Module # 12 assignment

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 Issaiah Jennings 

Module # 12 assignment



> # Install and load the 'forecast' package

> if (!require(forecast)) {  # Check if 'forecast' package is installed

+   install.packages("forecast")  # Install the package if not present

+ }

> library(forecast)  # Load the package

> 

> # Define the data for 2012 and 2013

> data_2012 <- c(31.9, 27, 31.3, 31, 39.4, 40.7, 42.3, 49.5, 45, 50, 50.9, 58.5) # Credit card charges for 2012

> data_2013 <- c(39.4, 36.2, 40.5, 44.6, 46.8, 44.7, 52.2, 54, 48.8, 55.8, 58.7, 63.4) # Credit card charges for 2013

> 

> # Combine the data into a single vector

> student_cc <- c(data_2012, data_2013)

> 

> # Create a time series object

> cc_series <- ts(student_cc, frequency = 12, start = c(2012, 1)) 

> # frequency = 12 (monthly), start = c(2012, 1) indicates the time series starts in January 2012

> 

> # Plot the time series

> plot.ts(cc_series, 

+         main = "Credit Card Charges (2012-2013)", 

+         ylab = "Charges", 

+         xlab = "Time", 

+         col = "blue")

> 








> # Apply Holt-Winters exponential smoothing to the time series

> hw_model <- HoltWinters(cc_series)

> 

> # Display the Holt-Winters model details

> print(hw_model)

Holt-Winters exponential smoothing with trend and additive seasonal component.


Call:

HoltWinters(x = cc_series)


Smoothing parameters:

 alpha: 0.4786973

 beta : 0

 gamma: 0.1


Coefficients:

           [,1]

a    51.4481469

b     0.6088578

s1   -6.6831338

s2  -10.5867440

s3   -6.6998393

s4   -3.0320795

s5   -1.4068647

s6   -4.0422184

s7    0.4727766

s8    6.6378768

s9    1.4431586

s10   5.6809745

s11   5.7999737

s12  12.6976853

> 

> # Plot the Holt-Winters model results

> plot(hw_model, 

+      main = "Exponential Smoothing Model", 

+      col = "blue")




> 

> # Generate a forecast for the next 12 months

> forecast_hw <- forecast(hw_model, h = 12)

> 

> # Plot the forecast

> plot(forecast_hw, 

+      main = "Holt-Winters Forecast (Next 12 Months)", 

+      col = "blue")

> 

> # Print the forecast values

> print(forecast_hw)

         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95

Jan 2014       45.37387 42.36940 48.37834 40.77893 49.96881

Feb 2014       42.07912 38.74815 45.41009 36.98484 47.17340

Mar 2014       46.57488 42.94668 50.20309 41.02602 52.12374

Apr 2014       50.85150 46.94863 54.75437 44.88258 56.82042

May 2014       53.08557 48.92614 57.24501 46.72427 59.44688

Jun 2014       51.05908 46.65801 55.46014 44.32822 57.78993

Jul 2014       56.18293 51.55282 60.81304 49.10179 63.26407

Aug 2014       62.95689 58.10854 67.80523 55.54199 70.37179

Sep 2014       58.37103 53.31386 63.42819 50.63676 66.10530

Oct 2014       63.21770 57.96000 68.47540 55.17674 71.25866

Nov 2014       63.94556 58.49469 69.39642 55.60917 72.28194

Dec 2014       71.45213 65.81471 77.08954 62.83044 80.07381


> 

The time series data shows monthly credit card charges for a student in 2012 and 2013. There are noticeable increases in charges towards the end of each year. The Holt-Winters Exponential Smoothing Model was used to predict future charges, considering both trends and seasonality. The model used a smoothing parameter (alpha) of 0.4787, giving moderate weight to recent data, while the trend component was set to zero (beta = 0). The seasonal component was included with a smoothing parameter (gamma) of 0.1. The coefficients showed seasonal adjustments, like lower charges in January and higher charges in December.


Forecasts for 2014 showed a steady increase in charges, starting at 45.37 in January and reaching 71.45 in December. The confidence intervals showed a range of uncertainty, with values between 40.78 and 49.97 in January and between 62.83 and 80.07 in December. These results match the pattern seen in previous years, showing a rise in charges, especially later in the year.

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