Lecture 5:Multiple Regression
Analysis: OLS Asymptotics
So far we focused on properties of OLS that hold for any sample
Properties of OLS that hold for any sample/sample size
Expected values/unbiasedness under MLR.1 MLR.4
Variance formulas under MLR.1
Lecture 2:
The Simple
Regression Model
1
The Simple Regression Model
Definition: Explains variable y in terms of variable x
General Assumption: E(u)=0
Why not loss generality?
2
The Simple
Regression Model
Interpretation of the simple linear regressio
Lecture 1:
Introduction the Nature of
Econometrics and Economic Data
1
The Nature of Econometrics and Economic Data
What is econometrics?
Econometrics = use of statistical methods to analyze economic data
Econometricians typically analyze nonexperiment
Multifactor Explanations of Asset Pricing
Anomalies
FF (1996)
Motivation
What are the identified anomalies (patterns) in stock returns?
DeBondt and Thaler (1985) find a reversal in long term returns: stocks with low
long-term past returns tend to have hig
Dependence in time-series data
(3)
1
Outline
The Moving Average Model and ARMA Models
The MA(1) model
The MA(q) model
ARMA(p,q) models.
Some model selection approaches
2
These Moving Average models are very different from the
Autoregressive models both
Vector autoregression VAR
1
VAR
So far we have focused mostly on models where y depends on
past y.
More generally we might want to consider models for more
than one variable.
For example, the change the price of an asset may be related
to the previous
Dependence in time-series
data (2)
1
More on the AR(1) Model
AR(1) model
The AR(1) model can describe several different types of time-series data. The
value of 1 turns out to be very important in describing the nature of the data.
In this section, we will
Ch10 Basic Regression Analysis
with Time Series Data
The nature of time series data
Temporal ordering of observations; may not be arbitrarily reordered
Typical features: serial correlation/nonindependence of observations
How should we think about the
Ch8 Heteroscedasticity
Consequences of heteroscedasticity for OLS
OLS still unbiased and consistent under heteroscedastictiy!
Also, interpretation of R-squared is not changed
Unconditional error variance is unaffected by
heteroscedasticity (which refer
Dependence in time-series
data (1)
1
Random time-series data
Random time-series data example: compounded returns rt IID ~ N(0,1)
Each number rt is independently drawn from N(0,1)
A time-series plot (rt versus t):
rt can be very different from rt-1
The con
How to write a term paper
Grading Guidelines
Writing (30%)
Double space, font size 12; No more than 15 pages
Clearly describe research question, model, analysis, and conclusion
The results are displayed in tables/figures (not the output directly from SAS
CH7: Qualitative Information
Multiple Regression Analysis:
Qualitative Information
Qualitative Information
Examples: gender, race, industry, region, rating grade,
A way to incorporate qualitative information is to use dummy variables
They may appear
Multiple Regression
Chapter 4
Analysis: Inference
Statistical inference in the regression model
Hypothesis tests about population parameters
Construction of confidence intervals
Sampling distributions of the OLS estimators
The OLS estimators are rand
Ch3: Multiple Regression
Chapter 3Estimation
Analysis:
Multiple Regression
Analysis: Estimation
Definition of the multiple linear regression model
Explains variable
Intercept
Dependent variable,
explained variable,
response variable,
in terms of variable
Chapter 6: Multiple Regression
Analysis: Further Issues
More on Functional Form
More on using logarithmic functional forms
Convenient percentage/elasticity interpretation
Slope coefficients of logged variables are invariant to rescalings
Taking logs
Appendix C: Fundamentals of Mathematical
Statistics
1
Populations, Parameters, and Random Sampling
Econometrics is concerned with statistical inference: learning about the
characteristics of a population from a sample of the population.
Population: a we