PPT 13 Introduction to Autoregressive Models (1)

# PPT 13 Introduction to Autoregressive Models (1) - McGill...

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Unformatted text preview: McGill University Advanced Business Statistics MGSC-272 McGill University Advanced Business Statistics MGSC-272 Fall’09 Introduction to Autoregressive Models Read: Business Statistics (A Second Course) , Custom Edition for McGill University Longitudinal Data Analysis Given that the data over time can be correlated Data collected by making repeated observations on a process over time is analyzed. The past behavior can be examined for clues about future behavior. Correlation of a series with its own past history is called autocorrelation Definitions Time series … a sequence of observations collected from a process at fixed (and usually equally spaced) points in time. (Sequence plots, aka time series plots, are a graphic display of time series). Lag … an interval of time between observations in a time series. Definitions (continued...) Lag Length … the number of time periods back we reach to bring a past observation in line with a current observation. The values y t-1 is called the first lag of the sequence. We can plot the pairs ( y t , y t-1 ) to investigate a possible relationship. Autocorrelation Coefficient for the k th lag is represented by r k Note: r is a measure of the amount of memory a series has. Autocorrelation(lag 1) time period value (y t ,y t-1 ) 1st 16(y 1 ) × 2nd 21(y 2 ) 16(y 1 ) (21,16) 3rd 14(y 3 ) 21(y 2 ) (14, 21) 4th 20(y 4 ) 14(y 3 ) (20,14) 20(y 4 ) Autocorrelation ∑ ∑ =- = +--- = T t t k T t k t t k y y y y y y r 1 2 1 ) ( ) )( ( The formula below calculates the k th lag autocorrelation. Ken’s Auto-Body Shop The data listed below show the quarterly profits from Ken’s Auto-Body shop. Ken was hoping that the data will help predict future profit patterns. P r o fi t s 1 9 9 3 S p r i n g 5 . 5 6 S u m m e r 1 6 . 3 6 F a l l 2 . 1 2 W i n t e r 3 . 1 5 1 9 9 4 S p r i n g 5 . 1 1 S u m m e r 1 5 . 2 1 F a l l 5 . 7 2 W i n t e r 2 . 6 5 1 9 9 5 S p r i n g 4 . 1 2 S u m m e r 1 4 . 3 3 F a l l 5 . 2 5 W i n t e r 6 . 7 5 1 9 9 6 S p r i n g 6 . 3 1 S u m m e r 1 5 . 0 2 F a l l 2 . 8 3 W i n t e r 4 . 5 6 1 9 9 7 S p r i n g 4 . 8 1 S u m m e r 1 6 . 8 2 F a l l 4 . 7 5 W i n t e r 8 . 5 4 Sequence (Time Series) Plot 2 4 6 8 10 12 14 16 18 S p r i n g S u m m e r F a l l W i n t e r S p r i n g S u m m e r F a l l W i n t e r S p r i n g S u m m e r F a l l W i n t e r S p r i n g S u m m e r F a l l W i n t e r S p r i n g S u m m e r F a l l W i n t e r Ken’s Auto-Body Shop Quarterly Profits Profits Lag1 Lag2 Lag3 Lag4 Lag5 Lag6 Lag7 Lag8 Lag9 Lag10 Lag11 Lag12 1993 Spring 5.56 Summer 16.36 5.56 Fall 2.12 16.36 5.56 Winter 3.15 2.12 16.36 5.56 1994 Spring 5.11 3.15 2.12 16.36 5.56 Summer 15.21 5.11 3.15 2.12 16.36 5.56 Fall 5.72 15.21 5.11 3.15 2.12 16.36 5.56 Winter 2.65 5.72 15.21 5.11 3.15 2.12 16.36 5.56 1995 Spring 4.12 2.65 5.72 15.21 5.11 3.15 2.12 16.36 5.56 Summer 14.33 4.12 2.65 5.72 15.21 5.11 3.15 2.12 16.36 5.56 Fall 5.25 14.33 4.12 2.65 5.72 15.21 5.11 3.15 2.12 16.36 5.56 Winter 6.75 5.25 14.3314....
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## This note was uploaded on 02/28/2012 for the course MANAGEMENT MGSC 272 taught by Professor Smith during the Spring '12 term at McGill.

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PPT 13 Introduction to Autoregressive Models (1) - McGill...

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