# Financial Time Series II

(Est. February 2000, Revised: 6/19/2002)

Prerequisite: Financial Time Series I or Background Knowledge Describe Below.

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 S-Plus.  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, maximum-likelihood estimators, moment estimators), Statistical tests (Neyman-Pearson lemma, t-test), Confidence intervals

The major topics covered in the course, time permitting, are listed below for your reference.

Content

• Introduction: Chapter 1
• 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 non-linear stochastic models: Chapter 4
• Random walk hypothesis
• Stochastic variance models
• ARCH processes and other non-linear 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 non-integrated financial time series: Chapter 6
• Regression models
• ARCH-in-mean 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 Q-Q 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.
1. Project 1  ARMA, Splus or R Programming (Get tseries or fracdiff package.)
2. Project 2. Unit Root Test (Simulation and Data Analysis), Data
3. Project 3  Stochastic Volatility (Simulation), MerckData 3MData
4. Project 4  Pricing (Simulation)

## Lecture Notes:

Chapter 1: Introduction
• Topic 1: Asset Returns
Chapter 2: Univariate linear  stochastic models: basic concepts
• Topic 2: Introduction (Chapter 2.1-2.3)
• Topic 3: ARMA and Time Series Modeling (Chapter 2.3-2.5)
• Topic 4: Nonstationary Processes and ARIMA Models (Chapter 2.6-2.8)
• 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 3.2-3.4)
Chapter 4. Univariate non-linear 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 non-integrated  financial time series
Chapter 7. Regression techniques for integrated financial time series
Chapter 8. Further topics in the analysis of integrated financial time series