NONPARAMETRIC MODELING OF THE CROSS- MARKET FEEDBACK EFFECT.

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NONPARAMETRIC MODELING OF THE CROSS- MARKET FEEDBACK EFFECT

Kernel-Based Estimation with Uncorrelated Innovation Process Kernel-Based Estimation with Autocorrelated Innovation Process Kernel and bandwidth selection Applications References

Kernel-Based Estimation with Uncorrelated Innovation Process

Kernel-Based Estimation with Autocorrelated Innovation Process - 1

Kernel-Based Estimation with Autocorrelated Innovation Process - 2 m(x)=(1-0.5x)(1-0.8x)(1-x)(1-1.2x) (1)

Kernel-Based Estimation with Autocorrelated Innovation Process - 3

Kernel-Based Estimation with Autocorrelated Innovation Process - 4

Kernel-Based Estimation with Autocorrelated Innovation Process - 5

Kernel-Based Estimation with Autocorrelated Innovation Process - 6 Opsomer, Wang and Yang (2000) Carroll, Linton, Mammen and Xiao (2002)

Kernel-Based Estimation with Autocorrelated Innovation Process Calculate a preliminary estimate of m: 2.Calculate the corresponding residuals: 3.Consider a  -th order autoregression of 4.Calculate an approximation of 5.The estimator of m(x) then is:

Kernel and bandwidth selection - 1

Kernel and bandwidth selection - 2

Applications

Application 1

Dependent variable: RES Method: Least Squares Date: 06/14/04 Time: 20:21 Sample(adjusted): Included observations: 3562 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1) RES(-2) RES(-3) RES(-4) RES(-5) RES(-6) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat

Application 2

Dependent Variable: RES Method: Least Squares Date: 06/14/04 Time: 17:43 Sample(adjusted): Included observations: 3435 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1) RES(-2) RES(-3) RES(-4) RES(-5) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat

Application 3

Dependent Variable: RES Method: Least Squares Date: 06/22/04 Time: 13:58 Sample(adjusted): Included observations: 3321 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1) RES(-2) RES(-3) RES(-4) RES(-5) RES(-6) RES(-7) RES(-8) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat

Application 4

Dependent Variable: RES Method: Least Squares Date: 06/16/04 Time: 22:57 Sample(adjusted): Included observations: 1557 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1) RES(-2) RES(-3) RES(-4) RES(-5) RES(-6) RES(-7) RES(-8) RES(-9) RES(-10) RES(-11) RES(-12) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat

Application 5

Dependent Variable: RES Method: Least Squares Date: 06/18/04 Time: 16:01 Sample(adjusted): Included observations: 3353 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1) RES(-2) RES(-3) RES(-4) RES(-5) RES(-6) RES(-7) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat

Application 6

Dependent Variable: RES Method: Least Squares Date: 06/18/04 Time: 12:29 Sample(adjusted): Included observations: 1627 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1) RES(-2) RES(-3) RES(-4) RES(-5) RES(-6) RES(-7) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat

Application 7

References Alexander, C. (2001), Market Models: A Guide to Financial Data Analysis, John Wiley & Sons, Chichester, UK Andersen, T. G., T. Bollerslev and F. X. Diebold (2003), “Some Like It Smooth, and Some Like It Rough: Untangling Continuous and Jump Components in Measuring, Modeling and Forecasting asset Return Volatility”, PIER Working Paper Andersen, T. G., T. Bollerslev and F. X. Diebold (2002), “Parametric and Nonparametric Volatility Measurement”, NBER Technical Working Paper 279 Andersen, T. G., T. Bollerslev, F. X. Diebold and P. Labys (2001), “Modeling and Forecasting Realized Volatility”, NBER Working Paper 8160 Campbell, J. Y., A. W. Lo and A. C. MacKinlay (1997), The Econometrics of Financial Markets, Princeton University Press, Princeton, New Jersey Carroll, R. J., O. B. Linton, E. Mammen, Z. Xiao (2002), “More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors”, Discussion Paper Nr. EM/02/435, The Suntory Centre, London School of Economics and Political Science Gasser, Th. (2001), “Practical and Theoretical Aspects of Nonparametric Function Fitting”, Euroworkshop on Statistical Modeling 2001, Universitat Zurich Green, W. H. (1993), “Econometric Analysis”, Macmillan Publishing Company, New York Neumann, M. H. (1995), “Automatic Bandwidth Choice and Confidence Intervals in Nonparametric Regression”, The Annals of Statistics, Vol. 23, No. 6 Opsomer, J., Y. Wang and Y. Yang (2000), “Nonparametric Regression with Correlated Errors”, Manuscript Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press, Cambridge, UK Pyndick, R. S. and D. L. Rubinfeld (1998), Econometric Models and Economic Forecasts, McGraw-Hill, Singapore Ruppert, D., A. P. Wand, U. Holst and O. Hossjer (1995), “Local Polinomial Variance Function Estimation”, School of Operations Research and Industrial Engineering, Cornell University