Module 12 Assignment

 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 VoghlanLinks to an external site.'s notes and report the statistical outcome
c. Provide a discussion on time series and Exponential Smoothing Model results that you obtained. 




First, I entered all the given data into one vector and called it "Charge". Next, I converted it into a time series and called it "Chargetimeseries" and added a frequency of 12 with a starting point of January 2012. 
> plot.ts(Charge)








After inputting all the data into a time series, I made a plot of the time series data using the plot.ts() function. The result is above, and it shows the number of charges made over time. The charges increased over time but slowed down for a little bit and then increased again.








I used the HoltWinters() function to perform an exponential smoothing model as shown in the Avril Voghlan's notes. I specified the model to the times series data without taking into consideration or the trend and seasonality. It returned the coefficients and smoothing parameters. The alpha smoothing parameter is 0.8232442. That tells the weight of the most recent observation, and the estimated coefficient value is 62.44453.

HoltWinters plot is shown below. It shows how the observed/fitted values change over time and we can see a general increase over time.
> plot(Chargeforecast)










> Chargeforecast$SSE
[1] 835.3837


The sum of squared error of Chargeforecast was calculated and the result of the value is 835.3837.

The HoltWinters Exponential Smoothing Model was applied to the time series successfully and the data gathered from the student credit card charges and the fitted values were determined. The results showed an increase in charges and fitted values overtime. It provided an alpha parameter estimate as well as the coefficient estimate of 'a' without relying on the trend and the seasonal component. The model estimates that future value will be similar to the coefficient value 'a' which is 62.44453. 



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