lecture14 - Lecture 14: Correlation and Autocorrelation...

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Unformatted text preview: Lecture 14: Correlation and Autocorrelation Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794–4400 http://www.cs.sunysb.edu/ ∼ skiena Overuse of Color, Dimensionality, and Plots Four colors, three dimensions, and two plots to visualize five data points! Misleading Scales Neither the time dimension nor the data magnitudes are represented faithfully. Railroad Schedules as Time Series Which trains are fastest? Which trains stop moving? When do you see a passing train out the window? Variance and Covariance The variance of a random variable X is defined V ar ( X ) = σ 2 = summationdisplay ( X- μ x ) 2 /N ] = E [( X- μ x )] Dividing by N- 1 provides an unbiased estimate of σ 2 on sampled data, compensating for the difference between the sample mean and the population mean. The covariance of random variables X and Y , is defined Cov ( X, Y ) = E [( X- μ x )( Y- μ y )] If X and Y are “in sync” the covariance will be high; if they are independent, positive and negative terms should cancel out to give a score around zero. Correlation Coefficent Pearson’s correlation coefficient of random variables X...
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This note was uploaded on 01/02/2012 for the course FINANCE 347 taught by Professor Bayou during the Fall '11 term at NYU.

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lecture14 - Lecture 14: Correlation and Autocorrelation...

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