E4708. Financial Data Analysis. Professor S. Kou.
Final Solution, Dec. 22, 2011. 1:10pm-4:00pm.
Closed Book Exam. Total 100 pts.
1. (a) (2 pt) Market returns, individual stock returns, and the CPI. We
Financial Data Analysis Professor S. Kou, Department of IEOR, Columbia University Lecture 1.b Review of Mean Variance Analysis
1
Review of The Mean Variance Analysis
Consider a one period economy as b
Financial Data Analysis
Professor S. Kou, Department of IEOR, Columbia University
HWK 8 Solution
1. (a) Since
Ri
2
N ( i;
Xi jRi
);
N (Ri ; 1);
we have the posterior density
f (Ri jXi ) / f (Xi jRi )f
Financial Data Analysis. Mathematical Formula Sheet. -distribution 1 2 = 1 and 2 , respectively. 1 = 2 1 1 where 2 1 is a 2 distribution with d.f. 1 . Leptokurtic 4 3 Distributions. The kurtosis is de
E4709. Data Analysis for Financial Engineering. Professor S. Kou.
Midterm, Oct 20, 2011. 2:20pm-4:20pm.
Closed Book Exam. Total 100 pts.
1. (26 pts) Basic Facts from Empirical Finance.
(a) (2 pts) Wha
Data Analysis for Financial Engineers Professor S. Kou Department of IEOR, Columbia University Lecture 5. The second attempt to model the dependent structures: MA and ARMA models
1
1.1
The Moving Aver
Financial Data Analysis Professor S. Kou Department of IEOR, Columbia University Lecture 6. Seasonality, Unit Root Test, and Tests of Stationary
1
Seasonality
Last time we learned MA, ARMA, and ARIMA
E4708. Statistical Inference for FE. Professor S. Kou.
Final Exam, Aug 25, 2011, 2pm to 4:30pm.
Closed Book Exam. Total 45 pts.
1. (6 pts) Basic Facts.
(a) (1 pt) Describe the analogies of the null hy
E4702. Statistical Inference for Financial Engineering. Professor S. Kou.
Midterm, August 11, 2012. 2pm-4:30pm.
Closed Book Exam. Total 40 pts.
x
1. a. (4 pts) If x < 0, then P ( n( Mn ) x) = P (
Mn
M
Data Analysis for Financial Engineering Professor S. Kou, Department of IEOR, Columbia University Lecture 3. Fitting Stock Return Distributions and Introduction to Dependent Structures of Stock Return
Columbia University Department of IEOR Data Analysis for Financial Engineers E4709, Fall 2010 R 2:40pm-5:10pm, 303 Mudd Columbia Course Work Web Page Prof. Steven Kou 312 Mudd Building [email protected]
Columbia University M.S. Program in Financial Engineering
IEOR 4709:
Data analysis for Financial
Engineering
Tuesday 4:10 PM- 6.40 PM
Instructor: Rama CONT
Teaching Assistant: Ka Chun [email protected]
Likelihood Ratio Statistics, and Asymptotic Distribution
1
Likelihood Ratio Tests
Last time we discussed hypothesis testing. Consider two simple hypothesis, that is H0 : = 0
versus H1 : = 1 . Define =
Statistical Tests and Bayesian Statistics
1
Goodness of Fit Tests
Last time, we have seen goodness of fit tests. These are used to test the hypothesis: H0 : pi = i
for all i, versus H1 : pi 6= i for s
Bayesian Statistics
1
Introduction
The Bayes formula states:
P (H|D) =
P (D|H) P (H)
P (D)
If the prior and likelihood are known for all hypotheses, then Bayes formula computes the posterior
exactly.
Goodness of Fit Tests
1
Goodness of Fit Tests
Example: In practise, it is always very difficult to estimate the probability distribution of default
(bankruptcy events). Moodys KMV has defined the conc
Likelihood Ratio Statistics, and Asymptotic Distribution
1
Likelihood Ratio Tests
Last time we discussed hypothesis testing. Consider two simple hypothesis, that is H0 : = 0
versus H1 : = 1 . Define =
Lecture 9: Hypothesis Testing
1
Hypothesis Testing
Consider independent and identically distributed samples X1 , X2 , . . . , Xn coming from a Gaussian
distribution N (, 2 ) with unknown mean and unkn
Columbia University
Statistical Analysis and Time Series
IEOR-4709
A. Capponi
Spring 2017
Problem Set #2
Issued:
February 7, 2017
Due: BEFORE CLASS February 22, 2017
Note: Please put the number of hou
Midterm Sample Exam
Note: This exam is closed book, closed notes, calculators allowed. Show all
your work to receive full credit. Please, clearly write your first and last name on
the first page of th
Bayesian Statistics
1
Bayesian Hypothesis Testing
In Bayesian hypothesis testing, we use the posterior probabilities of the null and alternative hypothesis. More specifically, consider the null hypoth
Estimation in Asset Allocation
1
Announcements
The midterm exam will be on Wednesday, March 22, from 10:05am to 11:25am, Location
Mudd 1121.
Midterm review sheet has been posted. It contains all inf
Lecture 8: The EM Algorithm
1
The Expectation Minimization (EM) Algorithm
Suppose we have an estimation problem in which we have m independent samples of a random
variable X, cfw_x1 , x2 , . . . , xm
Columbia University
Statistical Analysis and Time Series
IEOR-4709
A. Capponi
Spring 2017
Problem Set #3
Issued:
March 1, 2017
Due: BEFORE CLASS March 20, 2017
Note: Please put the number of hours tha
COLUMBIA UNIVERSITY
Midterm Review Sheet
IEOR E4709: Statistical Analysis and Time Series
Spring 2017
Instructor: A. Capponi
Information
The midterm exam will be held on Thursday, March 22, from 10:05
Asset Allocation
1
Asset Allocation
Classical portfolio theory, as it existed in about 1975, has two main parts. The first is mean variance
analysis and constitutes a way to allocate assets in a world
Lecture 4: Consistency, Unbiasedness, Method of Moment
Estimator, and Maximum Likelihood Estimator (MLE)
1
Recapt from Last Time
An estimator of a parameter is a function f (X1 , X2 , . . . , Xn ) of
Columbia University M.S. in Financial Engineering
IEOR 4709:
Data analysis for Financial
Engineering
Lecture 5: Modeling volatility dynamics
Instructor: Rama CONT
Teaching Assistants:
Ka Chun [email protected]
Lecture 3: Consistency, Unbiasedness, Method of Moment
Estimator, and Maximum Likelihood Estimator (MLE)
1
Recapt from Last Time
Last time, we have seen the different notions of convergence of a seque
function [f,axe]=kernelregression(x,y)
% function [f,axis]=kernelregression(x,y)
% Computes the Nadaraya Watson estimator for a nonlinear regression of y(t)
% on x(t). Uses the kernel defined in kerne