Lecture 5 Time-Series Forecasting (cont’d) Business and Economic Forecasting.
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Transcript of Slide 1 Business and Economic Forecasting Chapter 5 Business and Economic Forecasting is a critical...
Slide 1
Business and Economic ForecastingChapter 5
Business and Economic Forecasting is a critical managerial activity which comes in two forms:
Quantitative Forecasting +2.1047%Quantitative Forecasting +2.1047% Gives the precise amount
or percentage
Qualitative ForecastingQualitative Forecasting Gives the expected direction Up, down, or about the same
2008 Thomson * South-Western
Slide 2
Managerial ChallengeExcess Fiber Optic
Capacity• High-speed data installation
grew exponentially• But adoption follows a typical
S-curve pattern, similar to the adoption rate of TV
• Access grew too fast, leading to excess capacity around the time of the tech bubble in 2001
• The challenge is to predict demand properly
1940 1960 1980 2000 2020
100% Color TVs
InternetAccess
Slide 3
The Significance of Forecasting• Both public and private enterprises operate under
conditions of uncertainty. • Management wishes to limit this uncertainty by predicting
changes in cost, price, sales, and interest rates. • Accurate forecasting can help develop strategies to
promote profitable trends and to avoid unprofitable ones. • A forecast is a prediction concerning the future. Good
forecasting will reduce, but not eliminate, the uncertainty that all managers feel.
Slide 4
Hierarchy of Forecasts• The selection of forecasting techniques depends in part on
the level of economic aggregation involved.
• The hierarchy of forecasting is:
• National Economy (GDP, interest rates, inflation, etc.)
»sectors of the economy (durable goods) industry forecasts (all automobile manufacturers)
> firm forecasts (Ford Motor Company)
»Product forecasts (The Ford Focus)
Slide 5
Forecasting CriteriaThe choice of a particular forecasting method depends on several criteria:
1.costs of the forecasting method compared with its gains
2.complexity of the relationships among variables
3.time period involved
4.lead time between receiving information and the decision to be made
5.accuracy needed in forecast
Slide 6
Accuracy of Forecasting• The accuracy of a forecasting model is measured by how
close the actual variable, Y, ends up to the forecasting variable, Y.
• Forecast error is the difference. (Y - Y)
• Models differ in accuracy, which is often based on the square root of the average squared forecast error over a series of N forecasts and actual figures
• Called a root mean square error, RMSE.
»RMSE = { (Y - Y)2 / N }
^
^
^
Slide 7
Quantitative Forecasting
• Deterministic Time Series » Looks For Patterns» Ordered by Time» No Underlying Structure
• Econometric Models» Explains relationships» Supply & Demand» Regression Models
Like technicalsecurity analysis
Like fundamentalsecurity analysis
Slide 8
Time SeriesExamine Patterns in the Past
TIME
To
X
XX
Dependent Variable
Forecasted Amounts
The data may offer secular trends, cyclical variations, seasonalvariations, and random fluctuations.
Slide 9
Time SeriesExamine Patterns in the Past
TIME
To
X
XX
Dependent Variable
Secular Trend
Forecasted Amounts
The data may offer secular trends, cyclical variations, seasonalvariations, and random fluctuations.
Slide 10
Time SeriesExamine Patterns in the Past
TIME
To
X
XX
Dependent Variable
Secular TrendCyclical Variation
Forecasted Amounts
The data may offer secular trends, cyclical variations, seasonalvariations, and random fluctuations.
Slide 11
Elementary Time Series Models for Economic Forecasting
1. Naive Forecast
Yt+1 = Yt
» Method best when there is no trend, only random error
» Graphs of sales over time with and without trends
» When trending down, the Naïve predicts too high
NO Trend
Trend
^
time
time
Slide 12
2. Naïve forecast with adjustments for secular trends
Yt+1 = Yt + (Yt - Yt-1 )» This equation begins with last period’s
forecast, Yt. » Plus an ‘adjustment’ for the change in the
amount between periods Yt and Yt-1.» When the forecast is trending up, this
adjustment works better than the pure naïve forecast method #1.
^
Slide 13
3. Linear Trend & 4. Constant rate of growth
• Used when trend has a constant AMOUNT of change
Yt = a + b•T, where
Yt t are the actual observations and
TT is a numerical time variable
• Used when trend is a constant PERCENTAGE rate
Log Yt = a + b•T,
where b b is the continuously compounded growth rate
Linear Trend Growth Uses a Semi-log Regression
Slide 14
More on Constant Rate of Growth Modela proof
• Suppose: Yt = Y0( 1 + G) t where g is the annual growth rate
• Take the natural log of both sides:» Ln Yt = Ln Y0 + t • Ln (1 + G)
» but Ln ( 1 + G ) g, the equivalent continuously compounded growth rate
» SO: Ln Yt = Ln Y0 + t • g
Ln Yt = + • t
where is the growth rate
^
^
Slide 15
Numerical Examples: 6 observations
MTB > Print c1-c3.
Sales Time Ln-sales
100.0 1 4.60517
109.8 2 4.69866
121.6 3 4.80074
133.7 4 4.89560
146.2 5 4.98498
164.3 6 5.10169
Using this salesdata, estimate sales in period 7using a linear and a semi-log functionalform
Slide 16
The linear regression equation isSales = 85.0 + 12.7 Time
Predictor Coef Stdev t-ratio pConstant 84.987 2.417 35.16 0.000Time 12.6514 0.6207 20.38 0.000
s = 2.596 R-sq = 99.0% R-sq(adj) = 98.8%
The semi-log regression equation isLn-sales = 4.50 + 0.0982 Time
Predictor Coef Stdev t-ratio pConstant 4.50416 0.00642 701.35 0.000Time 0.098183 0.001649 59.54 0.000
s = 0.006899 R-sq = 99.9% R-sq(adj) = 99.9%
Slide 17
Forecasted Sales @ Time = 7• Linear Model• Sales = 85.0 + 12.7 Time
• Sales = 85.0 + 12.7 ( 7)
• Sales = 173.9
• Semi-Log Model• Ln-sales = 4.50 + 0.0982
Time
• Ln-sales = 4.50 + 0.0982 ( 7 )
• Ln-sales = 5.1874
• To anti-log:
» e5.1874 = 179.0
linear
Slide 18
Sales Time Ln-sales
100.0 1 4.60517
109.8 2 4.69866
121.6 3 4.80074
133.7 4 4.89560
146.2 5 4.98498
164.3 6 5.10169
179.0 7 semi-log
173.9 7 linearWhich prediction do you prefer?
Semi-log isexponential
7
Slide 19
5. Declining Rate of Growth Trend
• A number of marketing penetration models use a slight modification of the constant rate of growth model
• In this form, the inverse of time is used
Ln Yt = 1 – 2 ( 1/t )• This form is good for patterns
like the one to the right• It grows, but at continuously
a declining rate time
Y
Slide 20
6. Seasonal Adjustments: The Ratio to Trend Method
Take ratios of the actual to the forecasted values for past years.
Find the average ratio. This is the seasonal adjustment
Adjust by this percentage by multiply your forecast by the seasonal adjustment» If average ratio is 1.02, adjust
forecast upward 2%
12 quarters of data
I II III IV I II III IV I II III IV
Quarters designated with roman numerals.
Slide 21
• Let D = 1, if 4th quarter and 0 otherwise
• Run a new regression:
Yt = a + b•T + c•D » the “c” coefficient gives the amount of the adjustment for the fourth
quarter. It is an Intercept Shifter.» With 4 quarters, there can be as many as three dummy variables; with 12
months, there can be as many as 11 dummy variables
• EXAMPLE: Sales = 300 + 10•T + 18•D12 Observations from the first quarter of 2005 to 2007-IV.
Forecast all of 2008.
Sales(2008-I) = 430; Sales(2008-II) = 440; Sales(2008-III) = 450; Sales(2008-IV) = 478
7. Seasonal Adjustments: Dummy Variables
Slide 22
Soothing Techniques8. Moving Averages
• A smoothing forecast method for data that jumps around
• Best when there is no trend• 3-Period Moving Ave is:
Yt+1 = [Yt + Yt-1 + Yt-2]/3
• For more periods, add them up and take the average
*
*
*
*
*
ForecastLine isSmoother
TIME
Dependent Variable
Slide 23
Smoothing Techniques9. First-Order Exponential Smoothing
• A hybrid of the Naive and Moving Average methods
• Yt+1 = •Yt +(1-)Yt
• A weighted average of past actual and past forecast, with a weight of
• Each forecast is a function of all past observations
• Can show that forecast is based on geometrically declining weights.Yt+1 = .•Yt +(1-)••Yt-1 +
(1-)2••Yt-1 + …
Find lowest RMSE to pick the best .
^ ^
^ ^
Slide 24
First-Order Exponential Smoothing Example for = .50
Actual Sales Forecast
100 100 initial seed required
120 .5(100) + .5(100) = 100
115
130
?
1
2
3
4
5
Slide 25
First-Order Exponential Smoothing Example for = .50
Actual Sales Forecast
100 100 initial seed required
120 .5(100) + .5(100) = 100
115 .5(120) + .5(100) = 110
130
?
1
2
3
4
5
Slide 26
First-Order Exponential Smoothing Example for = .50
Actual Sales Forecast
100 100 initial seed required
120 .5(100) + .5(100) = 100
115 .5(120) + .5(100) = 110
130 .5(115) + .5(110) = 112.50
? .5(130) + .5(112.50) = 121.25
Period 5 Forecast
MSE = {(120-100)2 + (110-115)2 + (130-112.5)2}/3 = 243.75RMSE = 243.75 = 15.61
1
2
3
4
5
Slide 27
Direction of sales can be indicated by other variables.
TIME
Index of Capital Goods
peakPEAK Motor Control Sales
4 Months
Example: Index of Capital Goods is a “leading indicator”There are also lagging indicators and coincident indicators
Qualitative Forecasting10. Barometric Techniques
Slide 28
LEADING INDICATORS*» M2 money supply (-14.4)
» S&P 500 stock prices (-11.1)
» Building permits (-15.4)
» Initial unemployment claims (-12.9)
» Contracts and orders for plant and equipment (-7.3)
COINCIDENT INDICATORS» Nonagricultural payrolls
(+.8)» Index of industrial
production (-1.1)» Personal income less
transfer payment (-.4)
LAGGING INDICATORS» Prime rate (+17.9)
» Change in labor cost per unit of output (+6.4)
*Survey of Current Business, 1995 See pages 182-183 in the textbook
Time given in months from change
Slide 29
Handling Multiple IndicatorsDiffusion IndexDiffusion Index: Suppose 11 forecasters predict stock prices in 6 months, up or down. If 4 predict down and seven predict up, the Diffusion Index is 7/11, or 63.3%.
• above 50% is a positive diffusion index
Composite IndexComposite Index: One indicator rises 4% and another rises 6%. Therefore, the Composite Index is a 5% increase.
• used for quantitative forecasting
Slide 30
Qualitative Forecasting11. Surveys and Opinion Polling Techniques
• Sample bias--» telephone, magazine
• Biased questions--» advocacy surveys
• Ambiguous questions
• Respondents may lie on questionnaires
New Products have nohistorical data -- Surveyscan assess interest in newideas.
Survey Research Centerof U. of Mich. does repeatsurveys of households onBig Ticket items (Autos)
Survey Research Centerof U. of Mich. does repeatsurveys of households onBig Ticket items (Autos)
Common Survey Problems
Slide 31
Qualitative Forecasting12. Expert Opinion
The average forecast from several experts is a Consensus Forecast.» Mean» Median» Mode» Truncated Mean» Proportion positive or negative
Slide 32
EXAMPLES:
• IBES, First Call, and Zacks Investment -- earnings forecasts of stock analysts of companies
• Conference Board – macroeconomic predictions
• Livingston Surveys--macroeconomic forecasts of 50-60 economists
Individual economists tend to be less accurate over time than the ‘consensus forecast’.
Slide 33
13. Econometric Models• Specify the variables in the model
• Estimate the parameters » single equation or perhaps several stage methods
»Qd = a + b•P + c•I + d•Ps + e•Pc
• But forecasts require estimates for future prices, future income, etc.
• Often combine econometric models with time series estimates of the independent variable.
» Garbage in Garbage out
Slide 34
example • Qd = 400 - .5•P + 2•Y + .2•Ps
» anticipate pricing the good at P = $20
» Income (Y) is growing over time, the estimate is: Ln Yt = 2.4 + .03•T, and next period is T = 17.
• Y = e2.910 = 18.357
» The prices of substitutes are likely to be P = $18.
• Find Qd by substituting in predictions for P, Y, and Ps
• Hence Qd = 430.31
Slide 35
14. Stochastic Time Series• A little more advanced methods incorporate into time
series the fact that economic data tends to drift
yt = + yt-1 + t
• In this series, if is zero and is 1, this is essentially the naïve model. When is zero, the pattern is called a random walk.
• When is positive, the data drift. The Durbin-Watson statistic will generally show the presence of autocorrelation, or AR(1), integrated of order one.
• One solution to variables that drift, is to use first differences.
Slide 36
Cointegrated Time Series• Some econometric work includes several stochastic
variable, each which exhibits random walk with drift» Suppose price data (P) has positive drift» Suppose GDP data (Y) has positive drift» Suppose the sales is a function of P & Y
» Salest = a + bPt + cYt
» It is likely that P and Y are cointegrated in that they exhibit comovement with one another. They are not independent.
» The simplest solution is to change the form into first differences as in: Salest = a + bPt + cYt