Regression Model

Assignment 4

The goal of this assignment is to firm up our understanding of time series modeling. Please answer all questions. Supply supporting documentation and show calculations as needed. Please submit a single well-formatted PDF or Word file. The instructor should not need to go searching for your answers! In addition, please upload an Excel file with your model outputs –

Download the file  DepartmentStoreSales.xlsx . The data contains data on the quarterly sales for a department store over a 6-year period.

Data Preparation

The goal is to develop a model that can forecast four quarters ahead and accounts for both trend and seasonality. Create the necessary variables (to account for trend and seasonality) and partition the data so that the last four quarters are designated as the validation period.

Regression Based Models

Fit a regression model with a trend and seasonality, using only the first 20 quarters as the training period.

1. Create a plot that shows the fit in the training period (and not the validation period). Include the plot in your write-up.

2. Create a plot of the residuals in the training period as a function of the time period. Include the plot in your assignment.

3. From the plots of the training period how do you expect the fit to be in the validation period?

4. Looking at the residual plot, discuss the fit, including whether or not the fit could potentially be improved? HINT: is there a pattern in the residuals.

5. Can you improve the fit? If so how? If not, why not?

 

Data Driven Models

Since the data has strong seasonality and trend, we will run a Holt-Winter’s exponential smoothing model. Set α=0.2, β=0.15 and γ=0.05 and select to run multiplicative Holt-Winter’s method. Request the forecasts on the validation period.

1. Create a plot that shows the fit in the training period. Include the plot in your assignment.

2. Analyze the results – how would you characterize the performance?

 

Now choose to run an additive Holt-Winter’s method, again with the parameters set at their default values. Run this method on the data. Request the forecasts on the validation period. If needed change the parameters from their default values to improve the fit.

1. What are your selected parameter values?

2. Analyze the results - how do they compare to the multiplicative model?

Model comparison 

1. Create a plot that plots the time series, the multiplicative prediction Holt-Winter’s model and your best additive Holt-Winter’s model. Include the plot in your assignment.

2. Comparing the performance of the Holt-Winter’s models, which one would you use and why?

3. Finally, compare the data driven method with the regression based approach. Which model would you choose and why?

4. What drives the differences between the performance (or lack thereof)?