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# a425_auto - Time Series Autocorrelation APS 425 Advanced...

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Time Series - Autocorrelation APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 1 APS 425 Winter 2010 Time Series Analysis: Autocorrelation Instructor: G William Schwer Instructor: G. William Schwert 585-275-2470 [email protected] Topics Causes of autocorrelation • Causes of autocorrelation • Diagnosing autocorrelation • Modeling autocorrelation

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Time Series - Autocorrelation APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 2 Autocorrelation • When the data used in regression model measure the same thing at different points in time, such as the price of Xerox stock, XRX t , it is not unusual for adjacent observations to be correlated with each other [APS_XRX.WF1] • Corr(XRX t , XRX t-1 ) > 0, means that when the stock price in period t-1 is above the sample average, it is likely that the stock price in period t will also be above the sample average • A graph of positively autocorrelated data shows smooth cycles, infrequently crossing the average Diagnosing Autocorrelation in Eviews • Calculate autocorrelations from “View” menu • Graph data from “View” menu
Time Series - Autocorrelation APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 3 Autocorrelation: Xerox Stock Price, 1970-1999 XRXP 80 120 160 200 Note: autocorrelations start at .98 and decay slowly to .76 •graph shows slowly moving, persistent pattern 0 40 70 75 80 85 90 95 00 05 10 Autocorrelation: Why? • Autocorrelation happens for many reasons –Information changes slowly through time, so the factors influencing a variable are likely to be similar in adjacent periods

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Time Series - Autocorrelation APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 4 Example: Random Walk Model for Stock Prices • If returns to stocks, r t , are random through time (unpredictable), perhaps because the market processes information efficiently and incorporates it into prices immediately, • Prices (or the logs of prices) will follow a random walk , since this period’s (log) price, log(P t ), equals last period’s (log) price, log(P t-1 ), plus this period’s random (continuously compounded) return: r t = log(P t ) - log(P t-1 ) = log(P t / P t-1 ) = log(1 + (P t -P t-1 )/ P t-1 )) Example: Random Walk Model for Stock Prices • While the changes in (log) prices are random and unpredictable, the (log) prices in consecutive months contain much of the same information – The (log) price at time t is just the (log) price at time 0 plus the sum of all returns between 0 and t log(P t ) = r t + r t-1 + . . . + r 1 + log(P 0 ) – So log(P t ) and log(P t-1 ) share t-1 past returns, which means they will be highly correlated
Time Series - Autocorrelation APS 425 - Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 5 Autocorrelation: Xerox Stock Returns, 1970-1999 XRX -.2 .0 .2 .4 .6 .8 Note: autocorrelations for returns are much smaller and returns vary

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## This note was uploaded on 03/03/2010 for the course APS 425 taught by Professor Schwert during the Spring '10 term at Rochester.

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a425_auto - Time Series Autocorrelation APS 425 Advanced...

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