For example,..IndexofHourlyTrafficFlowonLI.DistresswayMOTE6134016.8HOUR
For example,. Index of Hourly Traffic Flow on L.I. Distressway H O U R 2 4 6 0 0 3 4 6 7 1 0 1 1 3 4 1 6 8 F L O W
In parts...Index of Hourly TrafficFlowon L.I.Distressway0563218ii2146376013684HOURUDAYSEAS-ONWEEK
In parts. Index of Hourly Traffic Flow on L.I. Distressway H O U R - . 6 3 - . 2 1 . 2 1 . 6 3 1 . 0 5 - 1 . 0 5 0 3 4 6 7 1 0 1 1 3 4 1 6 8 S E A S O N W E E K D A Y U V a r i a b l e
Studying the Frequency DomainCannot identify the number of terms口Cannot identify frequencies from the time series口Deconstructing the variance, autocovariances and口autocorrelationsContributions at different frequenciesApparent large weights at different frequenciesUsing Fourier transforms of the dataDoes this provide “new' information about the series?
Studying the Frequency Domain Cannot identify the number of terms Cannot identify frequencies from the time series Deconstructing the variance, autocovariances and autocorrelations ◼ Contributions at different frequencies ◼ Apparent large weights at different frequencies ◼ Using Fourier transforms of the data ◼ Does this provide “new” information about the series?
Autocorrelation in RegressionY, = b'xt + &t口Cov(ct, &-1) + 0Ex. RealCons,= a + bReallncome + &, U.S.Data, quarterly,1950-2000口C3.00200TBnpOpisay?2
Autocorrelation in Regression Yt = b’xt + εt Cov(εt , εt-1 ) ≠ 0 Ex. RealConst = a + bRealIncome + εt U.S. Data, quarterly, 1950-2000 O b s e r v . # - 2 0 0 - 1 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 - 3 0 0 0 4 1 8 2 1 2 3 1 6 4 2 0 5 U n s t a n d a r d i z e d R e s i d u a l s . B a r s m a r k m e a n r e s . a n d + / - 2 s ( e ) R e s i d u a l