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 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 t**o**

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

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.

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. $.

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?

Estimate the following model: PRIME_{t}=
B_{0}
+ B_{1}
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 R^{2}.

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).

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. Choose at least 2 trend functions to use.

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) 0.54D^{2}y_{t} + 0.04 D^{2}y_{t-1} - 0.26 D^{2}y_{t-2}

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

a. (1 point) (1 –
0.45L+ 0.13L^{2}- 0.37L^{3}+ 0.28L^{4}) y_{t}

b. (2 points) (1 +
0.67L+ 0.26L^{2})(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. 0.61D^{2}y_{t} - 0.37 D^{2}y_{t-1} - 0.23 D^{2}y_{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