Fall 2013 Statistics 151 (Linear Models) : Lecture Eleven
Aditya Guntuboyina
03 October 2013
1
One Way Analysis of Variance
Consider the model
yij = i + eij
for i = 1, . . . , t and j = 1, . . . , ni
where eij are i.i.d normal random variables with mean z
Spring 2013 Statistics 153 (Time Series) : Lecture Thirteen
Aditya Guntuboyina
07 March 2013
1
Asymptotic Distribution of the Estimates for AR models
The following holds for each of the Yule-Walker, Conditional Least Squares and ML estimates:
For n large,
Fall 2013 Statistics 151 (Linear Models) : Lecture Two
Derek Bean
03 September 2013
1
Linear Model
We observe a random response variable Yi and fixed, non-random explanatory variables (predictors,
covariates) (Xi1 , Xi2 , . . . , Xip )T , i = 1, . . . , n
1
Econ 101A Fall 2015 Midterm 1
Suggested Solutions
Problem 1. Utility Maximization.
1. The derivatives are
u
= (x a)1 (y b) > 0
x
and
2u
= ( 1)(x a)2 (y b) < 0.
x2
for x a > 0, y b > 0. The rst derivative tells us that the utility function is
increasing
1
Econ 101A Fall 2014 Midterm 1
Suggested Solutions
Problem 1. Expenditure Minimization.
1. The derivatives are
u
1 1/2
= x1 (x2 x3 )1/2 > 0
x1
2
and
2u
1
= x3/2 (x2 x3 )1/2 < 0.
2
x1
4
for x1 > 0, x2 > 0, x3 > 0. The rst derivative tells us that the uti
Spring 2013 Statistics 153 (Time Series) : Lecture Twelve
Aditya Guntuboyina
05 March 2013
1
Plan
So Far:
1. Trend and Seasonality
2. Stationarity
3. ARMA models
Still to come in Time Domain Techniques:
1. How to t ARMA models to data.
2. ARIMA models
3.
1
Econ 101A
Midterm 1
Instructor: Stephen Bianchi
Tu 6 October 2015
Be sure to write your name and student ID on your blue/green
book(s). You may use one double sided sheet of handwritten notes.
Do not turn the page until instructed to do so.
3
Problem 1.
1
Problem Set 2
Econ 101A, Spring 2016
Due in class on Th February 18. No late Problem Sets accepted, sorry!
This problem set tests the knowledge that you accumulate in lectures 4 to 8. It is focused
on preferences, utility functions, and utility maximiza