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Trend Pattern
Although time series data generally exhibit random fluctuations, a time series may also show
gradual shifts or movements to relatively higher or lower values over a longer period of time.
If a time series plot exhibits this type of behavior, we say that a trend pattern exists. A trend
is usually the result of long-term factors such as population increases or decreases, changing
demographic characteristics of the population, technology, and/or consumer preferences.
To illustrate a time series with a trend pattern, consider the time series of bicycle sales
for a particular manufacturer over the past 10 years, as shown in Table 15.3 and Figure 15.3.
Note that 21,600 bicycles were sold in year one, 22,900 were sold in year two, and so on.
In year 10, the most recent year, 31,400 bicycles were sold. Visual inspection of the time
series plot shows some up and down movement over the past 10 years, but the time series
also seems to have a systematically increasing or upward trend.
The trend for the bicycle sales time series appears to be linear and increasing over time,
but sometimes a trend can be described better by other types of patterns. For instance, the
data in Table 15.4 and the corresponding time series plot in Figure 15.4 show the sales for
a cholesterol drug since the company won FDA approval for it 10 years ago. The time
series increases in a nonlinear fashion; that is, the rate of change of revenue does not increase
by a constant amount from one year to the next. In fact, the revenue appears to be growing
in an exponential fashion. Exponential relationships such as this are appropriate when the
percentage change from one period to the next is relatively constant.
Seasonal Pattern
The trend of a time series can be identified by analyzing multiyear movements in historical
data. Seasonal patterns are recognized by seeing the same repeating patterns over successive
periods of time. For example, a manufacturer of swimming pools expects low sales
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Trend Pattern
Although time series data generally exhibit random fluctuations, a time series may also show
gradual shifts or movements to relatively higher or lower values over a longer period of time.
If a time series plot exhibits this type of behavior, we say that a trend pattern exists. A trend
is usually the result of long-term factors such as population increases or decreases, changing
demographic characteristics of the population, technology, and/or consumer preferences.
To illustrate a time series with a trend pattern, consider the time series of bicycle sales
for a particular manufacturer over the past 10 years, as shown in Table 15.3 and Figure 15.3.
Note that 21,600 bicycles were sold in year one, 22,900 were sold in year two, and so on.
In year 10, the most recent year, 31,400 bicycles were sold. Visual inspection of the time
series plot shows some up and down movement over the past 10 years, but the time series
also seems to have a systematically increasing or upward trend.
The trend for the bicycle sales time series appears to be linear and increasing over time,
but sometimes a trend can be described better by other types of patterns. For instance, the
data in Table 15.4 and the corresponding time series plot in Figure 15.4 show the sales for
a cholesterol drug since the company won FDA approval for it 10 years ago. The time
series increases in a nonlinear fashion; that is, the rate of change of revenue does not increase
by a constant amount from one year to the next. In fact, the revenue appears to be growing
in an exponential fashion. Exponential relationships such as this are appropriate when the
percentage change from one period to the next is relatively constant.
Seasonal Pattern
The trend of a time series can be identified by analyzing multiyear movements in historical
data. Seasonal patterns are recognized by seeing the same repeating patterns over successive
periods of time. For example, a manufacturer of swimming pools expects low sales
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