Chapter 4

# Chapter 4 - Chapter 4 KVANLI PAVUR KEELING Time Series...

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Click to edit Master subtitle style 3/13/11 Chapter 4 – Time Series Analysis and Forecasting KVANLI PAVUR KEELING

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3/13/11 Chapter Objectives At the completion of this chapter, you should be able to: Understand the meaning of time series and the four components of the data Estimate the trend, seasonality, cyclical and noise components ∙ Use Excel macro to decompose
3/13/11 What is a Time Series? A time series consists of a variable (such as Sales) recorded across time Example: t Year Sales (millions of \$) 1 1985 1.7 2 1986 2.4 3 1987 2.8 4 1988 3.4 . . This is y1 This is y23 This is an example of annual data

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3/13/11 Time Series Data Time series data can be: ∙ annual (one value for each year) ∙ quarterly (4 values for each year) ∙ monthly (12 values for each year) Each time series value is made up of 3 or 4 components. These are: Monthly or quarterly data only
3/13/11 What is a Time Series?

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3/13/11 Sales Data for Video-Comp Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 2004 20 12 47 60 2005 40 32 65 76 2006 56 50 85 100 2007 75 70 101 123 Table 4.3
3/13/11 Trend (TR) Linear Trend TR = b 0 + b 1 t Trend is a steady increase or decrease in the time series This long-term growth or decay pattern can take a variety of shapes. If the rate of change in Y from one time period to the next is relatively constant, the trend is a linear trend .

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3/13/11 Linear Trends Yt t (a) Increasing trend Yt t (b) Decreasing trend
3/13/11 Employees Example 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 Number of employees (thousands) | 20 00 | 20 01 | 20 02 | 20 03 | 20 04 | 20 05 | 20 06 | 20 07 t Trend We’ll take a closer look at this example in the slides to follow

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3/13/11 Curvilinear Trend Trend can also be curvilinear Curvilinear trend is also called quadratic trend In this chapter, we will pay little attention to curvilinear trend Quadratic Trend TR = b 0 + b 1 t + b 2 t 2
3/13/11 Seasonality Seasonality (seasonal variation) is periodic variation (increases or decreases) within a calendar year in a time series. The key is that this variation in the time series follows the same pattern each year For example, sales are always high in December

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3/13/11 Seasonal Variation 40 35 30 25 20 15 10 Power consumption (millions kwh) | | Jan Jul Dec 200 2 Jan Jul Dec 200 3 Jan Jul Dec 200 4 Figure 13.5
3/13/11 Seasonal Variation Figure 13.6 Linear trend 4 3 2 1 Sales of Wildcat sailboats (millions of dollars ) | July 200 1 | July 200 2 | July 200 3 | July 200 4 t

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3/13/11 Cyclical Variation Cyclical variation describes a gradual cyclical movement about the trend.
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## This note was uploaded on 03/12/2011 for the course DSCI 2710 taught by Professor Hossain during the Summer '08 term at North Texas.

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Chapter 4 - Chapter 4 KVANLI PAVUR KEELING Time Series...

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