Question

The following two plots on the next page show exponentially weighted moving averages of the percentage change in the amount of household credit market debt. The time series is quarterly, from 1960 through the fourth quarter of 2011. In the first plot the weight for the EWMA w = 0.5, whereas in the second plot w = 0.9. The EWMA in both cases is shown as a red line with the surrounding data. (The Federal Reserve Bank of St. Louis provides these data online.)
(a) Which weight w do you think produces a better summary of the underlying trend in the percentage change in household debt? Explain your choice.

(b) In the fourth quarter of 2011, household credit debt was estimated to be $13.223 trillion. Having seen these plots, forecast household credit debit in the first quarter of 2012.
(c) Provide a range to accompany your forecast of household credit debt.

Answer 1

(a)        The EMWA with less smoothing follows the trends in debt more closely than the smoother series. The smoother series (with w = 0.9) falls behind the large peaks and troughs of this time series. Toward the end of the time series, the EWMA consistently runs below the observed data with this amount of smoothing. Though more jagged, the other series seems more in the middle of things.

 

(b)        Use the final smooth estimate of growth, 13.223(1.0018) ≈ $13.247 trillion.

 

(c)        The SD of deviations from the EWMA in the last few years is about 0.2%, implying a range of about 13.247(0.996) ≈ 13.19 to 13.247(1.004) ≈ 13.30.

13.247(0.996) ≈ 13.19 to 13.247(1.004) ≈ 13.30.