The Art of Forecasting
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1 Time Series The Art of Forecasting
2 Learning Objectives Describe what forecasting is Explain time series & its components Smooth a data series Moving average Exponential smoothing Forecast using trend models Simple Linear Regression Auto-regressive
3 What Is Forecasting? Process of predicting a future event Underlying basis of all business decisions Production Inventory Personnel Facilities
4 Forecasting Approaches Qualitative Methods Used when situation is vague & little data exist New products New technology Involve intuition, experience e.g., forecasting sales on Internet Quantitative Methods
5 Forecasting Approaches Qualitative Methods Used when situation is vague & little data exist New products New technology Involve intuition, experience e.g., forecasting sales on Internet Quantitative Methods Used when situation is stable & historical data exist Existing products Current technology Involve mathematical techniques e.g., forecasting sales of color televisions
6 Quantitative Forecasting Select several forecasting methods Forecast the past Evaluate forecasts Select best method Forecast the future Monitor continuously forecast accuracy
7 Quantitative Forecasting Methods
8 Quantitative Forecasting Methods Quantitative Forecasting
9 Quantitative Forecasting Methods Quantitative Forecasting Time Series Models
10 Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Causal Models
11 Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Causal Models Moving Average Exponential Smoothing Trend Models
12 Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Causal Models Moving Average Exponential Smoothing Trend Models Regression
13 Quantitative Forecasting Methods Quantitative Forecasting Time Series Models Causal Models Moving Average Exponential Smoothing Trend Models Regression
14 What is a Time Series? Set of evenly spaced numerical data Obtained by observing response variable at regular time periods Forecast based only on past values Assumes that factors influencing past, present, & future will continue Example Year: Sales:
15 Time Series vs. Cross Sectional Data Time series data is a sequence of observations collected from a process with equally spaced periods of time.
16 Time Series vs. Cross Sectional Data Contrary to restrictions placed on cross-sectional data, the major purpose of forecasting with time series is to extrapolate beyond the range of the explanatory variables.
17 Time Series vs. Cross Sectional Data Time series is dynamic, it does change over time.
18 Time Series vs. Cross Sectional Data When working with time series data, it is paramount that the data is plotted so the researcher can view the data.
19 Time Series Components
20 Time Series Components Trend
21 Time Series Components Trend Cyclical
22 Time Series Components Trend Cyclical Seasonal
23 Time Series Components Trend Cyclical Seasonal Irregular
24 Trend Component Persistent, overall upward or downward pattern Due to population, technology etc. Several years duration Response Mo., Qtr., Yr T/Maker Co.
25 Trend Component Overall Upward or Downward Movement Data Taken Over a Period of Years Sales Time
26 Cyclical Component Repeating up & down movements Due to interactions of factors influencing economy Usually 2-10 years duration Response Cycle Mo., Qtr., Yr.
27 Cyclical Component Upward or Downward Swings May Vary in Length Usually Lasts 2-10 Years Sales Time
28 Seasonal Component Regular pattern of up & down fluctuations Due to weather, customs etc. Occurs within one year Response Summer T/Maker Co. Mo., Qtr.
29 Seasonal Component Upward or Downward Swings Regular Patterns Observed Within One Year Sales Time (Monthly or Quarterly)
30 Irregular Component Erratic, unsystematic, residual fluctuations Due to random variation or unforeseen events Union strike War Short duration & nonrepeating T/Maker Co.
31 Random or Irregular Component Erratic, Nonsystematic, Random, Residual Fluctuations Due to Random Variations of Nature Accidents Short Duration and Non-repeating
32 Time Series Forecasting
33 Time Series Forecasting Time Series
34 Time Series Forecasting Time Series Trend?
35 Time Series Forecasting Time Series Smoothing Methods No Trend?
36 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models
37 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing
38 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
39 Time Series Analysis
40 Plotting Time Series Data ( X ) I n t ra - C a m p u s B u s P a ss en g e rs N u m b e r o f P a sse n g e rs / / / / /9 5 D a ta c ol lec te d b y C oo p S tu d e n t (1 0 /6 /9 5 ) M o n th / Y e ar
41 Moving Average Method
42 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
43 Moving Average Method Series of arithmetic means Used only for smoothing Provides overall impression of data over time
44 Moving Average Method Series of arithmetic means Used only for smoothing Provides overall impression of data over time Used for elementary forecasting
45 Moving Average Graph Sales Year Actual
46 Moving Average [An Example] You work for Firestone Tire. You want to smooth random fluctuations using a 3-period moving average , , , , ,000
47 Moving Average [Solution] Year Sales MA(3) in 1, ,000 NA ,000 ( )/3 = ,000 ( )/3 = ,000 ( )/3 = ,000 NA
48 Moving Average Year Response Moving Ave Sales NA NA
49 Exponential Smoothing Method
50 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
51 Exponential Smoothing Method Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant (W) Ranges from 0 to 1 Subjectively chosen Involves little record keeping of past data
52 Exponential Smoothing [An Example] You re organizing a Kwanza meeting. You want to forecast attendance for 1998 using exponential smoothing (α =.20). Past attendance (00) is: Corel Corp.
53 Exponential Smoothing E i = WY i + (1 - W)E i-1 Smoothed Value, E Time Y i i (W =.2) Forecast ^ Y i NA (.2)(6) + (1-.2)(4.0) = (.2)(5) + (1-.2)(4.4) = (.2)(3) + (1-.2)(4.5) = (.2)(7) + (1-.2)(4.2) = NA NA 4.8
54 Exponential Smoothing Attendance [Graph] Year Actual
55 W is... Prior Period Forecast Effect of Smoothing Coefficient (W) ^ Y i+1 = WY i + W(1-W)Y i-1 + W(1-W) 2 Y i Weight 2 Periods Ago 3 Periods Ago W W(1-W) W(1-W) % 9% 8.1% % 9% 0.9%
56 Linear Time-Series Forecasting Model
57 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
58 Linear Time-Series Forecasting Model Used for forecasting trend Relationship between response variable Y & time X is a linear function Coded X values used often Year X: Coded year: Sales Y:
59 Linear Time-Series Model Y $ = b + b X i i Y b 1 > 0 b 1 < 0 Time, X 1
60 Linear Time-Series Model [An Example] You re a marketing analyst for Hasbro Toys. Using coded years, you find Y i =.6 +.7X ^ i Forecast 2000 sales.
61 Linear Time-Series [Example] Year Coded Year Sales (Units) ? 2000 forecast sales: Y i =.6 ^ +.7 (5) = 4.1 The equation would be different if Year used.
62 The Linear Trend Model Year Coded Sales Excel Output Coefficients Inte rce pt X V ariable Ŷ = b. 743X i 0 + b1x i = Projected to year i
63 Time Series Plot ( X ) S u r g e r y D a t a ( T i m e S e q u e n c e P l o t ) N u m b e r o f S u r g e r i e s / / / / / 9 7 M o n t h / Y e a r S o u r c e : G e n e r a l H o s p i t a l, M e t r o p o l i s
64 Time Series Plot [Revised] ( X ) R e v i s e d S u r g e r y D a t a ( T i m e S e q u e n c e P l o t ) N u m b e r o f S u r g e r i e s / / / / / 9 7 S o u r c e : G e n e r a l H o s p i t a l, M e t r o p o l i s M o n t h / Y e a r
65 Seasonality Plot R e v i s e d S u r g e r y D a t a ( S e a s o n a l D e c o m p o s i t i o n ) M o n t h l y I n d e x J a n F e b M a r A p r M a y J u n J u l A u g S e p O c t N o v D e c M o n t h S o u r c e : G e n e r a l H o s p i t a l, M e t r o p o l i s
66 Trend Analysis ( X ) R e v i s e d S u r g e r y D a t a ( T r e n d A n a l y s i s ) N u m b e r o f S u r g e r i e s / / / / / / / 9 7 M o n t h / Y e a r S o u r c e : G e n e r a l H o s p i t a l, M e t r o p o l i s
67 Quadratic Time-Series Forecasting Model
68 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
69 Quadratic Time-Series Forecasting Model Used for forecasting trend Relationship between response variable Y & time X is a quadratic function Coded years used
70 Quadratic Time-Series Forecasting Model Used for forecasting trend Relationship between response variable Y & time X is a quadratic function Coded years used Quadratic model Y $ = b + b X + b X 2 i i 11 1 i
71 Quadratic Time-Series Model Relationships Y b 11 > 0 Y b 11 > 0 Year, X 1 Year, X 1 Y b 11 < 0 Y b 11 < 0 Year, X 1 Year, X 1
72 Quadratic Trend Model Year Coded Sales i i b X b X i 2 i Yˆ = b + + Excel Output Coefficients Inte rce pt X Variable X Variable X i. 214 X i Ŷ = +
73 Exponential Time-Series Model
74 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
75 Exponential Time-Series Forecasting Model Used for forecasting trend Relationship is an exponential function Series increases (decreases) at increasing (decreasing) rate
76 Exponential Time-Series Forecasting Model Used for forecasting trend Relationship is an exponential function Series increases (decreases) at increasing (decreasing) rate
77 Exponential Time-Series Model Relationships Y b 1 > 1 Year, X 1 0 < b 1 < 1
78 Exponential Weight Sales [Example Graph] Data Smoothed Year
79 Exponential Trend Model Ŷi b0b1 X i = or log Ŷ i = log b0 + X 1 log b1 Year Coded Sales Coefficients Interc ept X V ariable Excel Output of Values in logs antilog( ) = 2.17 antilog( ) = 1.2 Ŷ = ( )( 1. 2 ) i X i
80 Autoregressive Modeling
81 Time Series Forecasting Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
82 Autoregressive Modeling Used for forecasting trend Like regression model Independent variables are lagged response variables Y i-1, Y i-2, Y i-3 etc. Assumes data are correlated with past data values 1 st Order: Correlated with prior period Estimate with ordinary least squares
83 Time Series Data Plot ( X ) I n t ra - C a m p u s B u s P a ss en g e rs N u m b e r o f P a sse n g e rs / / / / /9 5 D a ta c ol lec te d b y C oo p S tu d e n t (1 0 /6 /9 5 ) M o n th / Y e ar
84 Auto-correlation Plot I n t r a - C a m p u s B u s ( A u t o C o r r e l a t i o n F u n c t i o n ± 2 σ L a g
85 Autoregressive Model [An Example] The Office Concept Corp. has acquired a number of office units (in thousands of square feet) over the last 8 years. Develop the 2nd order Autoregressive models. Year Units
86 Autoregressive Model Develop the 2nd order table Use Excel to run a regression model Excel Output [Example Solution] Coefficients Inte rce pt 3.5 X Varia ble X Varia ble Y i Year Y i Y i-1 Y i = Yi Yi 2
87 Evaluating Forecasts
88 Quantitative Forecasting Steps Select several forecasting methods Forecast the past Evaluate forecasts Select best method Forecast the future Monitor continuously forecast accuracy
89 Forecasting Guidelines No pattern or direction in forecast error e i = (Actual Y i - Forecast Y i ) Seen in plots of errors over time Smallest forecast error Measured by mean absolute deviation Simplest model Called principle of parsimony
90 Pattern of Forecast Error Trend Not Fully Accounted for Desired Pattern Error Error 0 0 Time (Years) Time (Years)
91 e Residual Analysis e 0 0 e Random errors T T Cyclical effects not accounted for e 0 0 Trend not accounted for T T Seasonal effects not accounted for
92 Principal of Parsimony Suppose two or more models provide good fit for data Select the Simplest Model Simplest model types: least-squares linear least-square quadratic 1st order autoregressive More complex types: 2nd and 3rd order autoregressive least-squares exponential
93 Summary Described what forecasting is Explained time series & its components Smoothed a data series Moving average Exponential smoothing Forecasted using trend models
94 You and StatGraphics Specification [Know assumptions underlying various models.] Estimation [Know mechanics of StatGraphics Plus Win]. Diagnostic checking
95 Questions?
96 Source of Elaborate Slides Prentice Hall, Inc Levine, et. all, First Edition
97 ANOVA
98 End of Chapter
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