Financial Time Series I

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Prerequisite: One semester probability and statistics courses.

• References

  • Rice, J.A. Mathematical Statistics and Data Analysis (Chapters 10-14)

  • R.S.Tsay, Analysis of Financial Time Series , Wiley, 2002.

• Internet Resources

                                                                   課程內容
 

Part 0. 概論

簡介(ppt)

Data Mining(ppt)

Part 1. 基礎機率，統計語言及其工具

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 R.  Finally, this topic will provide students the basic probability and statistics language for  the rest of this course.

• Discrete probability spaces:
  Definitions (random variable, distribution, expectation), binomial distribution, 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, covariance, correlation, partial correlation, skewness, kurtosis
  • Variance (Review on basic probability and application on inventory management)
• Statistics
  • Point estimators (maximum-likelihood estimators, moment estimators)
  • Statistical tests (Neyman-Pearson lemma, t-test)
  • Confidence intervals
  • Data collection (survey sampling and experiment); 李克特量表
  • Inference
• Programming Language 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.

Part 2. 線性模型

• 回歸模型     Association;  Regression; Introduction; DataAnalysis
• 變異數分析  Anova
• 列聯表      Discrete

        Part 3. 線性時間序列                     

• Chapter 1: Introduction
  • Topic 1: Asset Returns
    • Transparency     Time Allocation (1  lecture)
  Chapter 2: Univariate linear  stochastic models: basic concepts
  • Topic 2: Introduction 
    • Transparency     Time Allocation (4  lectures)
  • Topic 3: ARMA and Time Series Modeling 
    • Transparency     Time Allocation (3  lectures)
  • Topic 4: Nonstationary Processes and ARIMA Models 
    • Transparency     Time Allocation (3  lectures)
    Examples in Chapter 2 
    • Transparency
• R
  • R-programming for linear time series  (2  lectures)
  • Don't forget to load ts package and read Chapter 12 of reference manual in HELP session of R.
  • tseries: Time series analysis and computational finance

    • Package for time series analysis and computational finance

  • fracdiff: Fractionally differenced ARIMA (p,d,q) models

    • Maximum likelihood estimation of the parameters of a fractionally differenced ARIMA(p,d,q) model (Haslett and Raftery, Applied Statistics, 1989).

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Examinations

• No written in-class test.
  

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  Homework Assignment

• Homework 1: Due date: 10/24/02   Solution
• Homework 2: Due date: 11/07/02   Solution
• Homework 3: Due date: 12/05/02   Solution  
• Homework 4: Due date: 12/12/02   Solution
• Homework 5: Due date:      Solution

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. Bootstap method (Read the note and there are five assignments in total.)  This is an individual project but you can discuss with your classmates. Due date: 11/28/02 Answer
  2. Project 2. Logistic Regression and Model Selection, Load boot package first to get the data birthwt data Due date: 1/09 /03  Answer

  • On the third problem, you are asking to try a model with interaction terms.  The objective of this question is to ask you to do kind of model checking by constructing a bigger model.  Some of you encountered the following questions:

    • Why do we encounter computational problem?
    • How to choose proper interaction terms to construct a bigger model?  
  • I have no answer on the above two questions.  Instead, you should include some explanation on
    • Why do we encounter computational problem? 
    • Find a strategy of including some interaction terms and give reason to support your strategy.
  • Another possibility to get excellent score is to explain that there is no need to consider interaction term.

3. Project 3. Linear Time Series, Data Sets: Mortality,  Smoke, Temperature.  Due date: 1/16/03 (Get tseries or fracdiff package.)  You should download R-programming for linear time series.  Answer

Data appendix: 

Lottery: lottery.number, lottery.payoff, lottery2, lottery3

House: hstart

Software

• R programming language

  • （可由網路取得）at http://www.r-project.org/    –  

    Download at http://cran.r-project.org/

    Look for Precompiled Binary Distributions Windows (95 and later)

    Look for base.  Download rw1060.exe

  • Basic Introduction : from Institute of Statistics, NCTU; look for Splus

  • Tutorial by Venables and Ripley

  • R manuals: They are downloadable as PDF files:

    • An Introduction to R: It gives an introduction to the language and how to use R for doing statistical analysis and graphics.
    • A draft of the R language definition: Document the language per se. They are useful to know when programming R functions.
    • Writing R Extensions : It covers how to create your own packages, write R help files, and the foreign language (C, C++, Fortran, ...) interfaces.
    • R Data Import/Export : Describe the import and export facilities available either in R itself or via packages which are available from CRAN.
    • R Installation and Administration 
    • The R Reference Index : It contains all help files of the R standard packages in printable form.
  • Quick look up: Rcard, Rguide.
    • R-tutorial

• References.

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  Edited April 1, 2002