Module # 12 assignment- Time Series and Exponential Smoothing Model
4/10/25
The table below represents charges for a student credit card.
a. Construct a time series plot using R.
b. Employ Exponential Smoothing Model as outlined in Avril Voghlan's notes and report the statistical outcome
c. Provide a discussion on time series and Exponential Smoothing Model results that you obtained.
| Month | 2012 | 2013 |
| Jan | 31.9 | 39.4 |
| Feb | 27 | 36.2 |
| March | 31.3 | 40.5 |
| Apr | 31 | 44.6 |
| May | 39.4 | 46.8 |
| Jun | 40.7 | 44.7 |
| Jul | 42.3 | 52.2 |
| Aug | 49.5 | 54 |
| Sep | 45 | 48.8 |
| Oct | 50 | 55.8 |
| Nov | 50.9 | 58.7 |
| Dec | 58.5 | 63.4 |
A.
The time series plot illustrates a steady increase in student credit card charges from January to December for both 2012 and 2013, with 2013 consistently showing higher monthly charges than 2012. This suggests a year-over-year rise in credit card usage among students. Notably, the most significant increases occurred in February and July, while December recorded the highest charges in both years—$58.5 in 2012 and $63.4 in 2013. The upward trend is more pronounced in 2013, indicating either increased spending behavior or changes in credit access. Overall, the data reflects a growing reliance on credit cards among students over the two-year period.
B. 
The raw time series plot displays 24 monthly observations, representing a full two-year period from January 2012 to December 2013. On the x-axis, time progresses month by month, while the y-axis reflects the corresponding credit card charges. The plot reveals a general upward trend over the two years, with some fluctuations occurring around months 13 to 17 (early 2013), followed by a noticeable rise in charges toward the end of the period. This visualization aligns with the approach outlined in Avril Voghlan’s guide, presenting the raw time series data before applying any smoothing or forecasting techniques.
Now, the Holt-Winters Exponential Smoothing model can be applied. This is for short-term forecasts, and it is if " you have a time series that can be described using an additive model with increasing or decreasing trend and seasonality...". The exponentially smoothed time series plot maintains the overall upward trend observed in the original dataset but presents it in a much more stable and gradual form. Unlike the raw series, which includes short-term fluctuations—such as the noticeable dip around month 13—the smoothed plot minimizes these irregularities, resulting in a clearer depiction of the general pattern. The plot begins at the same initial value as the original series (31.9) but progressively smooths out sharp jumps and dips, offering a cleaner view of the underlying trend in credit card charges over the two-year period.
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