and maximum about 5 p.m., fairly standard in an English summer. Next, we make two new variables: decimalday will be handy for plotting, and hoursine is a quick and dirty way of incorporating the daily oscillation in temperature, with minimum about 5 a.m. We will open the file (I suggest you browse it to see what’s inside) and declare it to be a time series. Let’s look at a fairly small dataset: a few weather variables from an observation station to the South of London in August 2018. Identifying the threshold and fitting different models on either side allows you to improve causal understanding or prediction. The post-1986 data would throw your analysis out the birds near human habitation were no longer totally dependent on wild plants. Prior to that point, you might have studied the effect of the size of field margins on farms on the goldfinch population, on the basis that the birds eat seeds of wild plants that grow on the margins of cultivated land. This is generally ascribed to the birds learning how to forage in suburban gardens. Image copyright British Trust for Ornithology In these population data from the United Kingdom, you can see a sudden change in the time series at around 1986. The goldfinch is a small songbird found throughout Eurasia. The new threshold command allows you to look for these changes in a statistically informed way, which helps you avoid the potential for bias if you just eyeball line charts and pick the point that fits with your expectations. In time series analysis, sometimes we are suspicious that relationships among variables might change at some time. Threshold regression for time series in Stata
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