The exponentially weighted moving average is a one-sided moving average of the time series. The smoothed value  is an average of  and prior values. The regular moving average is two sided, averaging...

The exponentially weighted moving average is a one-sided moving average of the time series. The smoothed value
 is an average of
 and prior values. The regular moving average is two sided, averaging values on both sides of
. For example, a three-term moving average of
 is

(a) Which series will be smoother: a three-term moving average or a five-term moving average? Explain your thinking.

(b) What problem does a two-sided moving average have when the smoothing reaches the last value of the time series?

(c) The most common moving averages have an odd number of terms, such as the three-term and five-term averages in this exercise or the 13-term average used to smooth computer shipments in this chapter. What problem happens if you try to use a moving average with an even number of terms? Suggest a simple remedy for the problem.