time series analysis and index numbers introduction to business statistics, 5e kvanli/guynes/pavur...
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Time Series Analysisand Index Numbers
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Times Series
Time series represents a variable observed across time.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
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
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.
tbbTR o 1Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Trend
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 16.2
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
Seasonal Variation
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing Figure 16.5
Calculation of Seasonal Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Calculation of Seasonal Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Calculation of Seasonal Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Calculation of Seasonal Indexes
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Deseasonalizing Data
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Trend and Seasonal Variation
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing Figure 16.6
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
Cyclical Variation
Figure 16.7
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
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
Additive Structure
ttttt ICSTRy
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Multiplicative Structure
ttttt ICSTRy
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Linear Trend
tbbTRy ott 1ˆ
Figure 16.9
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Cyclical Activitywithout Seasonality
Ct yt
ˆ y t
tttt ICTRy
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Cyclical Activity
Figure 16.15
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Seasonal Variation
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
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
Price Indexes
simple aggregate price index P1
P0
100
weighted aggregate price index P1Q P0 Q
100
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Price Indexes
Laspeyres index P1Q0
P0 Q0
100
Paasche index P1Q1
P0Q1
100
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Prices for Items is 1990 and 1998
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing