Measles Series

Figure left: Measles time series for seven cities.

The picture on the left shows the weekly number of cases of measles for the cities indicated from 17th January 1948 to 11th December 1987. This data, and similar ones, appear in many places on the Internet. See here for the data used here, see here for other sets.

The measles time series data ar every different in character compared to the FTSE series. Each of the seven series show a similar pattern. Before the mid-1960s the series shows significant oscillations from near zero to several hundreds or thousands (for bigger cities like Birmingham and London). These oscillations are waves of measles epidemics which occurred on annual or biennial basis. However, after the mid-1960s the waves of epidemics are much reduced and this reduction was due to the impact of measles vaccination.

The measles series is probably not stationary as the series (the mean, the variance and other properties) are very different before and after the mid-1960s.

Autocorrelation

Autocorrelation is a measure of internal correlation within a time series. It is a way of measuring and explaining internal association between observations in a time series. For example, for the measles series you might ask "take an arbitrary spot in time, on the average what does the time series look like in four weeks time, compared to now?" In other words, you are asking a question about how strong is the internal association within the series at a period of four weeks. That association could be very strong and positive (i.e. the series in four weeks is similar to now), or be very strong and negative (i.e. the series in four weeks is very dissimilar to now) of there could be a weak or no relationship. Also, you might be interested in periods other than four weeks.

For example, you might be interested in periods of one week (and for measles, you might expect that the series does not change very much, so the association would be strong over periods of one week) or periods of 52 weeks, a year, and again you might expect a strong association as measles epidemics have a strong annual component.

Autocorrelation quantifies the internal association: assigning a value of +1 to perfect positive association, -1 to perfect negative association and zero to no association (note: autocorrelation measures linear association, in the same way that ordinary correlation between two variables does. So, sometimes autocorrelation can be zero for some kinds of nonlinear association).

Measles Autocorrelation...