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24 Time Series Analysis Time series data are vectors of numbers, typically regularly spaced in time. Yearly counts of animals, daily prices of shares, monthly means of temperature, and minute-by-minute details of blood pressure are all examples of time series, but they are measured on different time scales. Sometimes the interest is in the time series itself (e.g. whether or not it is cyclic, or how well the data fit a particular theoretical model), and sometimes the time series is incidental to a designed experiment (e.g. repeated measures). We cover each of these cases in turn. The three key concepts in time series analysis are trend, serial dependence, and stationarity. Most time series analyses assume that the data are untrended. If they do show a consistent upward or downward trend, then they can be detrended before analysis (e.g. by differencing). Serial dependence arises because the values of adjacent members of a time series may well be correlated. Stationarity is a technical concept, but it can be thought of simply as meaning that the time series has the same properties wherever you start looking at it (e.g. white noise is a sequence of mutually independent random variables each with mean zero and variance σ 2 0). 24.1 Nicholson’s blowflies The Australian ecologist, A.J. Nicholson, reared blowfly larvae on pieces of liver in laboratory cultures that his technicians kept running continuously for almost 7 years (361 weeks, to be exact). The time series for numbers of adult flies looks like this: blowfly - read.table(c:\\temp\\blowfly.txt,header=T) attach(blowfly) names(blowfly) [1] flies The R Book, Second Edition. Michael J. Crawley. © 2013 John Wiley Sons, Ltd. Published 2013 by John Wiley Sons, Ltd. 786