Goals

1
Goals

• Goals for this class
• To provide you with a set of simple and useful
  tools for forecasting using commonly available
  software.
• To help you understand the method choices
  involved, which are primarily based on
  characteristics of the data.
• To help you develop an understanding of how to
  fit a model.
• To make you aware of the strengths and weaknesses
  of these techniques.
• To generally pack your head with as much as I can
  about forecasting without causing PERMENANT
  damage.

2
Knowledge of Excel, computers and the world of
online data

• I assume you have access to your own computerif
  you dont you could be in trouble in this class.
• I assume you have fairly extensive knowledge of
  MS ExcelIf you havent used excelyou probably
  will be in trouble in this class.
• I assume you can search for, find, download, and
  put data into a spreadsheet

3
Math

• Because forecasting is inherently mathematical in
  natureyou are assumed to be very proficient in
  algebra.
• One prereq is stats I. We will use it.
• Sometimes I will describe concepts using
  calculus, but a thorough understanding of
  calculus is not requiredhowever, it would be
  nice.

4
Communication

• Forecasts are useless to the world unless they
  are communicated to the world.
• You will be required to write and explainLOTS.
• Your Individual forecasting projects will be
  presented to the class and you will be graded on
  the presentation in addition to the content of
  the project.

5
Individual Projects

• These can be about almost anything.
• It requires data, at least 40 periods (years,
  quarters, months, days, etc.,)
• For the individual forecasts, nobody is allowed
  to forecast GNP, GDP, or any other macro variable
  that I use in class as an example. Originality
  counts for youthe lack of originality counts
  against you.
• We will have a class dedicated to the development
  of the individual projects.

6
Grading

• The grading scheme is described in the syllabus.
• There will be a final exam that tests your
  general knowledge of forecasting at the end of
  this semester. Dont panic over this. Its
  intended to catch TOTAL fakersnot PARTIAL
  fakers.
• No extra creditI mean this
• Expect this class to use a lot of outside time.
  Most of the work you do will be at home, in front
  of a computerexpect to be called a nerd by your
  friends.
• Dont copy other peoples work I check trust
  me on this one, its much better to make your own
  mistakes because any grade is better than a
  GUARANTEED F!!!
• (undergrad) Groups.
• If you are panicked, see me.

7
Take out a sheet of paper

• Write down your name
• Your majoryou should have one by now!
• List your hobby or hobbies.
• What attracted you to business or economics as a
  field?
• Why are you taking forecasting?
• What kind of job are you hoping for AC (i.e.,
  after college).

8
The bookBusiness Forecasting, by Wilson and
Keating
List Price148.13 Amazon 28 used new
available from 87.98 One edition back will be
finenot much has changed. ForecastX
9
Chapter 1 Introduction to Business Forecasting

• forecasting
• act of making predictions about
• Occurrence of particular events in the future
• Value of particular variable at future date

10
Occurrence of Particular Event in Future

• Of Current Interest
• Will the FED continue to cut the discount rate?
• Will the Atlanta Braves win the pennant this
  year?
• Number of econ majors and/or the number of people
  enrolled in econ classes
• Will Britney Spears be re-arrested???
• Past Forecasting Projects
• Winner of 2004 U.S. presidential election in GA.
• Freshman losing HOPE after first year.
• Truck driver trainee lasting more than 6 months.
• Will UWG enrollment surpass 12,000 in the next 3
  years?

11
Value of Particular Variable in Future

• Of Current Interest
• Price of fuels
• Gallons of fuel consumed by GA in FY2008-FY2028
• Dow Jones Industrial Index
• UWG enrollment in Fall 2010 (or total enrollment
  in the Univ. System)
• Past Projects
• Annual number of tourists visiting Taiwan
• Monthly sales of smokeless tobacco
• Weekly offering at a local church
• Daily coal consumption at Plant Yates

12
Uses of Forecasting in Business

• Planning
• schedule future needs (supply chain mgt.)
• highlight opportunities (emerging markets)
• recognize threats (Forecasting competitors
  expansions)
• Control Mechanism
• establish performance standards
• identify problem areas
• Communication -
• facilitate flow of information (reporting to
  public)
• stimulate discussion, understanding of
  relationships (seed for brainstorming, developing
  strategies)

13
Uses of Forecasting in Gov.

• Planning
• schedule future needs (infrastructure)
• highlight opportunities (resource development)
• recognize threats (security)
• Control Mechanism
• Budgeting
• Communication -
• facilitate flow of information (reporting to
  public)
• stimulate public discussion on important issues
  and arising public needs (Social Security taxes
  and benefits)

14
Wink, wink, nudge, nudge

• Remember, you all have individual projectsbe
  thinking about this as we go.
• Its never too early

15
Possible Forecasting Routes to Take

• Qualitative
• Quantitative
• Some combination of the two

16
Qualitative (Subjective) Forecasting

• where opinions of experts are used to provide
  subjective prediction of the future
• useful when lack of data or expertise makes
  quantitative forecasting impossible or impractical

17
Subjective Forecasting Methods (Retail Sales)

• Sales Force Composites--Getting info from the
  frontlines.
• Customer Surveys--Getting the info straight from
  the horses mouth.
• Jury of Executive Opinions--Let the experts meet
  and come to a consensus
• Delphi Method--Survey the experts anonymously

18
Sales Force Composites

• Get estimates of future sales from individual
  sales associates
• Add individual estimates to get total for region
  or product
• Possible problems -
• may be in the interest of sales force to bias
  forecasts downward if paid on commission or if
  quotas are involved

19
Customer Surveys

• where estimates of future sales come directly
  from customers
• -do you plan to buy a car in the next month?
• -how much are you looking to spend?
• Possible problem -
• Generally, this method is more accurate for
  corporate or industrial buyers than for the
  general populationVolatile.
• Why?!
• Members of the general population often do not
  have a clue what ACTUAL purchases they might make
  soon.

20
Customer Surveys, Cont.,

• Consumer Confidence Index supposed to measure
  the level of economic optimism in the economy.

21
Jury of Executive Opinions

• combine subjective predictions of those
  knowledgeable in fieldthe list of experts
  depends on the topic.
• e.g., who is going to win the next presidential
  election and why? You are the experts.
• Possible problem -
• strong personalities may dominate group
• http//www.youtube.com/watch?viSgKPmDLYto
• Who do you include as an authority?

22
Delphi Method

• Select participants.
• Participants submit individual forecasts.
• Results are summarized, presented back to the
  participants.
• They submit new revised forecasts, taking into
  account information from others.
• Repeat until no significant changes result.

23
Delphi Method

• Advantages -
• Requires little quantitative background
• Widely used, not time consuming
• Not dominated by strong personalities
• Disadvantage -
• May not reach consensus if you have people who
  are firm in their opinions
• There may be some question as to who is an
  authority in the field

24
Quantum Physics and Forecasting

• Heisenberg, with his famous uncertainty
  principle, established that the mere act of
  observation affects outcome.
• How is this potentially important in
  forecasting???
• Economic data (e.g., GDP) are not outside the
  potential influence of individual expectations.
• Never say the R word!!!
• It could happen

25
Heisenberg Uncertainty Principle, continued

• Another way to think of this
• Economic actors may adjust their expectations and
  behavior based on what analysts see in the data.
  Analysis is PART of the system, NOT independent
  of it.
• Note You will not find this mentioned in your
  text.

26
Quantative Forecasting

• Involves data
• And, a mathematical/statistical methodology.

27
Crude Quantitative Forecast Techniques

• Simple Naive Forecast -
• where actual value in the present period is used
  as a forecast for value in a future period
• Simple Naive Model -
• Ft At-1 where
• Ft Forecast for period t
• At-1 Actual value in previous period (t-1)

28
For Example U.S. Unemployment Rate Forecast

• using quarterly data, 1990q1-2000q1
• Simple Naive Model
• URFt URt-1 where
• URFt unemployment rate forecast for quarter t
• URt-1 actual rate in previous period (t-1)

29
(No Transcript)
30
U.S. Unemployment Rate1990q1-2000q1
31
Simple Naïve Model Forecast
When rate is falling, forecast is too
high. i.e., positive bias
When rate is rising, forecast is too low i.e.,
negative bias
32
Second Naive Model Forecast

• allows for trend in data by adding a fraction of
  change from previous period to current period
• Second Naive Model
• Ft At-1 P (At-1 - At-2) where
• Ft forecast for period t
• At-1 actual value in previous period (t-1)
• At-2 actual value in previous period (t-2)
• P fraction of change from t-2 to t-1

33
Second Naive Model (rising)

• Ft At-1 P (At-1 - At-2) P .5
• URF21990q4 UR1990q3 .5 (UR1990q3 -
  UR1990q2)
• 5.7 .5 (5.7 5.3)
• 5.7 .5 ( .4)
• 5.7 ( .2)
• 5.9
• Produces higher forecast than naïve model when
  unemployment rate is rising.

34
Second Naive Model (falling)

• Ft At-1 P (At-1 - At-2) P .5
• URF21999q4 UR1999q3 .5 (UR1999q3 - UR1999q2)
• 4.2 .5 (4.2 4.3)
• 4.2 .5 (-.1)
• 4.2 (-.05)
• 4.15
• Produces lower forecast than naïve model when
  unemployment rate is falling.

35
Second Naïve Model Forecast
Forecast is no longer biased when there is a
positive trend or negative trend in data.
36
Computing and Interpreting Forecast Errors

• Forecast Error Actual Value - Forecast Value
• when forecast is underestimate, error is
  positive,
• Actual Forecast
• Actual Forecast 0
• Error 0
• when forecast is overestimate, error is negative,
• Actual
• Actual Forecast
• Error

37
Measures of Forecast Accuracy

• Mean Error (ME)
• Mean Absolute Error (MAE)
• Mean Percentage Error (MPE)
• Mean Absolute Percentage Error (MAPE)
• Mean Squared Error (MSE)
• Root Mean Squared Error (RMSE)
• Theils U

38
Mean Error

• where
• At Actual value in period t
• Ft Forecast value in period t
• n Number of forecast periods

39
Joeys Made up data
40
Things to Consider with Mean Error

• Negative error is offset by positive, so it is
  not a good measure of fit, but is a measure of
  bias. In this situation, the fit is no good,
  but its not biased.

error
error
41
Mean Absolute Error

• where
• At Actual value in period t
• Ft Forecast value in period t
• n Number of forecast periods

42
Joeys Made up data
43
Mean Percentage Error

• where
• At Actual value in period t
• Ft Forecast value in period t
• n Number of forecast periods

44
MPE for Joeys Made up data
45
Things to Consider withME and MPE

• MPE has the same issues as ME, the positive and
  negative errors can be offsetting.
• DO NOT interpret ME or MPE as a measure of fit
  or accuracy of the model
• ME and MPE are generally used to measure the
  relative size and direction of model bias.

46
Mean Absolute Percentage Error

• where
• At Actual value in period t
• Ft Forecast value in period t
• n Number of forecast periods

47
Mean Squared Error

• where
• At Actual value in period t
• Ft Forecast value in period t
• n Number of forecast periods

48
Root Mean Squared Error

• where
• At Actual value in period t
• Ft Forecast value in period t
• n Number of forecast periods

49
Theils U

• if U
• model is more accurate than naïve model
• if U 1,
• model is less accurate than naïve model

50
Interpreting Measures of Bias

• ME and MPE are measures of bias
• ME 0, MPE 0
• Forecasts too low on average, have downward bias
• ME
• Forecasts too high on average, have upward bias
• Closer ME and MPE are to 0, the lower the bias

51
Interpreting Measures of Accuracy or Fit

• MAE, MAPE, MSE, RMSE, Theils U
• Always positive
• Lower the value, more accurate the forecast, the
  lower the error.
• These are used as a measure of fit

52
Measures of Forecast Accuracy

• Mean Error (ME)./- bias
• Mean Absolute Error (MAE).accuracy
• Mean Percentage Error (MPE)./- bias
• Mean Abs Pct Error (MAPE).accuracy
• Mean Squared Error (MSE).accuracy
• Root Mean Sq Error (RMSE).accuracy
• Theils U.accuracy relative to naïve model

53
Other things to keep in mindWithin vs Across
Series

• Theils U and MAPE are UNITLESS can be compared
  across series, because the type of units are
  unimportant.
• The other measures such as MAE, MSE, RMSE should
  only be compared within-seriesthese measures are
  not independent of units. Larger units means
  larger values of the measure.

54
Unemployment rate using our two naïve models
(simple and a modification)
Which does a better job in terms of bias?
Which does a better job in terms of fit?
55

• Announcement
• On Thursday, we will be having a guest speaker, I
  will email you the locationI HAVE BEEN TOLD
  THERE WILL BE FREE FOOD!!!
• Now, picking up where we left off

56
Calculations of Error Measures

• Link to Data

57
Example Naïve Forecast Further Modified Total
Houses Sold in the US 2003-2005
58
What to do?!?!

• What you do depends on what you know about the
  data.
• If you were a real estate agent, you just might
  know that housing sales are typically up in the
  spring and summer months and down in fall and
  winter.
• How could you formulate a naïve model that
  accounts for this type of repeating pattern?
• Maybe this might work..THSFTHS(t-12)

59
Total Houses Sold in the US, 1978-2004
60
Total Houses Sold in the US 2003-2004 (forecast
2005)
?
?
61
Total Houses Sold in the US 2003-2004 (Actual
2005 Updated Just Yesterday!)
Not too bad!
?
?
History doesnt repeat itself, but sometimes it
rhymes.Mark Twain
62
Seasonality

• A data series exhibits seasonality when changes
  occur predictably at given times over the month,
  year, or some other fixed time frame.
• Examples of data with seasonality
• Crime
• Retail (seasons within seasons)
• Employment (especially student or youth
  employment)
• DUIs
• Marriages

63
Recognizing Seasonality

• There are formal statistical tests for
  seasonality (we will see later), but the first
  test of seasonality is the eye-ball test,
  i.e., plot the data in Excel and
  look at itIf you can see an obvious recurring
  patternyep, it might be seasonality.

64
Example in the Retail Sector-The Gap-

• The Gap is a retail clothing store duh!?
• Why is it important for a retail clothing store
  to have some idea about future sales?
• Here we compare a couple of forecastsone made by
  the author of the book and one by me (maybe I can
  get a weekend job with the Gap as a greeter!).

65
Gap Clothing Salesmodifying the simple naïve
model another way.
Some series have recurring peaks and valleys in
the data. We can use the Naïve model to account
for these by building it into our model. What
might account for these high points?
66
The Gap Example
What patterns are discernable in the data ???
What explains these patterns?
67
Evaluation of the Two (Historic)
Hey, am I good or what?!
68
We aint done yet Evaluation of the Two
(Hold-Out)
Whahappen?
69
not done yet Knowledge of the Data is Important

• In those last quarters (i.e., the hold-out
  period), my forecast still relies on data from
  around the 2000-2001 recession, whereas the book
  forecast doesnt. My historic predictions are
  much better, but my method turns out to be a
  problem for my forecast in the more recent
  periods.
• So, which one is better??? Hmmmm
• Lets look take a look at the out-of-sample
  predictions

Not too different! Historically, Forecast A has
been below the actual, so we might use these two
forecasts as bounds
70
Good Practices

• Look at your dataare there any obvious
  anomalies? recessions, etc.?
• Graph your data over timedo you see any obvious
  trend, shifts, breaks, or patterns?
• Think about what might be the cause, and
  determine if you can feasibly incorporate that
  info somehow.

71
Real World Uses of the Naïve Model

• The stock market.

72
Case 1 A RANDOM WALK DOWN WALL STREET

• What is a random walk (aka the Drunkards walk,
  or a Martingale Memory-less process) ?
• Answer
• Random walk is a stock market theory proposed
  by Burton Malkiel (1973) that states that the
  past movement or direction of the value of a
  stock or overall market cannot be effectively
  used to predict its future movement.

73
What does this mean?

• stocks take a random and unpredictable path.
• The chance of a stock's future price going up is
  the same as it going down (coin flip, Bernoulli
  trial).
• it is impossible to outperform the market without
  assuming additional risk.
• technical analysis and fundamental analysis are
  largely a waste of time and are still unproven in
  outperforming the markets

74

• In theory, the market has already used all the
  available information to determine the market
  value of a stock.
• The only info that should affect the price now
  should be newly available info

75
What does a random walk look like?
76
A small test of the random walk theory of the
stock market

• We take a time series of the SP 500 prices and
  calculate the rate of return for each period.
• We forecast 2 models of the rate of return
• The first is a simple naïve model
• The second is a modified naïve model (P.5)

77
As a side note Why rates of return and not
prices?

• More recently, rates of return have been favored
  over simple prices. Mainly, this allows for
  meaningful comparisons of returns across
  different kinds of financial investments.
• So, we calculate the continuously compounded rate
  of return for the SP composite by
• FSPCOM ln(FSPCOMt / FSPCOMt-1)
• Using natural logs allows us to measure the rate
  of return continuously compounded instead of at
  the end of each compounding period.

78
Thinking the problem through with an eye on the
theory

• The theory of efficient capital markets argues
  that stock prices incorporate all relevant
  information immediately and therefore there is NO
  useful information in past patterns of stock
  prices.
• This implies a simple naïve model with no
• weight given to information past the previous
• period (AKA a Martingale Process) is, in theory,
• the best model.

79
A simple test of the random walk

• The first naïve model assumes all info is used
  immediately.
• The modified naïve model assumes some info from
  the more distant past is still useful, i.e., it
  take time for stock prices to adjust.
• Which is more correct, in the real world!?

80

• If the random walk model is more correct,
• the addition of information beyond last
• period's actual rate of return should be
• useless in forecasting a martingale (r.w.)
• process and they should actually result in
• larger forecasting errors. Thus, if the random
• walk theory is accurate, we expect the RMSE
• for the first-naïve model to be less than that of
• the second when applied to stock rates of
• return since it ignores information beyond last
• period.

81
The Data

• Link to excel file

82
Results

• It looks like the simple naïve model does a
  better job of predicting rate of return from the
  SP Composite, than does the modified naïve
  model.
• Thus, the process looks like a random walkso,
  there are situations where the simple naïve model
  is preferred.

83
Trends and Modeling

• Trend in a time series is defined as the
  long-term change in the level of the data.

84
Trends and Modeling

• Some forecasting models are designed to model
  trend behavior in a time series
• Other methods require the data to be stationary,
  i.e., display no appreciable trend.

85
De-trending

• A common practice to remove any linear trend is
  to first-difference the data, i.e., subtract
  successive observations of the levels of the
  data.
• 1st_Diff(x)X(t) X(t 1)
• This can easily be done in your favorite
  spreadsheet.

86
De-trending Aggregate Consumption Spending

• The series CON is quarterly personal consumption
  expenditure data from quarter 1 of 1980 through
  quarter 1 of 1997.
• The series DIFF_CON is the first-difference of
  the CON series, which is designed to eliminate
  any linear trend in the original series. Using a
  spreadsheet we calculated first differences as
  follows
• DIFF_CON CONt CONt-1

87
De-trended Consumption
88
De-trended Consumption

• Based upon examination of the time-series plot of
  CON and DIFF_CON, does first differencing of the
  data remove the trend present in the original
  series?
• Answer
• Weve removed the linear trends

89
A Little Experiment

• We now want to examine a couple of the naïve
  forecasting methods we know about and how they
  perform on data with and without trend.

90
A Little Experiment

• The first-naïve model assumes that the forecast
  for today is what was observed last period, and
  is incapable of tracking a linear trend.

91
A Little Experiment

• The second-naïve model adds an adaptive structure
  that tracks the directions of change between last
  period and the period before, and is capable of
  tracking a linear trend in the data.

92
A Little Experiment

• Soooo what!? Right?
• Well, we expect the second-naïve model to
  outperform the first when applied to data with a
  trend, since the first model ignores any trend
  behavior
• Furthermore
• If our assertions about modeling trend are
  correct, we expect the first-naïve model to have
  a lower RMSE for the linearly de-trended series
  (DIFF_CON) and higher RMSE for the series with
  trend (CON).

93
Estimations

• The Levels
• FORECAST_CON_ONE CONt-1
• FORECAST_CON_TWO CONt-1
• .5( CONt-1 - CONt-2)
• First Differences
• FORECAST_DIFFCON_ONE DIFF_CONt-1
• FORECAST_DIFFCON_TWO DIFF_CONt-1
• .5( DIFF_CONt-1 DIFF_CONt-2)

94
How do they perform?

• The first naïve model performs poorly (higher
  RMSE)
• on the data with the trend left in.

• The naïve model performs well (lower RMSE)
• on the data with the detrended data.

• The second naïve model performs reasonably
• well (lower RMSE) on either

95
Again, knowing your data

• In this example, knowing to de-trend and use the
  naïve model improves the fit.