Statistics for Environmental Engineers

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14-,


12-


yt 10 86



• ••



• •



•• ■* . *


Series A: y = 10.11



14


12


10


8


6

0


10


20    30


Time (Days)


40


50


FIGURE 41.3 Time series of simulated environmental data. Series A is random, normally distributed values with n = 10 and с = 1. Series B was constructed using the random variates of Series A to construct serially correlated values with p = 0.8, to which a constant value of 10 was added.


Autocorrelation and Trend Analysis


Sometimes we are tempted to take an existing record of environmental data (pH, temperature, etc.) and analyze it for a trend by doing linear regression to estimate a slope. A slope statistically different from zero is taken as evidence that some long-term change has been occurring. Resist the temptation, because such data are almost always serially correlated. Serial correlation is autocorrelation between data that constitute a time series. An example, similar to the regression example, helps make the point.


Figure 41.3 shows two time series of simulated environmental data. There are 50 values in each series. The model used to construct Series A was yt = 10 + at, where at is a random, independent variable with N(0,1). The model used to construct Series B was yt = 10 + 0.8et-1 + at. The ai are the same as in Series A, but the ei variates are serially correlated with p = 0.8.

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