Which of the following statements about moving averages is true?
Group of answer choices, multiple possible answers
It can be used to smooth a series.
Given a data set with 15 yearly observations, a 5-year moving average will have fewer observations than a 3-year moving average.
Given a data set with 15 yearly observations, a 5-year moving average is smoother than a 3-year moving average.
None of the others
None of the given statements are true.
The statement that is true about moving averages is:
- It can be used to smooth a series.
To determine which of the statements about moving averages is true, let's break down each statement and analyze it:
1) "It can be used to smooth a series."
This statement is true. Moving averages are commonly used in time series analysis to smooth out fluctuations and highlight underlying trends. By calculating the average of a selected number of past data points, moving averages provide a more stable representation of the data and help remove short-term noise.
2) "Given a data set with 15 yearly observations, a 5-year moving average will have fewer observations than a 3-year moving average."
This statement is false. A moving average represents a rolling window of data points. The window size determines the number of observations included in the calculation. In this case, a 5-year moving average will include more observations than a 3-year moving average. Therefore, the statement is incorrect.
3) "Given a data set with 15 yearly observations, a 5-year moving average is smoother than a 3-year moving average."
This statement is true. Moving averages with longer window sizes tend to provide a smoother representation of the data. By incorporating more historical observations, the fluctuations in the series are averaged out, resulting in a smoother trend line. Therefore, a 5-year moving average will be smoother than a 3-year moving average.
Based on these analyses, the correct statement among the given options is: "Given a data set with 15 yearly observations, a 5-year moving average is smoother than a 3-year moving average."