Lecture Business statistics in practice (7/e): Chapter 16 - Bowerman, O'Connell, Murphree

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Chapter 16 - Times series forecasting and index numbers. This chapter includes contents: Time series components and models, time series regression, multiplicative decomposition, simple exponential smoothing, Holt-Winter’s Models, the Box Jenkins methodology (optional advanced section), forecast error comparisons, index numbers.

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Nội dung Text: Lecture Business statistics in practice (7/e): Chapter 16 - Bowerman, O'Connell, Murphree

Chapter 16 Times Series Forecasting and Index Numbers McGrawHill/Irwin Copyright © 2014 by The McGrawHill Companies, Inc. All rights reserved.
Time Series Forecasting 16.1 Time Series Components and Models 16.2 Time Series Regression 16.3 Multiplicative Decomposition 16.4 Simple Exponential Smoothing 16.5 HoltWinter’s Models 16.6 The Box Jenkins Methodology (Optional Advanced Section) 16.7 Forecast Error Comparisons 16.8 Index Numbers 162
LO16-1: Identify the components of a times series. 16.1 Time Series Components and Models Trend Longrun growth or decline Cycle Longrun up and down fluctuation around the trend level Seasonal Regular periodic up and down movements that repeat within the calendar year Irregular Erratic very shortrun movements that follow no regular pattern 163
LO16-1 Time Series Exhibiting Trend, Seasonal, and Cyclical Components Figure 16.1 164
LO16-1 Seasonality Some products have demand that varies a great deal by period ◦Coats, bathing suits, bicycles This periodic variation is called seasonality ◦Constant seasonality: the magnitude of the swing does not depend on the level of the time series ◦Increasing seasonality: the magnitude of the swing increases as the level of the time series increases Seasonality alters the linear relationship between time and demand 165
LO16-2: Use time series regression to forecast time series having 16.2 Time Series Regression linear, quadratic, and certain types of seasonal patterns. Within regression, seasonality can be modeled using dummy variables Consider the model: yt = 0 + 1t + Q2Q2 + Q3 Q3 + Q4 Q4 + t ◦For Quarter 1, Q2 = 0, Q3 = 0 and Q4 = 0 ◦For Quarter 2, Q2 = 1, Q3 = 0 and Q4 = 0 ◦For Quarter 3, Q2 = 0, Q3 = 1 and Q4 = 0 ◦For Quarter 4, Q2 = 0, Q3 = 0 and Q4 = 1 The coefficient will then give us the seasonal impact of that quarter relative to Quarter 1 ◦Negative means lower sales, positive lower sales 166
LO16-3: Use data transformations to forecast time series Transformations having increasing seasonal variation. Sometimes, transforming the sales data makes it easier to forecast ◦Square root ◦Quartic roots ◦Natural logarithms While these transformations can make the forecasting easier, they make it harder to understand the resulting model 167
LO 4: Use multiplicative decomposition and moving averages to 16.3 Multiplicative Decomposition forecast time series having increasing seasonal variation. We can use the multiplicative decomposition method to decompose a time series into its components: Trend Seasonal Cyclical Irregular 168
LO 16-5: Use simple exponential smoothing to forecast a time 16.4 Simple Exponential Smoothing series.  Earlier, we saw that when there is no trend, the least squares point estimate b0 of β0 is just the average y value ◦yt = β0 + t  That gave us a horizontal line that crosses the y axis at its average value  Since we estimate b0 using regression, each period is weighted the same  If β0 is slowly changing over time, we want to weight more recent periods heavier  Exponential smoothing does just this 169
LO16-6: Use double exponential smoothing to forecast a time 16.5 Holt–Winters’ Models series.  Simple exponential smoothing cannot handle trend or seasonality  Holt–Winters’ double exponential smoothing can handle trended data of the form yt = β0 + β1t + t ◦Assumes β0 and β1 changing slowly over time ◦We first find initial estimates of β0 and β1 ◦ Then use updating equations to track changes over time  Requires smoothing constants called alpha and gamma 1610
LO16-7: Use multiplicative Winters’ method to forecast a Multiplicative Winters’ Method time series.  Double exponential smoothing cannot handle seasonality  Multiplicative Winters’ method can handle trended data of the form yt = (β0 + β1t) ∙ SNt + t ◦Assumes β0, β1, and SNt changing slowly over time ◦We first find initial estimates of β0 and β1 and seasonal factors ◦ Then use updating equations to track over time  Requires smoothing constants alpha, gamma and delta 1611
LO16-8: Use the Box–Jenkins methodology to forecast a time series. 16.6 The Box–Jenkins Methodology (Optional Advanced Section) Uses a quite different approach Begins by determining if the time series is stationary ◦The statistical properties of the time series are constant through time Plots can help If nonstationary, will transform series 1612
LO16-9: Compare time series models by using forecast errors. 16.7 Forecast Error Comparison Forecast errors: et = yt ŷt Error comparison criteria ◦Mean absolute deviation (MAD) n n et yt yˆ t MAD t 1 t 1 n n ◦Mean squared deviation (MSD) n n 2 e t ( yt yˆ t ) 2 MSD t 1 t 1 n n 1613
LO16-10: Use index numbers to compare economic data over 16.8 Index Numbers time. Index numbers allow us to compare changes in time series over time We begin by selecting a base period Every period is converted to an index by dividing its value by the base period and then multiplying the results by 100 ◦Simple (quantity) index yt it 100 y0 1614