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UNR * STAT 758 * Fall 2006

Time Series Analysis. Lecture 1. UNR * STAT 758 * Fall 2006. Data Plot. UNR * STAT 758 * Fall 2006. UNR * STAT 758 * Fall 2006. UNR * STAT 758 * Fall 2006. UNR * STAT 758 * Fall 2006. Theory of Probabilities & Statistics. Probability (a fair coin will show about 50% of tails). Model.

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UNR * STAT 758 * Fall 2006

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  1. Time Series Analysis Lecture 1 UNR * STAT 758 * Fall 2006

  2. Data Plot UNR * STAT 758 * Fall 2006

  3. UNR * STAT 758 * Fall 2006

  4. UNR * STAT 758 * Fall 2006

  5. UNR * STAT 758 * Fall 2006

  6. Theory of Probabilities & Statistics Probability (a fair coin will show about 50% of tails) Model Observations Statistics (a coin that shows 90 tails out of 100 throws is probably not fair) UNR * STAT 758 * Fall 2006

  7. Seasonal Analysis UNR * STAT 758 * Fall 2006

  8. What is the period? R-code par(bg='yellow') plot(co2,lwd=2,col=4,xlab='Time, years',ylab='CO2 in parts per million (ppm)', main='Mauna Loa Atmospheric CO2 Concentration') abline(v=seq(1950,2006,by=10),lty=2) abline(h=seq(320,360,by=10),lty=2) UNR * STAT 758 * Fall 2006

  9. R-code # This line adds yearly grid abline(v=seq(1950,2006,by=1),lty=2) UNR * STAT 758 * Fall 2006

  10. R-code # Filter with 1-year window and plot a trend f<-filter(co2,rep(1,12)/12) points(f,col=2,type='l',lwd=2) UNR * STAT 758 * Fall 2006

  11. R-code # Plot series minus trend plot(co2-f,ldw=2,col=4,lwd=2, xlab='Time, years',ylab='CO2-trend',main='Detrended CO2 series') abline(h=seq(-4,4,by=2),lty=2) abline(v=seq(1950,2006,by=1),lty=2) UNR * STAT 758 * Fall 2006

  12. R-code # Perform seasonal analysis and plot season component m<decompose(co2) plot(m$figure,lwd=2,type='p',pch=19,col=4, xlab='Month',ylab='Seasonal component') axis(1,at=seq(1,12)) grid(col='black',lty=2) UNR * STAT 758 * Fall 2006

  13. R-code m<decompose(co2) plot(m) UNR * STAT 758 * Fall 2006

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