What do you observe here and how might you model this behavior? Oscillatory, is the period fixed?

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Time series

• Yt for t=0,1,2,…

• Time may be discrete, e.g. days, hours, seconds, etc., for regularly spaced observa/ons

• Typically, ‘errors’ are correlated, so not independent

- Longitudinal data (or repeated measures)

- Growth data

Textbooks

• Cryer & Chan Time Series Analysis with applica4ons in R

• ChaTield The analysis of 4me series

• Box, Jenkins, Reinsel Time series analysis: forecas4ng and control (4th ed)

• Wei Time series analysis : univariate and mul4variate methods (2nd ed)

• Diggle Time Series - A Biosta4s4cal Introduc4on

• Kendall & Ord Time Series (3rd ed)

Canadian Snow Hare Population (annual trappings, 1905 - 1935

What do you observe in the above /me series?

• Amplitude, periodicity, smoothness

Daily Numbers of Paramecium aurelia per ml (the ‘predator’)

Oscillatory, is the period fixed?

How does this contrast previous examples?

 How would you describe the overall pattern? 

What do you observe here?

How might you model this behavior?

Exercise – in small groups

• Choose three of the /me series presented above.

• Outline the similari/es and/or differences between the /me series, and comment on dis/nc/ve features.

• Write down a few sentences describing what you’re seeing. 

Descrip/ve methods

• Plots vs /me

• Smoothing – eg moving averages: replace xt with m(xt ),for example – m(xt )=(xt-1 + xt +xt+1)/3

• Seasonal decomposi/on Level? Trend? Seasonal component? Cyclical (non-seasonal, period not fixed)?

Attachments:

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