Idea Transcript
FPM
Time Series Analysis (2014-15)
IIM Ahmedabad
Time Series Analysis Instructors: Apratim Guha [AG] & Vineet Virmani [VV] No. of Sessions [AG]: 20 No. of Sessions [VV]: 10
Area: Eco, F&A, P&QM AY: 2014-15 (Slot 9-10)
Course Objectives This course introduces the theory and methods of time series analysis for research in economics and finance. The objective of the course is two-fold. First is to give participants enough technical background to enable them to read research papers in applied time series analysis. The second is to introduce select advanced topics useful for analysis of macroeconomic and financial time series. After introducing fundamental concepts in time series analysis, the course covers the theory of stationary ARMA processes and reviews the relevant asymptotic distribution theory. This forms the bulk of roughly half the course and forms the basis for studying Vector Autoregressions (VARs) which is discussed next. Moving on from considering covariance stationary processes, the course next introduces the econometrics of unit roots. The core of the remaining portion consists of studying linear combinations of unit root processes, i.e. Cointegrated Systems (VECMs), and models with conditional heteroskedasticity (GARCH). We end the course by introducing State Space representations of time series models and Bayesian methods.
Pre-requisites There are no prerequisites for the course, except perhaps a lack of aversion to maths. A prior interest in the subject would definitely help. We will use the R programming language for illustrating the examples as well as for assignments. Participants will be required to learn the basics of the language on their own. Although the course is designed as an elective for the 2nd year FPM students, senior FPM students are encouraged to participate. First year FPM students with enough background in statistics maybe allowed to credit the course after prior permission from instructors.
Academic Integrity Academic integrity is a fundamental value and is strictly enforced. Any indication of academic dishonesty (including but not limited to cheating, plagiarism and falsification) will be dealt with seriously. Please refer to the FPM Manual for the IIMA policy on upholding academic integrity.
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FPM
Time Series Analysis (2014-15)
IIM Ahmedabad
Textbooks We will be using the following textbooks for the course: • Fumio Hayashi (2007). Econometrics. John Wiley & Sons [hereafter referred to as Hayashi] • Ruey Tsay (2009). Analysis of Financial Time Series. Wiley, India. [hereafter referred to as Tsay] While by and large we’ll follow Hayashi’s (for theory) and Tsay’s (for methods) texts, we would often need to refer to Hamilton’s Time Series Analysis text. If you need to brush up your basic probability and statistics, a good book is Amemiya’s Introduction to Statistics and Econometrics. For special topics we’ll supplement the materials in the text with select research papers and survey articles.
References Books 1. Takeshi Amemiya (1994). Introdution to Statistics and Econometrics. Harvard University Press. 2. James Hamilton (1994). Time Series Analysis. Princeton University Press.
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FPM
Time Series Analysis (2014-15)
IIM Ahmedabad
Sessions Outline
1. Review of Probability [AG] • Random Variables, Moments and Distributions Reading: Handout provided in class 2. Review of Limit Theorems and Modes of Convergence - I [AG] • Convergence in Probability, in Mean Square and in Distribution Reading: Hayashi, Ch. 2 (pp. 88 - 97) 3. Review of Limit Theorems and Modes of Convergence - II [AG] • Law of Large Numbers for Stationary Processes • The Central Limit Theorem (CLT) Reading: Hayashi, Ch. 2 (pp. 88 - 97); Hamilton, Ch. 7 (pp. 180 - 199) 4. Fundamental Concepts in Time Series Analysis [AG] • Need for Ergodic Stationarity • CLT for Ergodic Stationary Martingale Difference Sequences Reading: Hayashi, Ch. 2, Section 2.2 (pp. 97 - 109) 5. Modelling Serial Correlation - I [AG] • Introduction to Linear MA and AR Processes • Filters Reading: Hayashi, Ch. 6 (pp. 365 - 375); Tsay, Chapter 2 6. Modelling Serial Correlation - II [AG] • ARMA Processes • Vector Processes Reading: Hayashi, Ch. 6 (pp. 375 - 383; 387 - 392); Tsay, Chapter 2 7. Modeling Serial Correlation - III: Estimating AR models [AG] • Estimation of AR(p), ARMA(p, q) and VARs Reading: Hayashi, Ch. 6 (pp. 392 - 400); Tsay, Chapter 2
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FPM
Time Series Analysis (2014-15)
IIM Ahmedabad
8. Frequency Analysis - I [AG] • Autocovariance-Generating Function and the Spectrum Reading: Hayashi, Ch. 6 (pp. 383 - 387) 9. Frequency Analysis - II [AG] • Estimating the Spectrum Reading: To be decided 10. Frequency Analysis - III [AG] • Applications of Frequency Analysis Reading: To be decided 11. Asymptotics for Serially Correlated Processes - I [AG] • Asymptotics for Samples Means of Serially Correlated Processes Reading: Hayashi, Ch. 6 (pp. 400 - 406) 12. Review of Large Sample Distribution of the OLS Estimator [AG] • Asymptotic Distribution of the OLS Estimator Reading: Hayashi, Ch. 2 (pp. 109 - 117) 13. Review of GMM [AG] • Large Sample Properties of GMM Reading: Hayashi, Ch. 3 (pp. 198 - 217) 14. Asymptotics for Serially Correlated Processes - II [AG] • Incorporating Serial Correlation in GMM • Kernel-based estimation of long-run variance: The Newey-West Estimator Reading: Hayashi, Ch. 6 (pp. 407 - 413, 418 - 428) 15. Vector Autoregressions (VARs) [AG] • Maximum Likelihood Estimation of AR models • An Introduction to VARs Reading: Hayashi, Ch. 6 (pp. 392 - 400); Hamilton, Ch. 5 (pp. 117 - 126)
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FPM
Time Series Analysis (2014-15)
IIM Ahmedabad
16. Univariate Non-stationary Processes: I [AG] • Models of Non-stationary Time Series: The ARIMA Process • Meaning of Unit Root Tests • Unit Roots in Macroeconomics Reading: Hayashi, Ch. 9 (pp. 557 - 572); Hamilton, Ch. 15 (pp. 435 - 452) 17. Univariate Non-stationary Processes: II [AG] • Brownian Motion and the Functional CLT • Test Statistics for the Dickey-Fuller-type Tests • On Observational Equivalence of Unit Root & Covariance Stationary Processes Reading: Hayashi, Ch. 9 (pp. 573 - 605); Hamilton, Ch. 17 (pp. 475 - 490; 515 - 516) 18. Analysis of Cointegrated Systems: I [AG] • The Engle-Granger Error-Correction Model Reading: Hayashi, Ch. 10 (pp. 623 - 641); Dickey et al (1991) 19. Analysis of Cointegrated Systems: II [AG] • The Beveridge-Nelson Decomposition • Alternative Representations of Cointegrated Systems Reading: Hayashi, Ch. 10 (pp. 643 - 665); To be decided 20. Analysis of Cointegrated Systems: III [AG] • The Vector Error Correction Model • Johansen’s Maximum Likelihood Procedure • Testing for Cointegration Reading: Hayashi, Ch. 10 (pp. 643 - 665); To be decided 21. Time Series Models with Conditional Heteroskedasticity: The ARCH Model [VV] • Properties and Weakness of the ARCH Model • Building an ARCH Model Reading: Tsay, Ch. 3 (pp. 110 - 131) 22. The Genearlized ARCH Model [VV] • The Generalized ARCH (GARCH) Model Reading: Tsay, Ch. 3 (pp. 131 - 140)
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FPM
Time Series Analysis (2014-15)
IIM Ahmedabad
23. The GARCH (G)ungle [VV] • EGARCH, GARCH-M and IGARCH Reading: Tsay, Ch. 3 (pp. 140 - 157) 24. Multivariate Models of Volatility - I [VV] • Multivariate GARCH Reading: Tsay, Ch. 10 (pp. 506 - 513) 25. Multivariate Models of Volatility - II [VV] • The BEKK Model Reading: Tsay, Ch. 10 (pp. 513 - 521) 26. Multivariate Models of Volatility - III: Modeling Correlation [VV] • Dynamic Conditional Correlation Models Reading: Tsay, Ch. 10 (pp. 521 - 549) 27. State Space Representation of Time Series Models - I [VV] • Example of State-Space Representations • The Kalman Filter Reading: Tsay, Ch. 11 (pp. 558 - 577) 28. State Space Representation of Time Series Models - II [VV] • Time Varying Parameters Reading: Tsay, Ch. 11 (pp. 577 - 591) 29. State Space Representation of Time Series Models - III [VV] • Unobserved Components Model Reading: Tsay, Ch. 11 (pp. 577 - 591) 30. State Space Representation of Time Series - IV: Applications [VV] • Finding the Output Gap Reading: R. Domenech & V. Gomez. Estimating Potential Output, Core Inflation, and the NAIRU as Latent Variables, Journal of Business and Economic Statistics, Vol. 24, 3, pp. 354-365.
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