A time series is a sequence of measurements moving through time. The population of the United States as shown by decennial census, gross national product by year, unemployment by quarters, daily prices on the New York Stock Exchange are all time series. The use of time series data in regressions has been discussed above, but movements over time are themselves often important economic phenomena to be measured and analyzed. Foremost is the problem of measuring long-run economic growth, that is, the secular trend. In addition, when data are available for intervals shorter than a year, economic time series are subject to seasonal variation: More ice cream is sold in July than in January; more farm labor is employed in September than December. Not only is seasonality interesting in its own right, but for many purposes data must be seasonally adjusted before other relationships can be studied.
Table 9.1 shows annual per capita consumption of dried and of frozen fruits in the United States for the period 1944-59. A glance at the table is sufficient to show that, while there is year-to-year variation, the growth of consumption has a strong central tendency. Indeed, the time path of the data can be described as a stochastic relationship between consumption, ϒ, and time, Τ, in the form ϒ = f(Τ) + u The systematic part of this function, called the trend of the data, is the