For this assignment, I will be answering the following questions:
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.
For these two parts, please see the following R code and its associated output:
c. Provide a discussion on time series and Exponential Smoothing Model result you led to.
Through the output, we can first see with the Time Series plot, it clearly shows the fluctuations in charges throughout the months and years. Furthermore, it does seem to peak in charges around mid-year, which may refer to high spending during the winter holiday months.
When we review the Exponential Smoothing model and its impact on the dataset, the first thing to take away is both parameters (beta and gamma) are set to FALSE which means that without trend and seasonality, it will emphasize the short-term variations of the data.
Looking at the high alpha value (0.8232442), this indicates that the forecasts are primarily influenced by recent observations. As for the coefficient ‘a’ value (62.44453), we can see that the model expects future values to revolve around this particular value. Now, when this new model is plotted, it more closely aligns with one another as opposed to the first plot which did not appear to be as closely aligned. Moving on the calculation of the sum-of-squared-errors (SSE), the value outputted was 835.38 which may infer that a model containing both trend and seasonality may better capture the underlying patterns in the data. Thus, it is key that you a strike a good balance between model refinement and goals of the analysis to increase model accuracy and reliability.
