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Russell

Eiample of Uses of the Univariate Phase Map Movie, Classical Data Sets

The author has in previous papers, shown that the univariate phase map movie has been useful in exploring time senes data in a number of settings. In this section, we will examine a few of the classical data sets in the public domain: the airline passenger data set, the variable star magnitude data set, and the plant yield data set found in Box, Hunter, and Hunter (1978).

The first of the classical data sets that we will examine is the airline passenger data set. This data set contains the number of passengers on airlines by month for a number of years. This data set goes well beyond our synthetic data sets as it is a good example of both seasonality and growth. The time order plot of the airline passenger data is presented in FigurÄ™ 11 below. Upon examination of the time order plot, we see that we expect a seasonality of 12 months.

In addition to the apparent seasonality of the data in the time order plot, growth from year to year is evident. However the data appears to have some noise affecting both the relative sizes and placement of the intermediate peaks during each cycle. This might be taken as suggestive of some sort of change in the travel pattems over time. Another Ä…uestion that might be raised by the analyst looking at this time order plot is, "Were the early years essentially from the same model as the later years?" That is, can we reasonably fit one single model to the entire data set?

The Airline Passenger Data

Air Lino Poaotnfor Ooia

FigurÄ™ 11. The airline passenger data set in a traditional time order plot. NotÄ™ the seasonality and the growth from year to year.