Downlod the Excel data of E-commerce Retail Sales and follow the steps below for time series forecasting. To be able to receive full credit, you must show your computations in the space provided for each question.
1. The series begin with the first quarter of 2013 and end with the first quarter of 2018. Show the time plot series that display quarterly e-commerce retail sales as a percent of total U.S. retail sales.
Show your plot in the space provided below:
2. Calculate the moving averages for each observation in the data based on periods 1, 2, 3, and 4. Show the time plot of quarterly e-commerce retail sales along with the moving-average forecasts based on a span of k=4. Make sure to include the labels of x and y axes and adjust the values on the plot to show the possible changes more clearly over the time.
Show your plot in the space provided below:
3. Use the figure from question #2 to interpret the seasonal regularity to the time series data (e-commerce retail sales). For instance, in which quarters do you observe percent sales are the lowest or the highest, or in which quarters do you observe a rise or a decline? Compare and contrast the component that you observe in the time series and the moving averages.
4. Calculate the centered moving average (CMA) and show the time plot of quarterly e-commerce retail sales along with the centered moving-average forecasts based on a span of k=4. Make sure to include the labels of x and y axes and adjust the values on the plot to show the possible changes more clearly over the time. In the space provided below, show your plot, and compare and interpret the trend of two series.
5. Calculate the seasonal ratio of quarterly e-commerce retail sales and average these ratios by quarter.
Show the resulting ratios based on the periods of 1, 2, 3 and 4 in the table below:
6. Regress the de-seasonality component of quarterly e-commerce retail sales on time component. In the space provided below, show your regression output and the regression equation using trend-and-season predictive model from the simple linear regression output.
7. Create a plot using de-seasonality component of quarterly e-commerce retail sales along with a linear trend fit and interpret the graph. In the space provided below, show your plot and label x and y axes, and adjust the values on the plot.
8. Compute a forecast for the series of third quarter on the time plot of quarterly e-commerce retail sales. Note that the series end on the first quarter with t=21. Make sure to include the seasonality ratio for the appropriate quarter corresponding to the value of t.
Data Analysis Questions for Monthly Sales for Office Supply and Stationery Stores:
The Census Bureau tracks a variety of retail and service sales using the Monthly Retail Trade Survey. Consider the monthly sales (in millions of dollars) from January 2014 through April 2018 for office supply and stationery stores.
1. Create a time plot for monthly sales for office supply and stationary stores with the months labeled “1” for January, “2” for February, and so on. Show your plot in the space provided below:
2. Interpret the characteristics of monthly sales for this sector in terms of time series component, such as trend, seasonality, cyclical pattern etc. over the time. Do you observe any pattern from the data that repeats itself at a regular interval?
3. In which month do you observe a dramatic increase or decrease for the sales? Explain the reason very briefly.
4. Regress the monthly sales to a time variable and show the regression output in the space provided below. Interpret the results in terms of explained variability and the significance of the model.
5. Create indicator variables to represent each month as a category. Consider December data as a baseline model. How many indicator variables do we need to recode months as different categories?
6. Explain very briefly the reason why we need indicator variables, in other words why we need to recode each month as a different category and include in the regression analysis?
7. Regress the monthly sales to a time variable along with all indicator variables. The new model captures the linear trend along with the seasonal pattern in the time series. Show the output of the trend-and-season model and the multiple regression equation including all indicator variables in the space provided below. Interpret the results in terms of model fit which is reflected in explained variability and the significance of the trend-and-season model.
8. Compare and contrast the model fits of trend-only model and trend-and-season model in terms of explained variability and the significance of the model.
9. Test the significance of each indicator variable and report if there is any insignificant variable exists in the trend-and-season model.
10. Explain very briefly the reason why some coefficients of the indicator variables are negative from trend-and-season model.
11. Report the indicator variable that shows the highest coefficient in the trend-and-season model and explain very briefly why one of the coefficients is quite high relative to other coefficients of indicator variables.
12. What are the predicted monthly sales for the month of August using the trend-and-season model? Explain the results very briefly.