To find the first centered value in the smoothed series, we need to calculate the moving average for the year 1988.
The first centered value is obtained by taking the average of the five values before and the four values after the given year. In this case, the five values before 1988 would be from 1984 to 1988, and the four values after 1988 would be from 1988 to 1991.
Therefore, the first centered value in the smoothed series is for the year 1988.
To compute all the nine-year moving averages, we lose eight years of values at the beginning and eight years of values at the end. This is because when calculating the moving average, we need a minimum of nine years of data for each average.
Since the time series was first recorded in 1984, the first nine-year moving average can be calculated for the year 1992 (1984 + 8 years). This implies that we lose data from 1984 to 1991 (eight years) at the beginning.
Similarly, if the time series continues up to the present year, the last nine-year moving average can be calculated for the year 2016. Hence, we lose data from 2017 to present (eight years) at the end.
In summary, when computing all the nine-year moving averages, we lose a total of sixteen years of values - eight years at the beginning and eight years at the end.
Consider a nine-year moving average used to smooth a time series that was first recorded in 1984.
Which year serves as the first centered value in the smoothed series?
How many years of values in the series are lost when computing all the nine-year moving averages?
1 answer