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M-estimates in Regression Models with Autocorrelated Errors

Student: Mikhail Shishkanov

Supervisor: Elena R. Goryainova

Faculty: Faculty of Economic Sciences

Educational Programme: Statistical Modelling and Actuarial Science (Master)

Year of Graduation: 2020

The paper compares methods for estimating coefficients of a linear regression model with autocorrelated errors using the OLS, M-Huber and M-Tukey estimates. Residuals were modeled using such distributions as Normal, Student with 2,3,4 degrees of freedom, Tukey-Huber with 5 and 10% pollution coefficient, Logistic, Laplace. Autocorrelation was added using the autoregression (AR) process of 1,2,3 order. OLS-estimates were effective only in the case of errors, simulated with a normal distribution. OLS has shown the worst result in cases with outliers. Huber's M-estimates most accurately estimated regression with erorrs, modelled by Logistic distribution and AR(1,2) process . In all other cases the highest accuracy was shown by Tukey's estimates. Estimates of the regression of the yield to maturity 1-year US Treasury bond on 3-year yield to maturity and regression of stock prices of Bank of America on J.P.Morgan with 1st order autoregression in residuals, Tukeys' M-estimator gave the best forecast.

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