Granger-causality tests

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Linear Regression models Used to describe the dependence of the mean value of one variable on one or more other variables. E(Y | x) – the regression of Y on x. • x is the explanatory variable, or regressor. Y – the mean of variable y. ○ i.e. (y is the occurrences of embezzlement and x is the individuals yearly income) • Since it’s linear E(Y|x) – β 0 +β 1 x ○ β are our regression coefficents. ○ Y is of unknown variance σ 2 ○ Given a sample of n independent pairs of observations (x i , y i ) the best estimators of β 0 +β 1 is given by the method of Least Squares. • i.e. minimize Σ(y i - β 0 - β 1 x 1 ) • Gauss-Markov theorem states that the least squares estimator gives the unbiased* estimator of a parameter having minimum variance. • It’s good to note the least-squares regression of x on y is not in general the same line as the leastsquares regression of y on x. – i.e. what is meant by the line of best fit to a data set depends on what assumptions are made about the nature of any deviations from a fitted line Goal – select parameters so as to minimize the sum of the squared residuals • OLS – Ordinary least squares estimation ○ Best linear unbiased estimates if and only if the Gauss-Markov assumptions are satisfied.
Time series models Standard regression can’t be applied Common forms • Autoregressive models • Moving average models • Box-Jenkins (Combines these 2) • ARCH - Autoregressive conditional heteroskedasticity • GARCH – Generalized ARCH ○ Frequently used for financial time series • VAR – Vector autoregression ○ Used to understand inter-relationships of variables represented by systems of equations Estimates difference equations containing stochastic components
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Page 3 and 4: What is causality? What do you thin
Page 5 and 6: Sir Clive William John Granger •B
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Page 20 and 21: Recursive VARs Each error term i
Page 22 and 23: Continuous VAR Can correct for dis
Page 24 and 25: Performance VARs capture comovem
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Page 30 and 31: Tian, G. Wan, G. Interaction among
Page 32 and 33: Applications of Granger Causality W
Page 34 and 35: Microfit software Microfit has impr
Page 36: Granger causality is a statistical

Granger-causality tests

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