Chapter 6: Forecasting

1
Chapter 6 Forecasting

• Challenges in Forecasting
• Qualitative Methods
• Trend Analysis
• Cyclical or Seasonal Variation
• Econometric Forecasting
• Eviews and Forecasting
• Forecasting Reliability Statistics
• ARIMA

2
What is Forecasting?

• Predicting the future
• Not goal setting!
• Plan for future scenarios
• Can be qualitative or quantitative
• Statistical techniques take out human bias

3
Macro Forecasting

• Macroeconomic Forecasting Prediction of
  aggregate economic behavior
• Frequently in media
• International, National, State level
• GDP, Unemployment, Interest Rates, Exports,
  Imports, Government Spending, etc.
• VERY difficult see examples

4
Economic forecasting is difficult!

• Remember this graph?
• WSJ Article

5
Micro Forecasting

• Microeconomic Forecasting Prediction of partial
  economic data
• Firm sales
• Industry sales
• Product Sales
• Ignored by public and media
• Usually more accurate
• What we are concerned with
• Applicable to business manager

6
Forecasting Challenges

• Changing Expectations your expectations effect
  the accuracy of the forecast!
• Simultaneous relations
• Data Quality
• Human Behavior not always rational
• Events that cant be forecast (example 9-11)

7
Qualitative Analysis

• Intuitive Approach
• Expert Opinion
• Personal Insight and Experience
• Panel Consensus
• Surveys

8
Trend Analysis and Projection

• Trend Analysis Forecasting the future path of
  economic variables based on historical patterns.
• Time series data
• Secular Trend long run pattern
• Cyclical Fluctuation expansion and contraction
  of overall economy (business cycle)
• Seasonality annual sales patterns (Christmas,
  holidays, etc.) tied to weather, traditions,
  customs
• Irregular or random shocks unpredictable (9-11,
  Enron, accounting scandals)
• Womens clothing example

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Figure 6.1
Figure 6.1
Cyclical pattern in sales is much different than
secular trend
Sales ()
Secular trend
Cyclical patterns
0
2
4
6
8
10
12
14
16
18
20
Years
(a)
10
Figure 6.1b
Seasonal patterns, random fluctuations, etc cause
deviations from the cyclical pattern

Fall
Sales ()
peak
Easter
peak
Seasonal
pattern
Long-run trend
(secular plus cyclical)
Random
fluctuations
J
F
M
A
M
J
J
A
S
O
N
D
Months
(b)
11
Linear Trend Analysis

• Assume constant change over time
• Can use regression line
• Test is time trend significant in regression
  model?
• Drawbacks?

12
Sales

3,358 889.2 t
10
Sales revenue
(billions)
5
Data on Microsoft sales, time trend is pretty
good estimation since they increase every year
0
Just timetrend explains 81!
Year

5
1980
1985
1990
1995
2000
Predictor
t
-ratio
Coefficient


St. Dev.

Constant



3,358.0
3.10
1,084.0

The regression equation is
TIME
889.2
7.46
119.3

SEE
2
2
1996
R
81.0
R
79.6
13
Linear Trend on Taurus Data
Does not work well for this data time trend in
Eviews regression?
14
Eviews

• LS QTAURUS C TIME

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Constant Growth Trend

• Assumes constant percentage change over time
• Sales grow 5 per year forever
• Problems?

16
Indices of Leading Economic Activity

• Suppose that you know that your sales closely
  follow another series.
• Furthermore, suppose that other series leads your
  sales activity.
• In this case, you have a leading economic
  indicator.
• Can be used for forecasting purposes.

See later that best forecasting regression models
have leading indicators as independent variables
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Leading Indicators of Macroeconomy

• Dept. of Commerce publishes Business Conditions
  Digest which provides a lengthy list (300) of
  indicators that lead, lag, and coincidentally
  move with the macroeconomy.
• Table 6.3
• For forecasting purpose, lets focus on the
  leading indicators.
• There are 11 series that makeup an index of
  leading indicators.

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Leading Economic Indicators

• Avg. weekly hours of manufacturing employment
• Avg. weekly claims of initial unemployment
• Manufacturing new orders of consumer goods
• Vendor performance (deliveries from suppliers)
• Contracts and orders for plant and equipment.
• Building permits
• Change in manufacturing unfilled orders for
  durables
• Change in sensitive materials prices
• Index of stock prices
• Money supply (M2)
• Index of consumer expectations

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Leading Indicator to Predict Recession

• Figure 6.4 in Hirschey
• Leading indicators predicted recession
• Coincident indicators occur during recession
• Lagging indicators followed recession
• Would be useful to have these for your firms
  sales?

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Leading Indicators for Power Transformers

• Prediction based on relation to other time series
  of data
• Using leading (lagging or coincident) indicators
  to forecast
• Housing Starts
• Distribution Transformers
• Turbine Orders
• Capacity Utilization
• DJUI

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Problems with Non Econometric Techniques

• Dont consider economic relationships
• Many assumptions
• Will not catch turning point WSJ article
• Do not learn from error
• Only direction of change no magnitude
• For these reasons using your econometric models
  to forecast should be more accurate!

22
Econometric Forecasting

• Can use your models to forecast
• More precise than other techniques
• Considers changes in demand drivers
• The better your demand model the better the
  forecast

23
Econometric Forecasting

• In general forecasting is predicting the future
• In econometrics it is estimating the value of the
  dependent variable for observations that are not
  part of the data set.

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Ex-Post vs. Ex-Ante Forecasts

• How can we compare the forecast performance of
  our model? There are two ways.
• Ex Ante Forecast into the future, wait for the
  future to arrive, and then compare the actual to
  the predicted.
• Ex Post Fit your model over a shortened sample
• Then forecast over a range of observed data
• Then compare actual and predicted.

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Ex-Post and Ex-Ante Estimation Forecast Periods

• Suppose you have data covering the period
  1980.Q1-2001.Q4

Ex-Post Forecast Period
The Future
Ex-Post Estimation Period
??????????????????????????????????????????????????
?????????9???????????? 2001??
Ex-Ante Forecast Period
Ex-Ante Estimation Period
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Conditional Unconditional
Forecasts

• Ex-Post forecasts are known as unconditional
  forecasts,
• There is no uncertainty as to the values of the
  independent variables in the forecast range.
• Ex-Ante forecasts are typically conditional
• They usually depend on your predictions of the
  independent variables. The exception is when you
  have lags.

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Examining the In-Sample Fit

• One thing that can be done, once you have fit
  your model is to examine the in-sample fit.
• That is, over the period of estimation, you can
  compare the actual to the fitted data.
• It can help to identify areas where your model is
  consistently under or over predicting.
• Simply estimate equation and look at resids or
  forecast over entire estimation sample.

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First do an ex post forecast

• Use model to forecast dependent variable
• Compare to actual data
• Tells you how good your model is at prediction
• Not really a forecast
• Do this for your project

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Eviews

• Demand for chicken data
• 1951 to 1994
• Estimate equation LS Y C PB PC YD
• Look at resids or forecast for in-sample fit of
  model
• Estimate model over a short sample period, 1951
  1990
• Forecast 1991 1994
• Confidence Band and Forecast Stats (because it
  knows actual values next slide)
• Graph Y and YF from 1991 to 1994
• Gets worse after 1991, as expected

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Forecast Error

• Evaluate graphically and statistically
• Good model fit does not mean good at
  forecasting
• Graphically, is there systematic over- or
  under-prediction over a range of the forecasts?
• U RMSE smaller the better
• U ???(1/n?(fi xi)2 -- difference between
  forecast and actual summed
• More formal measures (Theil Inequality sum to 1)
• Bias portion - Should be zero
• How far is the mean of the forecast from the mean
  of the actual series?
• Variance portion - Should be zero
• How far is variation of forecast from forecast of
  actual series variance?
• Covariance portion - Should be one
• What portion of forecast error is unsystematic
  (not predictable)

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Ex Ante Forecast (out of sample)

• Specify and estimate the equation that has as its
  dependent variable the item that we wish to
  forecast.
• Obtain values for the independent variables for
  the observations for which we want a forecast and
  substitute them into our forecasting equation
  (forecast independent to forecast dependent!).

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Chicken Example

• Y 31.5 0.73PC 0.11PB 0.23YD
• Y demand for chicken, PC price of chicken, PB
  price of beef, YD disposable income
• Data yearly 1951 to 1994
• Suppose we know that we know data for 1995
  PC6.5, PB61.8, YD200.62
• YF 31.5 0.73(6.5) 0.11(61.8) 0.23(200.62)
  79.7

33
Eviews Example

• Estimate equation for 1951 to 1994 (where we have
  demand data)
• Find data on PB, PC, YD for 1995-1997 (easy for
  me since it already happened)
• You will have to guess at values for your
  independents (this is why lags and leading
  indicators are valuable in forecasting models)
• LS Y C PB PC YD
• Forecast button
• Now it forecast 1995 to 1997
• No Stats and nothing to compare to (future)

34
Forecast Reliability

• I looked up real data on chicken demand
• YEAR FORECAST ACTUAL
• 1995 79.7 80.3
• 1996 81 81.9
• 1997 82.6 83.7
• Not too bad!

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More complex forecasting without independents

• ARIMA
• Takes out the unrealistic requirement of knowing
  your independent variables
• Highly refined curve fitting
• Used for stock market and stock prices
• Based entirely on patterns of movement of time
  series data
• Ignores economic theory
• AR Autoregressive
• MA Moving Average

36
AR and MA

• AR Dependent variable tomorrow is a function of
  past values of dependent variable
• Yt f(Yt-1, Yt-2 )
• MA Dependent variable is a function of past
  values of the error term (remember actual Y is Y
  error)
• Eviews can do this
• Complicated and outside scope of this class
• Popular among economic forecasting firms

37
Homework

• What is the difference between ex post and ex
  ante forecasts? What are the uses of each?
• Get the new data file on the directory
  BEEF_Forecast.wf1 and use it to answer the
  following questions
• Would a linear trend analysis be a good way to
  forecast this data? How do you know (graph and
  regression)?
• Estimate LS B C P YD over the period 1960 to
  1982
• Examine the in-sample fit of the model

38
Homework

• Estimate the equation from 1960 to 1979
• Forecast beef demand for 1980 to 1982
• How good does the model appear to do in terms of
  forecasting known values (graphically)?
• What does the RMSE stat suggest about the
  forecast?
• Are the bias, covariance and variance stats close
  to what is expected?
• I have also inserted price and income forecasts
  from 1983 to 1987
• Now do an ex ante forecast of beef demand from
  1983 to 1987