T, 6:00pm to 9:00pm
Tisch T-LC25
Final Exam:
Schedule exceptions
Class will not meet on:
Class will meet on:
This course will cover practical time series forecasting techniques with particular
emphasis on the Box-Jenkins (ARIMA) method, and conditional volatility (ARCH) models. Illustrative
examples applying these techniques to actual data (primarily financial and economic time series)
will be presented in class, and you will perform a variety of data analyses on the computer. To gain a
deeper understanding of how the methods work, we will also spend a considerable amount of class time
discussing their mathematical/statistical underpinnings. However, most of your grade will be based on
data analysis homework problems and projects.
The level of presentation will be somewhere between MBA and MS. MBA students should have no
problem handling the data analysis aspects of the course, but will probably find the theory challenging at
times. Ph.D. students should also be able to profit from this course, if they want to learn basic forecasting
methodology presented at what (for them) should be a rather comfortable mathematical level.
This is a statistics course, and therefore we will not attempt to delve deeply into economic issues. We
are concerned here with the statistical analysis and forecasting of time series. No background in economics
is required for this course. On the other hand, statistical analysis of economic data, which you will
be doing, does form a part of econometrics, and hopefully will often lead to insights of an economic
nature.
One introductory level statistics course covering random variables, expected value,
the normal distribution, conditional probability, hypothesis testing, confidence intervals, p -values, correlation
and linear regression. It is particularly important that you have some previous exposure to linear
regression, because much of the material presented in this course (including the ARMA and ARCH
models) is essentially an outgrowth of linear regression. Furthermore, linear regression itself provides a
method of forecasting, through trend-line fitting.
Course Work:
There will be weekly homework assignments (data analysis and theory), which count for 50% of
the grade. Some of the problems will be demanding, and I will be happy to help you if you run into
difficulties. You are free to work with others on homework problems, but it will be assumed that you
understand what you have submitted. There will be two data analysis projects (5 pages maximum), each
of which counts for 25% of the grade. In the first, which will be due in the middle of the semester, you
will analyze a data set of your choice using ARIMA methods. In the second, due near the end of the
semester, you will analyze a data set of your choice using ARCH methods. I will be happy to discuss
your projects with you before you hand them in.
You will receive a copy of all handouts used in the lectures. Much of the material in the text will
not be covered. On the other hand, some of the material in the handouts is not covered in the text.
These are the handouts I have prepared. I may make some small changes during the course of the
semester. I may decide to skip some handouts. In parentheses are the recommended readings from
Enders (E) Diebold (D) and Granger (G) to go roughly with some of the handouts.
Introduction
Chapter 1: Basic Concepts of Forecasting. (D, Chapts 1,3). (G, 1-21).
Linear Prediction of a Random Variable. (D, Chapt 2).
Chapter 2: Trend-Line Fitting and Forecasting. (D, Chapt 5). (G, 23-46).
Chapter 3: Forecasting from Time Series Models
Part I: White Noise and Moving Average Models. (E, 63-66). (D, 117-123, 138-145, 172-175). (G,
47-56).
Part II: Autoregressive Models. (E, 68-72, 76-77, 166-170). (D, 145-152, 177-178). (G, 57-62).
Part III: Mixed Autoregressive - Moving Average Models. (E, 67-68). (D, 152-153, 178-179). (G,
63-65).
Part IV: The Box-Jenkins Approach to Model Building. (E, 78-87). (D, Chapt 7). (G, 65-75).
Part V: More on Model Identification; Examples. (E, 88-99). (D, 28, 82-86 discusses AIC and
SIC ). (G, 75-82).
The Corrected AIC (AICC )
Analysis of Google Series, The Constant Term, Problems with t -ratios
Integrated Moving Averages
Forecast Intervals. (E, 99-101). (D, 41, 175-176, 179-180). (G, 105-108).
Nonlinear Models
Chaos and Nonlinear Time Series
Best Linear Forecasts VS. Best Possible Forecasts
Some Drawbacks of Black-Scholes
ARCH Models and Conditional Volatility (E, 135-158). (D, Chapt 14).
Estimation and Automatic Selection of ARCH Models (E, 162-165).
Long Memory in Volatility
The Durbin-Watson Test. (D, 28-29). (G, 130).
Analysis of Dow and Deflated Dow Series
Differencing and UnitRoot Tests (E, 176-188, 211-261). (D, Chapt 13).
ARCH-M Models (E, 158-162).
Chapter 4, Part I: Cycles and the Seasonal Component. (E, 111-118). (G, 93-100).
Modeling the Federal Reserve Board Production Index
Chapter 4, Part II: Low Cost Forecasting Methods. (This includes Exponentially Weighted Moving
Averages, and the Holt-Winters Method). (G, 100-104
Optional Textbooks:
• C.W.J. Granger, "Forecasting in Business and Economics", 2’nd Ed. (Harcourt Brace).
• F.X. Diebold, "Elements of Forecasting", 4’th Ed. (Thomson).
• W. Enders, "Applied Econometric Time Series". (Wiley).
• T. Mills, "The Econometric Modelling of Financial Time Series", 2’nd Ed. (Cambridge).
You may wish to buy one or more of the books, for supplementary reading. The first few handouts
of the course were taken from Granger, as were some of the homework problems in the first few
problem sets. Therefore, you might find Granger helpful, at least for the first few weeks. However, most
of my lectures are not designed to coordinate exactly with any of the books. Comparing the Diebold and
Enders books, I would say that Diebold has more practical examples, and is more enjoyable to read.
Enders is written at a considerably higher level, but does contain many real data examples and perceptive
data analyses. Enders (but not Diebold) discusses ARCH models.
Software: For the ARIMA examples presented in class on the computer, I will use Minitab. All data
sets used in class and in homework problems are available on the course website, in Minitab Portable
(.MTP) and .TXT format. The file ReadMe describes the data sets.
For the ARIMA calculations, I recommend that you use Minitab Version 16 for Windows. (Older versions
should be fine also). Minitab is available for your use in all graduate and undergraduate PC labs of
the Stern School. In addition, it is available for purchase at the bookstore. (It will be with the textbooks
for the course B01.1305.) Finally, a time-limited version of Minitab can be rented from
http://www.e-academy.com.
For the ARCH calculations, you should use TSP, Version 4.4 or 5.0, available on the Stern linux computers
sales and grid. We do not have a PC version, but I will show you how to reach these machines
remotely using ssh.
If you are strongly inclined, you may (after consulting with me) use any other software you want, provided
that it performs the necessary calculations. Any problems arising from this decision, however, are
the responsibility of the student.
TBA
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