Chapter 6: Time Series Analysis

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Chapter 6: Time Series Analysis

ATM 552 Notes: Time Series Analysis - Section 6a Page 118analysis on the lag correlation function on the interval -T L T L . The resulting spectrumcan be smoothed, or the number of lags can be chosen to achieve the desired frequencyresolution. The Fourier transform pair of the continuous spectrum and the continuous lagcorrelation are shown below.T L( k) = r( )e ik dT Lr( )= 12k *k *( k)e ik dk(6.27)The maximum number of lags L determines the bandwidth of the spectrum and the numberof degrees of freedom associated with each one. The bandwidth is 1 cycle/2T L , andfrequencies 0, 1 cycle/2T L , 2/2T L, 3/2T L, ..., 1/2t. There are12t1=T Lt2T L(6.28)of these estimates. Each withT L tN1 = N Ldegrees of freedom. (6.29)The lag correlation method is rarely used nowadays, because Fast Fourier Transformalgorithms are more efficient and widespread. The lag correlation method is important forintellectual and historical reasons, and because it comes up again if you undertake higherorder spectral analysis.Copyright 2005 Dennis L. Hartmann 1/25/05 5:04 PM 118

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