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NONPARAMETRIC MODELING OF THE CROSS- MARKET FEEDBACK EFFECT.

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Presentation on theme: "NONPARAMETRIC MODELING OF THE CROSS- MARKET FEEDBACK EFFECT."— Presentation transcript:

1 NONPARAMETRIC MODELING OF THE CROSS- MARKET FEEDBACK EFFECT

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

3 Kernel-Based Estimation with Uncorrelated Innovation Process

4 Kernel-Based Estimation with Autocorrelated Innovation Process - 1

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

6 Kernel-Based Estimation with Autocorrelated Innovation Process - 3

7 Kernel-Based Estimation with Autocorrelated Innovation Process - 4

8 Kernel-Based Estimation with Autocorrelated Innovation Process - 5

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

10 Kernel-Based Estimation with Autocorrelated Innovation Process - 7 1.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:

11 Kernel and bandwidth selection - 1

12 Kernel and bandwidth selection - 2

13 Applications

14 Application 1

15

16 Dependent variable: RES Method: Least Squares Date: 06/14/04 Time: 20:21 Sample(adjusted): 7 3568 Included observations: 3562 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1)0.0178260.0166351.0715960.2840 RES(-2)0.1761090.01655510.637560.0000 RES(-3)0.0969680.0167865.7767980.0000 RES(-4)0.0608750.0167863.6265860.0003 RES(-5)0.0987790.0165555.9665400.0000 RES(-6)0.1255080.0166357.5446770.0000 R-squared0.112173 Mean dependent var0.055124 Adjusted R-squared0.110925 S.D. dependent var2.414972 S.E. of regression2.277096 Akaike info criterion4.485362 Sum squared resid18438.45 Schwarz criterion4.495769 Log likelihood-7982.430 Durbin-Watson stat2.013146

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19 Application 2

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21 Dependent Variable: RES Method: Least Squares Date: 06/14/04 Time: 17:43 Sample(adjusted): 6 3440 Included observations: 3435 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1)0.0606880.0169553.5794280.0003 RES(-2)0.1144780.0169236.7645330.0000 RES(-3)0.0823530.0169784.8506650.0000 RES(-4)0.0856980.0169235.0639100.0000 RES(-5)0.1184750.0169546.9878520.0000 R-squared0.067172 Mean dependent var0.079875 Adjusted R-squared0.066084 S.D. dependent var4.195597 S.E. of regression4.054598 Akaike info criterion5.639034 Sum squared resid56388.38 Schwarz criterion5.647974 Log likelihood-9680.042 Durbin-Watson stat2.003669

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23

24 Application 3

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26 Dependent Variable: RES Method: Least Squares Date: 06/22/04 Time: 13:58 Sample(adjusted): 9 3329 Included observations: 3321 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1)-0.0593480.017315-3.4274630.0006 RES(-2)0.1415080.0172538.2019160.0000 RES(-3)0.1389600.0173757.9978980.0000 RES(-4)0.0575610.0174583.2971240.0010 RES(-5)0.0984820.0174585.6410780.0000 RES(-6)0.0778840.0173754.4825970.0000 RES(-7)0.1025090.0172535.9415150.0000 RES(-8)0.0817760.0173144.7232160.0000 R-squared0.128119 Mean dependent var0.129397 Adjusted R-squared0.126277 S.D. dependent var5.397193 S.E. of regression5.044927 Akaike info criterion6.077049 Sum squared resid84320.12 Schwarz criterion6.091763 Log likelihood-10082.94 Durbin-Watson stat2.003742

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28

29 Application 4

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31 Dependent Variable: RES Method: Least Squares Date: 06/16/04 Time: 22:57 Sample(adjusted): 13 1569 Included observations: 1557 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1)0.3062430.02538912.062260.0000 RES(-2)0.0958910.0264473.6258170.0003 RES(-3)0.0352570.0264841.3312830.1833 RES(-4)-0.0170350.026363-0.6461860.5183 RES(-5)0.0208530.0263510.7913330.4289 RES(-6)-0.0121250.026344-0.4602590.6454 RES(-7)-0.0273690.026345-1.0388610.2990 RES(-8)0.0218440.0263490.8290160.4072 RES(-9)0.1065410.0263534.0428950.0001 RES(-10)-0.0795810.026482-3.0051280.0027 RES(-11)0.0914950.0264133.4639720.0005 RES(-12)0.0450670.0253561.7773580.0757 R-squared0.162628 Mean dependent var0.041739 Adjusted R-squared0.156666 S.D. dependent var9.488767 S.E. of regression8.713841 Akaike info criterion7.175380 Sum squared resid117313.4 Schwarz criterion7.216617 Log likelihood-5574.033 Durbin-Watson stat2.000088

32

33 Application 5

34

35 Dependent Variable: RES Method: Least Squares Date: 06/18/04 Time: 16:01 Sample(adjusted): 8 3360 Included observations: 3353 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1)-0.0480150.017239-2.7852680.0054 RES(-2)0.1428120.0170458.3783920.0000 RES(-3)0.0857560.0171514.9999770.0000 RES(-4)0.0330970.0172021.9240170.0544 RES(-5)0.0909290.0171485.3027060.0000 RES(-6)0.1566800.0170429.1937530.0000 RES(-7)0.0741120.0172354.3001570.0000 R-squared0.088736 Mean dependent var0.100117 Adjusted R-squared0.087102 S.D. dependent var4.088733 S.E. of regression3.906608 Akaike info criterion5.565302 Sum squared resid51065.27 Schwarz criterion5.578073 Log likelihood-9323.228 Durbin-Watson stat2.013843

36

37

38 Application 6

39

40 Dependent Variable: RES Method: Least Squares Date: 06/18/04 Time: 12:29 Sample(adjusted): 8 1634 Included observations: 1627 after adjusting endpoints VariableCoefficientStd. Errort-StatisticProb. RES(-1)0.2091310.0247668.4442900.0000 RES(-2)0.0545370.0253052.1552110.0313 RES(-3)-0.0091470.025206-0.3628800.7167 RES(-4)0.0260020.0252141.0312560.3026 RES(-5)0.1057110.0252194.1917190.0000 RES(-6)0.0085630.0253200.3381730.7353 RES(-7)0.0797630.0247843.2182710.0013 R-squared0.083179 Mean dependent var0.010706 Adjusted R-squared0.079784 S.D. dependent var1.020863 S.E. of regression0.979292 Akaike info criterion2.800320 Sum squared resid1553.601 Schwarz criterion2.823529 Log likelihood-2271.060 Durbin-Watson stat2.009729

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43 Application 7

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50 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 03-025 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

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