Prerequisite
Part 0. Basic Concepts of Statistics and Probability
Introduce the basic ideas and methods of probability and statistical theory
and
the practice of statistics. In addition, we will implement approaches to
simulation and
the statistical analysis of data through the use of software, mainly SPlus.
Finally,
this topic will provide students the basic probability and statistics language
for
the second part of this course.

Discrete probability spaces:
Definitions (random variable, distribution,
expectation), binomial distribution, random walk, conditional probabilities,
Bayes formula, independence

Continuous models
General probability spaces, Random variables
and their distributions, normal and lognormal distributions, expectation,
variance, higher moments, Chebychev's inequality, joint distribution, marginal
distribution, convolution, covariance, correlation, partial correlation,
skewness, kurtosis

Statistics
Point estimators (bias, mean square error,
consistency, maximumlikelihood estimators, moment estimators), Statistical
tests (NeymanPearson lemma, ttest), Confidence intervals
The major topics covered in the course, time permitting,
are listed below for your reference.
Content

Univariate linear stochastic models: Chapters
2 and 3

autocorrelation, ACF, and PACF

ARMA processes

Box & Jenkins ARIMA modeling

Forecasting and model building (selection)

Unit root tests

ARFIMA processes

Univariate nonlinear stochastic models: Chapter
4

Random walk hypothesis

Stochastic variance models

ARCH processes and other nonlinear models

Modeling return distributions: Chapter 5

Two models for return distributions

Tail shapes and method of estimation

Model central part of return distributions

Pricing European Option

Regression techniques for nonintegrated financial
time series: Chapter 6

Regression models

ARCHinmean regression models

Misspecification test

Multivariate linear regression models

Vector autoregression

Vector ARMA models

Programming Language: Splus or R
Introduction to the programming environment,
and introduction to writing functions, generating random variables and
binary trees, transformations of data and QQ plots, the central limit
theorem illustrated by simulation, confidence intervals, the use and manipulation
of data, maximization of likelihood function.
Examinations

No written exam in the spring
of 2002.
Problem Sets and Programming Exercises

Homework should be turned in on time. No late
homework will be accepted without legitimate reasons.

There will be 2 to 4 programming assignments. You
are expected to write your own codes and turn in your source
code.
Do not copy.
Never
ask your friends to write programs for you.

Project
1 ARMA, Splus or R Programming (Get tseries or fracdiff package.)

Project
2. Unit Root Test (Simulation and Data Analysis), Data

Project
3 Stochastic Volatility (Simulation), MerckData,
3MData

Project
4 Pricing (Simulation)
Lecture Notes:
Chapter 1: Introduction
Chapter 2: Univariate linear stochastic
models: basic concepts

Topic 2: Introduction (Chapter 2.12.3)

Topic 3: ARMA and Time Series Modeling (Chapter
2.32.5)

Topic 4: Nonstationary Processes and ARIMA Models
(Chapter 2.62.8)
Examples in Chapter 2 (Chapter 2.5, 2.7, 2.8)
Chapter 3. Univariate linear stochastic models:
further topics

Topic 5: Unit Root Test and ARIMA Models (Chapter
3.1)

Topic 6: Long Memory Processes: ARFIMA Models
(Chapter 3.23.4)
Chapter 4. Univariate nonlinear stochastic models

Topic 7: ARCH related models

Topic 8: Additional nonlinear models
Chapter 5. Modeling return distributions

Topic 9: Return distribution and Pricing

Topic 10: Value at Risk
Supplement:

Topic 11: Revisit Linear and Nonlinear Time Series

Topic 12: Maximum Likelihood Estimate and Least
Squares Method
Not Covered:
Chapter 6. Regression techniques for nonintegrated
financial time series
Chapter 7. Regression techniques for integrated
financial time series
Chapter 8. Further topics in the analysis
of integrated financial time series
Data appendix: click
here.
References.
Edited April 1, 2002