What do you expect it to look like?

Obviously, minimum temperatures are warmer in summer than in winter. To quantify this (which would be useful for, say, tourism brochures), a smooth line representing the seasonal average minimum is shown. This line was computed by taking the average temperature for each day of the year, averaging over the 5 years shown, and then taking 'moving averages' or averages of groups of successive days. The more days averaged, the smoother the line. The lower graph shows deviations from the seasonal average.

There are other patterns that are not so obvious. For instance, is there a tendency for a warm minimum to be followed by another warm minimum?

To investigate this question, the deviations from the seasonal average line were graphed as above. The suspected pattern can be seen by the upward (positive) relation in this graph. The 'correlation coefficient', a measure of the strength of the linear association, is 0.49 (1 is perfect association, 0 is no association, -1 is perfect negative association).

So there is indeed a tendency for the minimum temperature on one day to be similar to that of the previous day, even after accounting for the seasonal effect.

Does the maximum daily temperature behave the same way? If you really think about it you can see before looking at the graph that it doesn't.

This graph shows the daily maximum, seasonal smooth average, and deviations from the maximum. The maximum temperature is much more variable in summer. Note also that the bumps in the lower graph seem to have 'holes' in them. These show the well-known summer pattern of high temperatures usually being followed by high or low temperatures depending on whether the front has come through, but not usually by medium temperatures.

Another way of displaying these patterns is with 'boxplots'.

These are monthly boxplots of daily maximum temperatures. Each box contains the middle half of the values for that month. For instance, about a quarter of days in January are hotter than about 30 degrees, and a quarter are cooler than about 21 degrees. These boxplots show the same data as the boxplot graph in the upper right hand corner of the Statistical Consulting Centre webpages.

The data were obtained from Rob Hyndman's Time Series Data Library.