Time Series Analysis and Index Numbers

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Time Series Analysisand Index Numbers
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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2
Times Series

• Time series represents a variable observed
  across time.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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3
Components of a Time Series

• Trend (TR)
• Seasonal variation (S)
• Cyclical variation (C)
• Irregular activity (I)

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
4
Trend

• 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.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
5
Trend
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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Figure 16.2
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Seasonality

• Seasonal variation refers to periodic increases
  or decreases that occur within a calendar year in
  a time series. The key is that these movements
  in the time series follow the same pattern each
  year.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
7
Seasonal Variation
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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Figure 16.5
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Calculation of Seasonal Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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9
Calculation of Seasonal Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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10
Calculation of Seasonal Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
11
Calculation of Seasonal Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
12
Deseasonalizing Data
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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Trend and Seasonal Variation
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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Figure 16.6
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Cyclical Variation

• Cyclical variation describes a gradual cyclical
  movement about the trend it is generally
  attributable to business and economic conditions.
  The length of the cycle is the period of that
  cycle and is measured from one peak to the next.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
16
Cyclical Variation
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
Figure 16.7
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Irregular Activity

• Irregular activity consists of what is left
  over after accounting for the effect of any
  trend, seasonality, or cyclical activity.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
18
Additive Structure
Introduction to Business Statistics, 5e
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19
Multiplicative Structure
Introduction to Business Statistics, 5e
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20
Linear Trend
Introduction to Business Statistics, 5e
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Figure 16.9
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Cyclical Activitywithout Seasonality
Introduction to Business Statistics, 5e
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22
Cyclical Activity
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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Figure 16.15
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Seasonal Variation
Introduction to Business Statistics, 5e
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Four Step Procedure for Decomposition

• Determine the seasonal index
• deseasonalized the data
• Determine the trend component
• Determine the cyclical component.

Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing
25
Price Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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Price Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
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Prices for Items is 1990 and 1998
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur (c)2000 South-Western
College Publishing