Question

The following table gives monthly data for four years in million tons of consumption of ice cream in a country. Plot the series and comment on the visible seasonality and trend. Estimate the centered moving averages for this monthly series. Plot CMA and comment. Next, estimate the S,I component which only includes seasonal and irregular movements of the series. Then find the seasonal indexes for the twelve months removing the irregular component. Find the de-seasonalized levels for the series. Plot De-seasonalized Y and comment. Then estimate the trend values for the four sample years and the 12 months of the year 2015 using linear regression. Finally, make the forecast for the 12 months of 2015 using the Ratio-to-Moving Average method to capture the Trend and Seasonal patterns, using Excel. Plot the forecasted values for the 60 periods including 12 months of the year 2015. Plot the errors for in-sample periods and calculate RMSE. Comment on the error plot with respect to the existence of pattern or lack of visible pattern. Month/Year 2011 2012 2013 2014 Jan 840 900 1150 1350 Feb 860 920 1175 1380 Mar 880 950 1205 1415 Apr 950 1090 1280 1525 May 1050 1230 1390 1685 Jun 1150 1360 1510 1845 Jul 1200 1440 1580 1925 Aug 1140 1350 1500 1835 Sep 1100 1310 1450 1770 Oct 1050 1250 1400 1685 Nov 900 1100 1260 1445 Dec 880 1070 1230 1415

Answer 1

Explanation:

. Plot the series: Create a line graph with the months on the x-axis and the ice cream consumption in million tons on the y-axis. This will give you a visual representation of the data.

2. Identify seasonality and trend: Examine the plotted series for any recurring patterns or trends over time. Seasonality refers to regular patterns that repeat within a specific period, such as yearly or monthly. Trend refers to the overall direction of the data over time, whether it's increasing, decreasing, or stable.

3. Estimate centered moving averages (CMA): Calculate the moving averages by taking the average of a specified number of periods, such as 3 or 5, and assigning it to the middle month of that period. For example, to calculate the CMA for February 2011, you would take the average of January, February, and March 2011. Repeat this for all the months in the series.

4. Plot the CMA: Create a line graph with the months on the x-axis and the CMA values on the y-axis. This will help smooth out the data and show the underlying trend more clearly.

5. Estimate the seasonal and irregular components: Subtract the CMA values from the original series to obtain the irregular component. The seasonal component can be calculated by subtracting the irregular component from the original series.

6. Find seasonal indexes: Calculate the average value for each month across all years. Divide each monthly average by the overall average for all months to obtain the seasonal index for that month. This will provide a measure of how each month deviates from the overall average.

7. De-seasonalize the series: Divide the original series by the corresponding seasonal indexes to remove the seasonal component. This will give you the de-seasonalized levels for the series.

8. Plot the de-seasonalized values: Create a line graph with the months on the x-axis and the de-seasonalized levels on the y-axis. This will show the underlying trend without the seasonal fluctuations.

9. Estimate trend values using linear regression: Use the de-seasonalized data to fit a linear regression model that estimates the trend component. This will help determine the overall direction and rate of change in the data.

10. Make forecasts using the Ratio-to-Moving Average method: Calculate the ratio of the de-seasonalized series to the corresponding moving averages. Multiply the ratio by the average seasonal index for the respective month to capture both trend and seasonal patterns. This will give you the forecasted values for the 12 months of 2015.

11. Plot the forecasted values: Create a line graph with the months on the x-axis and the forecasted values on the y-axis. This will show the projected values for the 12 months of 2015.

12. Plot the errors and calculate RMSE: Calculate the difference between the forecasted values and the actual values for the in-sample periods. Plot these errors on a line graph to visualize any patterns or lack thereof. Calculate the Root Mean Squared Error (RMSE) to measure the overall accuracy of the forecasts.