Approved by University Studies Sub-Committee.

Approved by Faculty Senate February 10th, 2003

University Studies Course Approval

Department or Program: Economics and Finance

Course Number: FIN 335

Semester Hours: 3

Frequency of Offering: Once Each Semester

Course Title: Forecasting Methods

Catalog Description:

A study of the techniques and processes used in business forecasting. Primary emphasis on univariate time series. Techniques studied include simple smoothing methods, decomposition methods, Box-Jenkins ARIMA methods and regression. Prerequisites: Math 140 or its equivalent and DIS 220 or its equivalent or instructor’s permission.

This is an existing course previously approved by A2C2: Yes

This is a new course proposal: No

Department Contact Person: Matt Hyle Email: mhyle@winona.edu

University Studies Approval is requested in: Flag Requirements: Mathematics and Statistics

Attachments: The syllabus explains what are typically covered in this course and addresses the coverage for the two outcomes for mathematics and statistics (a-b). The syllabus is included in this application for purposes of illustration. Each faculty member is still responsible for his/her own course syllabus. Examples of assignments to students are also included in this application. They illustrate some of the learning activities that students undertake aside from exams and in-class work.

As required by the approval process, the following address the two outcomes listed for Mathematics and Statistics flag:

a. practice the correct application of mathematical or statistical models that are appropriate to their prerequisite knowledge of those areas

In order to generate a useful forecast, one must typically decompose the data into a possible trend effect, a possible seasonal effect, and a possible cyclical effect. Students learn to look at a data series, identify its time series properties (trend, seasonal and cyclical effects, or weak stationarity) with graphical and statistical analysis (including hypothesis testing). Then, they learn to apply the appropriate forecasting technique(s), given the goals of the forecast.

b. make proper use of modern mathematical or statistical methods appropriate to their level of prerequisite knowledge, to include, if statistics is used in a substantive way, the use of a statistical package with graphics capability when appropriate.

Multivariate regression analysis and ARIMA modeling are too complex for students to hand calculate the results. Moreover, most students lack the mathematical sophistication to “program” Excel to generate the desired results. Consequently, successful completion of almost any assignment requires a student use either JMP or SPSS.

In addition, one of the foci of this course is to get students to visually analyze their results. They must plot or graph the forecasts and model fits in order to find outliers and to help in choosing the best model.

Students are required to analyze the residuals (unexplained portion) of statistical forecasting models. Besides visually checking for randomness, students test for randomness and “normality” in the residuals.

Finally, when comparing different forecasting models, students perform hypothesis tests on the forecasting models, use statistics to test the forecasting properties. Students compare plots of the different forecasts.

FIN 335 - FORECASTING METHODS

Professor

e-mail:

Office Hours –Posted on my office door. They are subject to change during the semester.

Class Hours: MWF 8-8:50PM, 11-11:50PM, 12-12:50PM, and1-1: 50PM. I am usually in my office ten or so minutes before class as well. There may be occasional deviations from this weekly schedule.

TEXT

The required text is Elements of Forecasting, 2^nd edition, by Francis X. Diebold

COURSE OBJECTIVES

Each student in the course will 1) gain a rudimentary knowledge of several common forecasting techniques, 2) learn how to evaluate the accuracy of a forecasting model, 3) gain an appreciation of the importance of data quality, and 4) observe and encounter some of the common problems in building a forecasting model.

UNIVERSITY STUDIES

University policy requires the following information for your benefit. Finance 335 fulfills the 3 s.h. of a Mathematics/Statistics Flag course required in the University Studies Program. As such, this courses seeks to

a. practice the correct application of mathematical or statistical models that are appropriate to their prerequisite knowledge of those areas; and

Letters in parenthesis below identify these outcomes.

DETERMINATION OF FINAL GRADES

Each student's course grade depends on the student's point total from exams (48%), assignments (48%) and class participation. There are 3exams, each graded on 100 points. Various assignments given out in class. At the end of the semester, the assignment scores are totaled and scaled to 100 basis. There is no deviation from this procedure - no extra credit is given.

Assignments (a, b)

Students receive homework assignments in class. Students may work in groups of no more than three. Assignments are to be turned in or postmarked by the due date. All assignments are due on the date indicated on the assignment: late assignments lose 1/3 of the total value for each day it is late.

Exams (a, b)

Exams consist of definitions, short answer and short problems. Each exam covers part of the course. The first exam covers Chapters 1-4. The second exam covers chapters 4-8. The final exam covers Chapters 9 and parts of Chapters 10, 11 and 12.

Reading Assignments (a, b)

Students should keep up with the reading assignments. Lecture topics do not cover all of the text. All students are capable of understanding much of the reading assignments without assistance from the instructor. Lectures are a combination of explanations of important / difficult points and extensions of the text. Reading the assigned material by the scheduled date is very important.

Computer Software (a, b)

Much of the data manipulation can be accomplished in most spreadsheet programs, including Excel. Basic regression tools are usually accessible in spreadsheets. However, for some of the time series analysis, students need access to a software package that performs ARIMA models. There are three such packages available on campus at this time: JMP, SASS, and SPSS. Any student with a new laptop has JMP on it. For students with older laptops, the IT lab on the second floor of Somsen will load JMP or SASS onto your machine. SPSS is available in the computer lab on the second floor of Somsen and the third floor of Somsen.

Students should choose the package that is easiest for them to use. Each package has advantages and disadvantages. In class, I alternate among the packages.

TOPIC AND READING SCHEDULE:

WEEKS TOPIC READING

PART I Getting Started

1-5 Introduction and Review (a) Chapters 1-2

Primer on Regression (a) Appendix to 1

Visual Inspection of Data (a,b) Chapter 3

Trends (a,b) Chapter 4

1^st Exam over Part I

PART II Modeling Time Series

6-10 Seasonality (a,b) Chapter 5

Modeling Cycles( a,b) Chapters 6 and 7

Forecasting Cycles Chapter 8

2^nd Exam over Part II

PART III Forecasting

11-15 Trends, Seasonality and Cycles (a,b) Chapter 9

Regression Models (a,b) Chapter 10: pages 241-250, 259-276

Evaluating Forecasts (a) Chapter 11: pages 287-294

Stochastic Trends, Unit Roots (a.b) Chapter 12: pages 323-352

3^rd (Final) Exam over Part III

FIN 335 1^st Assignment (a, b)

1. (2 points) Describe the distribution of the daily noon Swedish Krone to U.S. dollar exchange rate, include a histogram.

2. (2 points) Test at the 99% confidence level, whether its distribution is normal.

3. (4 points) In the previous year and a half, the average exchange rate was 9.68 Krone per U.S. dollar with a standard deviation of 0.753.

a. Test at the 95% confidence level, if the exchange rate has increased from 9.68 Krone per U.S. $.

b. Test at the 95% confidence level if the standard deviation is different from 0.753 Krone per U.S. $.

FIN 335 2nd Assignment (a, b)

1. (2 points) Find the predicted error (Actual – Predict) for each month.

2. (2 points) Describe the distribution of the errors. Is it symmetrical?

3. (2 points) Test at the 99% confidence level, whether its distribution is normal.

4. (2 points) Test at the 95% confidence level if the mean predicted error is zero.

5. (2 points) Construct a 99% confidence interval for the mean predicted error.

6. (2 points) Looking at your answers to questions 1-5 what conclusions (not statistical ones) can one draw about the monthly forecasts over these two years?

FIN 335 3rd Assignment (a, b)

Estimate the following model: PRIME_t= B₀ + B₁ FFR_t + e_t

where PRIME is the monthly prime interest rate, and FFR is the monthly federal funds rate,

using the data below from 1997.01 through 2001.12.

1. (1 points) Write estimated equation.

2. (2 points) Does the model fit the data? Explain by interpreting the R².

3. (2 points) Test at the 99% confidence level, whether the intercept is statistically different from 0.

4. (2 points) Interpret the slope coefficient.

5. (2 points) Test at the 95% confidence level, whether the slope is statistically different from 1.

6. (2 points) Test at the 95% confidence level whether there is 1^st order autocorrelation present.

7. (2 points) Write the estimated model with autocorrelation present.

FIN 335 4^th Assignment (a, b)

1. (6 points) Using data from 1959 through 1989, estimate the following three trend functions – linear, polynomial, and growth – for real personal consumption expenditures per capital (in 1996 dollars).

2. (6 points) Graph the predicted values for each trend function and the actual values over time for that period. Graph the residuals over time for each trend function. After looking at each graph, and comparing the measures of goodness of fit for each trend function, explain which trend function appears to fit the data the best and which one appears to fit the worst.

3. (6 points) Use each trend function to perform an in-sample forecast for 1990 to 2000.

4. ( 6 points) For each trend function, compute measures of forecast goodness of fits.

5. (6 points) Graph the predicted values for each trend function and the actual values. After looking at that graph, and comparing the goodness of fit measures, explain which trend function appears to forecast the best, and which one appears to forecast the worst.

FIN 335 5^th Assignment (a, b)

1. (6 points) Using data from 1993.1 through 1996.4, estimate appropriate possible trend functions for this firm’s exports (number of units shipped).

3. (8 points) Re-estimate the trend functions over the same period with dummy variables for seasonal adjustment. Analyze the results, and, if you have to, re-estimate the equations with only the statistically significant dummies.

4. (6 points) Graph the predicted values for each trend function and the actual values over time for that period. Graph the residuals over time for each function. After looking at each graph, and comparing the measures of goodness of fit for each trend function, explain which trend function appears to fit the data the best and which one appears to fit the worst. Choose at least 2 trend functions to use.

5. (6 points) Use the remaining functions to perform an in-sample forecast for 1997 and 1998.

6. (10 points) For each function compute measures of forecast goodness of fits and decompose its MSE.

7. (6 points) Graph the predicted values for each trend function and the actual values. After looking at that graph, and comparing the goodness of fit measures, explain which trend function appears to forecast the best, and which one appears to forecast the worst.

FIN 335 6^th Assignment (a)

1. (3 points) Rewrite the following equations, using backshift operators

a. (1 point) 0.87y_t + 0.65y_t-1 + 0.44y_t-2 +0.31y_t-3 +0.11y_t-4

b. (2 points) 0.54D²y_t + 0.04 D²y_t-1 - 0.26 D²y_t-2

2. (3 points) Rewrite the following equations without backshift operators

a. (1 point) (1 – 0.45L+ 0.13L²- 0.37L³+ 0.28L⁴) y_t

b. (2 points) (1 + 0.67L+ 0.26L²)(1-L) y_t

3. (4 points) Rewrite and simplify (if possible) the following equations using backshift operators

a. 0.88Dy_t + 0.64 Dy_t-1 - 0.55 Dy_t-2 + 0.25y_t-3 +0.07y_t-4

b. 0.61D²y_t - 0.37 D²y_t-1 - 0.23 D²y_t-2 + 0.55 Dy_t-3 -0.25y_t-3 +0.22y_t-4

FIN 335 7^th Assignment (a, b)

In the data file for this assignment there are three data series (y1, y2 and y3). For each of the data series, perform the following:

1. (5 points) Check to see if the data series is weakly stationary.

2. (10 points) Find the best ARMA(p,q) representation (i.e. find the “best” combination of p and q)

3. (5 points) Check to see if the residuals from your best ARMA model appear to be white noise.

4. (5 points) Write out the best estimated ARMA model.

FIN 335 8^th Assignment (a, b)

In the data file for data series y1 perform the following:

1. (5 points) Check to see if the data series is weakly stationary.

2. (10 points) Find the best ARMA(p,q) representation (i.e. find the “best” combination of p and q) over the first 77 observations.

3. (5 points) Check to see if the residuals from your best ARMA model appear to be white noise.

4. (5 points) Write out the best estimated ARMA model.

5. (5 points) Forecast ahead 5 periods using the best ARMA model. Include a 95% confidence level for the forecast.

6. (15 points) Find the best ARIMA(p,d,q) model over the first 77 observations.

7. (5 points) Check to see if the residuals from your best ARIMA model appear to be white noise.

8. (5 points) Write out the best estimated ARIMA model.

9. (5 points) Forecast ahead 5 periods using the best ARIMA model. Include a 95% confidence level for the forecast.

10. (20 points) Compare accuracy of the two forecasts. Explain which model you would choose.

FIN 335 9^th Assignment (a, b)

In the data file for quarterly series y, perform the task below.

I. (40 points) Estimate an ARIMA model.

a. (20 points) Excluding the last six quarters, find the best ARIMA model. There may be seasonality in the data.

b. (5 points) Check the residuals for white noise.

b. (5 points) Write the estimated ARIMA model with and without lag operators.

c. (10 points) Use the estimated model to generate a forecast for the last six quarters and a 95% forecast interval. Graph the forecast and the interval.

II. (75 points) Estimate a trend model with ARIMA errors

a. (30 points) Excluding the last six quarters, find the best trend (with seasonal adjustments, if necessary) model.

b. (20 points) Analyze the residuals and find the best ARIMA model for the residuals. Check the residuals from that model for white noise properties.

c. (10 points) Re-estimate the trend model with the ARIMA error model.

d. (5 points) Write out the estimated model without lag operators.

e. (10 points) Use the estimated model to generate a forecast for the last six quarters and a 95% forecast interval. Graph the forecast and the interval.

III. (30 points) Comparing the forecasts

a. (5 points) Graph both forecasts and their intervals along with the actual data.

b. (5 points) Visually, which model performs best in the first two quarters, the last two quarters and over the entire 6 quarters? Explain.

c. (10 points) Calculate the appropriate measures of forecast accuracy and diagnosis.

d. (5 points) Which model is the most accurate? Explain.

e. (5 points) Which model would you use to forecast ahead two periods? Which model would you use to forecast ahead 6 periods? Explain.

IV. (30 points) Final Model and Forecast

a. (10 points) Re-estimate each model over the entire data sample.

b. (10 points) Using the appropriate model, generate a two period ahead forecast with a 95% forecast interval. Does it appear reasonable? Explain

c. (10 points) Using the appropriate model, generate a six period ahead forecast with a 95% forecast interval. Does it appear reasonable? Explain