Thursday, May 27, 2010

Exploratory Analysis of Chaves and Koenraadt

A couple of days ago I mentioned the Chaves and Koenraadt paper on malaria. I've looked over it a bit since but would really have to repeat the analysis myself in order to come up with anything conclusive as the time series analysis is so poorly documented. To recap, here is the temperature time series from Kericho in Kenya that they use:

One of the models they fit is the basic structural model. This model consists of a stochastic trend a seasonal component and residual noise. The stochastic trend is a local linear trend model:

Beta is a simple random walk with random error term Xi. It acts as the slope of the I(2) stochastic trend Mu which also has an additional random error term Eta. According to the paper this is what Mu looks like (I think):

The trend shows that temperature increased by about 0.08 C over the period when we remove the seasonal and noise components. Unfortunately, the authors do not provide a confidence interval in the chart and so it is hard to tell if this is a significant increase or not. But they do provide estimates of the standard deviations of eta and xi, which are 0.29 and 0.12 respectively.* Both of these are larger than the entire increase in temperature shown by the trend, suggesting that the increase is insignificant.

* They actually give the variances in the paper and these are the square roots of the variance.

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