis, 30 (4), Jiang, G. and J. Knight (1997). A Nonparametric Approach to the Estimation of Di usion Processes, with an Application to a Short Term Interest Rate Model. Econometric Theory, 13, ls Ritchken, P. and L. Sankarasubramanian (1995). Volatility Structures of Forward Rates and the Dynamics of the Term Structure Mathematical-Finance 5(1), Stanton, R. (1997). A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk. Journal of Finance 52, No. 5, Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5(2),

7 5 Other Topics Nonlinear dynamics, Tail index estimation, Stochastic Dominance, Bootstrap, 7