topic1 - Financial Econometrics Estimation and Inference...

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Financial Econometrics Estimation and Inference Gerald P. Dwyer Trinity College, Dublin January 2011
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About Me Professor Federal Reserve Bank of Atlanta Research Brief summary [email protected] and http://www.jerrydwyer.com
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What is Financial Econometrics? Financial econometrics is the use of econometric procedures What sorts of questions? What factors a/ect stock returns and how much do they do so? Interest rates on government debt have increased substantially. Are they likely to go down? Statistical analysis to inform an economic analysis How likely is it that a portfolio will lose 20 percent of its value in any given 12-month period? Are stock prices mean reverting? Are stock returns mean reverting? What is the e/ect of a recession on stock prices? Is the value of the euro likely to go up or down? What does it depend on? Mostly time series data
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Topics covered Estimation Summarizing data and behavior of returns Univariate time series Univariate volatility Nonlinear time series Market microstructure Continuous time econometrics Value at Risk Multivariate time series Factor models of returns Multivariate volatility
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Purpose of inference What are plausible and implausible values of estimates of a particular parameter? Point estimate -4 -2 0 2 4 Beta hat 0.0 0.1 0.2 0.3 0.4 prob Particular estimated value
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Criteria for estimators Classical statistics Minimum Variance Unbiased Estimators (MVUE) or Best Linear Unbiased Estimator (BLUE) or Ordinary Least Squares (OLS) Maximum likelihood Conditional on the data, pick the most likely value
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OLS Least squares with x y i = x i β + ε i , i = 1 , ..., N E y i = E x i = 0 E ε i = 0 , E ε 2 i = σ 2 , E ε i ε j = 0 8 i 6 = j b β = xy x 2 = xx β x 2 + x ε x 2 = β + x ε x 2 Suppose that x is not stochastic x e.g. treatments of crops on plots time trend quarterly dummy variables E b β = E β + E x ε x 2 = β + x E ε x 2 = β
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Why x nonstochastic? E x ε x 2 If x is not random, then E x ε x 2 = x E ε x 2 If x is random, then E x ε x 2 6 = E x ε E x 2 in general Expectations operator is a linear operator E ax = a E x if a is a constant If x x 2 is a constant, then E x ε x 2 = x x 2 E ε In general, E x ε x 2 6 = E ( x ε ) E x 2 and E x ε x 2 6 = E h x x 2 i E ε
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Right-hand side variable (x) stochastic and least squares works The case with x stochastic in which least squares works: x and ε are independent E x ε x 2 = E [ f ( x ) ε ] with f ( x ) = x x 2 E [ f ( x ) ε ] = E f ( x ) E ε = 0 because x and ε are independent and E ε = 0
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OLS is MVUE and BLUE Var h b β i around true value a minimum among estimators that are unbiased b β = x i y i x 2 i = w i y i , w i = x i x 2 i b β a linear function of the y i and is unbiased Best Linear Unbiased Estimator (BLUE)
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This note was uploaded on 06/20/2011 for the course ECON 803 taught by Professor Pp during the Spring '11 term at Thammasat University.

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topic1 - Financial Econometrics Estimation and Inference...

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