Samenvatting Advanced Econometrics van de Master Econometrics and Operational Research aan de VU. Deze samenvatting omvat de volgende onderwerpen: linear regression, non linear models, stationarity, forecasting, value at risk, impulse response functions, fading memory, ergodicity, bounded moments, ...
Chapter 1
Recap: Simple Linear Regression
The Linear Regression Model
The linear regression model is specified as:
yt = α + βxt + ϵt , (1)
where:
• yt is the dependent variable (also known as the endogenous variable or target).
• xt is the independent variable (also known as the exogenous variable or predictor).
• α is the intercept term.
• β is the slope parameter, which measures the effect of a one-unit change in xt on yt .
• ϵt is the error term, representing unexplained variability.
Assumptions in Linear Regression
For the Ordinary Least Squares (OLS) method to provide meaningful estimates, certain
assumptions must be satisfied:
• Linearity: The relationship between yt and xt is linear.
• Exogeneity: The error term is uncorrelated with the regressors, i.e., E(ϵt | xt ) = 0.
• Homoscedasticity: The variance of the error term is constant, i.e., Var (ϵt | xt ) = σ2 .
• No Perfect Multicollinearity: The regressors are not perfectly collinear.
• Independence: The observations are independently and identically distributed (i.i.d).
Ordinary Least Squares (OLS) Estimation
The OLS method estimates the parameters α and β by minimizing the sum of squared
residuals:
T
(α̂, β̂) = arg min ∑ (yt − α − βxt )2 . (2)
α,β t=1
1
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