Question

Consider a nine -year moving average used to smooth a time series that was first recorded in 1961. a. Which year serves as the first centered value in the smoothed series? b. How many years of values in the series are lost when computing all the nine-year moving averages?

Answer 1

a. 1965

b. 8 years

Explanation:

For answers to questions like these it can work to consider the smallest possible dataset.

Dataset

For our purpose, consider the 9 years/values to be averaged to be ...

1, 2, 3, 4, 5, 6, 7, 8 ,9

Observations

a. The center value of the data set is 5. Its number is 5-1=4 more than the first one.

The first centered value is from the year 1961 +4 = 1965.

b. The 4 values at the beginning, and the 4 values at the end do not have a corresponding "average" value. That is, 4+4 = 8 values in the series are lost with respect to the number of average values.

8 years of values are lost.