Based on the original slides from Levine, et. all, First Edition, Prentice Hall, Inc
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1 Based on the original slides from Levine, et. all, First Edition, Prentice Hall, Inc
2 Process of predicting a future event Underlying basis of all business decisions Production Inventory Personnel Facilities
3 Select several forecasting methods Forecast the past Evaluate forecasts Select best method Forecast the future Monitor continuously forecast accuracy
4 Quantitative Forecasting Time Series Models Causal Models Moving Average Exponential Smoothing Trend Models Regression
5 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:
6 Trend Cyclical Seasonal Irregular
7 Persistent, overall upward or downward pattern Due to population, technology etc. Several years duration Response Mo., Qtr., Yr T/Maker Co.
8 Overall Upward or Downward Movement Data Taken Over a Period of Years Sales Time
9 Repeating up & down movements Due to interactions of factors influencing economy Usually 2-10 years duration Response Cycle Mo., Qtr., Yr.
10 Upward or Downward Swings May Vary in Length Usually Lasts 2-10 Years Sales Time
11 Regular pattern of up & down fluctuations Due to weather, customs etc. Occurs within one year Response Summer T/Maker Co. Mo., Qtr.
12 Upward or Downward Swings Regular Patterns Observed Within One Year Sales Time (Monthly or Quarterly)
13 Erratic, unsystematic, residual fluctuations Due to random variation or unforeseen events Union strike War Short duration & nonrepeating T/Maker Co.
14 Erratic, Nonsystematic, Random, Residual Fluctuations Due to Random Variations of Nature Accidents Short Duration and Non-repeating
15 Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
16 (X 1000) Intra-Campus Bus Passengers Number of Passengers /83 07/86 05/89 03/92 01/95 Data collected by Coop Student (10/6/95) Month/Year
17
18 Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
19 Series of arithmetic means Used only for smoothing Provides overall impression of data over time Used for elementary forecasting
20 Sales Actual Year
21 Year Response Moving Ave Sales NA NA
22
23 Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
24 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
25 E i = W Y i + (1 - W) E i-1 Time Y i Smoothed Value, E 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
26 Attendance Actual Year
27 ^ Y i+1 = W Y i + W (1-W) Y i-1 + W (1-W) 2 Y i Weight W is... Prior Period 2 Periods Ago 3 Periods Ago W W(1-W) W(1-W) % 9% 8.1% % 9% 0.9%
28
29 Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
30 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:
31 Y b b X i 0 1 1i Y b 1 > 0 Time, X 1 b 1 < 0
32 Year Coded Year Sales (Units) ? 2000 forecast sales: Y i = (5) = 4.1 The equation would be different if Year used.
33 Year Coded Sales Excel Output Co efficien ts In te rc e p t X V a ria b le Ŷ b. 743X i 0 b1x i Projected to year i
34
35 Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
36 Used for forecasting trend Relationship between response variable Y & time X is a quadratic function Coded years used
37 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 0 1 1i 11 1i
38 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
39 Year Coded Sales Ŷ i Ŷ i b b X b X i 2 i Coefficients In te rce p t X V a ria b le X V a ria b le Excel Output X i. 214 X i
40
41 Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
42 Used for forecasting trend Relationship is an exponential function Series increases (decreases) at increasing (decreasing) rate
43 Used for forecasting trend Relationship is an exponential function Series increases (decreases) at increasing (decreasing) rate
44 Y b 1 > 1 0 < b 1 < 1 Year, X 1
45 Sales 8 6 Data 4 2 Smoothed Year
46 Ŷi b0b1 X i or log Ŷ i log b0 X 1 log b1 Year Coded Sales C o e f f ic ie n t s In t e rc e p t X V a ria b le Excel Output of Values in logs a n tilo g ( ) = a n tilo g ( ) = 1.2 Ŷ ( )( 1. 2 ) i X i
47
48 Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive
49 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
50 (X 1000) Intra-Campus Bus Passengers Number of Passengers /83 07/86 05/89 03/92 01/95 Data collected by Coop Student (10/6/95) Month/Year
51 1 Intra-Campus Bus Passengers (Auto Correlation Function Plot Lag
52 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
53 Develop the 2nd order table Use Excel to run a regression model Excel Output Coefficients In te rce p t 3.5 X V a ria b le X V a ria b le Y i Year Y i Y i-1 Y i Yi Yi 2
54 Given a time series of data X t where t is an integer index and X t are real numbers, The model is generally referred to as an ARIMA(p,d,q) model where parameters p, d, and q are non-negative integers that refer to the order of the autoregressive, integrated, and moving average parts of the model respectively.
55
56 Select several forecasting methods Forecast the past Evaluate forecasts Select best method Forecast the future Monitor continuously forecast accuracy
57 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
58 e e 0 0 e Random errors T T Cyclical effects not accounted for e 0 0 T Trend not accounted for T Seasonal effects not accounted for
59 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
60 Described what forecasting is Explained time series & its components Smoothed a data series Moving average Exponential smoothing Forecasted using trend models
61 Step-by-Step Graphic Guide to Forecasting through ARIMA Modeling using R:
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