Comparing Fitted Models with the fit.models Package
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1 Comparing Fitted Models with the fit.models Package Kjell Konis Acting Assistant Professor Computational Finance and Risk Management Dept. Applied Mathematics, University of Washington
2 History of fit.models fit.models originally a function in the S-PLUS Robust Library for fitting a model robustly and by maximum likelihood fit.models extended to support models fit using other robust packages: robustbase, MASS::rlm fit.models extended to compare nested models fit.models becomes its own package
3 Comparing Robust and MLE fits library(factoranalytics) library(robust) Robust fit single factor model sf.rob <- lmrob(ham1 ~ SP500.TR, data = managers) Maximum likelihood fit single factor model sf.mle <- lm(ham1 ~ SP500.TR, data = managers) Fit model both ways sf.fm <- fit.models(c(robust = "lmrob", MLE = "lm"), HAM1 ~ SP500.TR, data = managers)
4 Generic Functions: summary(sf.fm) Calls: Robust: lmrob(formula = HAM1 ~ SP500.TR, data = managers) MLE: lm(formula = HAM1 ~ SP500.TR, data = managers) Residual Statistics: Min 1Q Median 3Q Max Robust: MLE: Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept): Robust: MLE: SP500.TR: Robust: e-12 MLE: e-14 Residual Scale Estimates: Robust: on 58 degrees of freedom MLE: on 58 degrees of freedom
5 Generic Functions: plot(sf.fm) Residuals vs. Fitted Values Robust MLE Residuals Fitted Values
6 Generic Functions: plot(sf.fm) Normal QQ Plot of Modified Residuals Robust MLE Empirical Quantiles of Modified Residuals Standard Normal Quantiles
7 Generic Functions: plot(sf.fm) Scale Location Robust MLE Modified Residuals Fitted Values
8 Generic Functions: plot(sf.fm) Modified Residuals vs. Leverage Robust MLE Modified Residuals Leverage
9 Comparing Nested Models Fit multifactor model mf <- lm(ham1 ~ EDHEC.LS.EQ + SP500.TR + US.10Y.TR, data = managers) Fit single factor model sf <- lm(ham1 ~ SP500.TR, data = managers) Create fit.models object nst.fm <- fit.models("tf" = mf, "SF" = sf) Generic function: coef(nst.fm) (Intercept) EDHEC.LS.EQ SP500.TR US.10Y.TR TF SF NA NA
10 Generic Function: summary(nst.fm) Calls: TF: lm(formula = HAM1 ~ EDHEC.LS.EQ + SP500.TR + US.10Y.TR, data = managers) SF: lm(formula = HAM1 ~ SP500.TR, data = managers) Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept): TF: SF: EDHEC.LS.EQ: TF: SF: SP500.TR: TF: SF: e-14 US.10Y.TR: TF: SF:
11 Generic Function: summary(nst.fm) Residual Statistics: Min 1Q Median 3Q Max TF: SF: Residual Scale Estimates: TF: on 56 degrees of freedom SF: on 58 degrees of freedom Multiple R-squared: TF: SF:
12 Times Series Factor Models for Asset Returns Names of 6 hypothetical asset managers assets <- paste("ham", 1:6, sep = "") Fit single factor model sfm <- fittsfm(assets, "SP500.TR", data = managers) Fit 3 factor model tfm <- fittsfm(assets, c("edhec.ls.eq", "SP500.TR", "US.10Y.TR"), data = managers) Create fit.models object fm <- fit.models(sfm, tfm) Reference: Eric Zivot and Jiahui Wang (2006). Modeling Financial Time Series with S-PLUS. Chapter 15.
13 fittsfm Output Call: fittsfm(asset.names = assets, factor.names = "SP500.TR", data = managers) Model dimensions: Factors Assets Periods Regression Alphas: HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 (Intercept) Factor Betas: HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 SP500.TR R-squared values: HAM1 HAM2 HAM3 HAM4 HAM5 HAM
14 fittsfm Output Residual Volatilities: HAM1 HAM2 HAM3 HAM4 HAM5 HAM
15 fit.models Comparison Calls: sfm: fittsfm(asset.names = assets, factor.names = "SP500.TR", data = managers) tfm: fittsfm(asset.names = assets, factor.names = c("edhec.ls.eq", "SP500.TR", "US.10Y.TR"), data = managers) Model dimensions: Factors Assets Periods sfm: tfm: Regression Alphas: HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 sfm: tfm:
16 fit.models Comparison Factor Betas: HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 EDHEC.LS.EQ: sfm: tfm: SP500.TR: sfm: tfm: US.10Y.TR: sfm: tfm: R-squared values: HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 sfm: tfm: Residual Volatilities: HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 sfm: tfm:
17 Comparison of Estimated Correlation Matrices HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 HAM1 HAM HAM HAM HAM HAM SFM TSM
18 Comparison of Estimated Correlation Matrices HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 HAM1 HAM HAM HAM HAM HAM SFM TSM Sample
19 Thank You
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