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MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Time Series Analysis and Moving Averages** This document details a time series analysis where moving averages are used to forecast future values. The table is organized with four main columns: 1. **Month**: Sequential month numbers from 1 to 12. 2. **Time Series Value**: Recorded values for each month ranging from 9.4 to 10.6. 3. **3-Month Moving Average Forecast**: Averages based on the preceding three months. 4. **4-Month Moving Average Forecast**: Averages based on the preceding four months. **Incomplete Data:** - The table for the 3-month and 4-month moving averages is not filled out. **Forecast Evaluation:** Below the table, there's a question about which moving average provides better forecasts based on Mean Squared Error (MSE): - The options indicate choices between 3-month and 4-month moving averages, considering whether the MSE is smaller or larger. **Question:** Using the more accurate approach identified, calculate the moving average forecast for the next month, rounding to two decimal places. **Note**: The document does not provide the completed calculations or the resulting MSE, so calculation details are omitted. **Additional Help:** - A "Need Help?" section is present for further guidance. This educational material invites learners to apply concepts of moving averages and evaluate forecasts using statistical measures like MSE.
Transcribed Image Text:**Time Series Analysis and Moving Averages** This document details a time series analysis where moving averages are used to forecast future values. The table is organized with four main columns: 1. **Month**: Sequential month numbers from 1 to 12. 2. **Time Series Value**: Recorded values for each month ranging from 9.4 to 10.6. 3. **3-Month Moving Average Forecast**: Averages based on the preceding three months. 4. **4-Month Moving Average Forecast**: Averages based on the preceding four months. **Incomplete Data:** - The table for the 3-month and 4-month moving averages is not filled out. **Forecast Evaluation:** Below the table, there's a question about which moving average provides better forecasts based on Mean Squared Error (MSE): - The options indicate choices between 3-month and 4-month moving averages, considering whether the MSE is smaller or larger. **Question:** Using the more accurate approach identified, calculate the moving average forecast for the next month, rounding to two decimal places. **Note**: The document does not provide the completed calculations or the resulting MSE, so calculation details are omitted. **Additional Help:** - A "Need Help?" section is present for further guidance. This educational material invites learners to apply concepts of moving averages and evaluate forecasts using statistical measures like MSE.
### Transcription for Educational Website #### Time Series Data and Moving Average Forecast This table displays the time series data for a duration of 12 months along with columns for calculating the 3-month and 4-month moving averages for forecasting purposes. The values are presented as follows: - **Month**: Sequential number from 1 to 12. - **Time Series Value**: Data points for each month. - **3-Month Moving Average Forecast**: Calculated forecast using the average of the previous three months. - **4-Month Moving Average Forecast**: Calculated forecast using the average of the previous four months. #### Data Overview: | Month | Time Series Value | 3-Month Moving Average Forecast | 4-Month Moving Average Forecast | |-------|--------------------|--------------------------------|--------------------------------| | 1 | 9.6 | | | | 2 | 9.4 | | | | 3 | 9.5 | | | | 4 | 9.7 | | | | 5 | 9.9 | | | | 6 | 9.8 | | | | 7 | 9.8 | | | | 8 | 10.6 | | | | 9 | 10.0 | | | | 10 | 9.8 | | | | 11 | 9.7 | | | | 12 | 9.7 | | | #### Analytical Question: - Does the three-month or four-month moving average provide better forecasts based on Mean Squared Error (MSE)? Explain. - The four-month moving average provides more accurate forecasts because its MSE is larger than that of the three-month moving average. - The four-month moving average provides more accurate forecasts because its MSE is smaller than that of the three-month moving average. - The three-month moving average provides more accurate forecasts because its MSE is larger than that of the four-month moving average. - The three-month moving average provides more accurate forecasts because its MSE is smaller than that of the four-month moving average. #### Further Calculation: (c) Using the more accurate approach, calculate the moving average forecast for the next month. (
Transcribed Image Text:### Transcription for Educational Website #### Time Series Data and Moving Average Forecast This table displays the time series data for a duration of 12 months along with columns for calculating the 3-month and 4-month moving averages for forecasting purposes. The values are presented as follows: - **Month**: Sequential number from 1 to 12. - **Time Series Value**: Data points for each month. - **3-Month Moving Average Forecast**: Calculated forecast using the average of the previous three months. - **4-Month Moving Average Forecast**: Calculated forecast using the average of the previous four months. #### Data Overview: | Month | Time Series Value | 3-Month Moving Average Forecast | 4-Month Moving Average Forecast | |-------|--------------------|--------------------------------|--------------------------------| | 1 | 9.6 | | | | 2 | 9.4 | | | | 3 | 9.5 | | | | 4 | 9.7 | | | | 5 | 9.9 | | | | 6 | 9.8 | | | | 7 | 9.8 | | | | 8 | 10.6 | | | | 9 | 10.0 | | | | 10 | 9.8 | | | | 11 | 9.7 | | | | 12 | 9.7 | | | #### Analytical Question: - Does the three-month or four-month moving average provide better forecasts based on Mean Squared Error (MSE)? Explain. - The four-month moving average provides more accurate forecasts because its MSE is larger than that of the three-month moving average. - The four-month moving average provides more accurate forecasts because its MSE is smaller than that of the three-month moving average. - The three-month moving average provides more accurate forecasts because its MSE is larger than that of the four-month moving average. - The three-month moving average provides more accurate forecasts because its MSE is smaller than that of the four-month moving average. #### Further Calculation: (c) Using the more accurate approach, calculate the moving average forecast for the next month. (
Expert Solution
Introduction
Moving Averages are a forecasting tool that work by projecting the data value for a specific time based on the dataset's monthly average values. 
For instance, to estimate the value of the data for period n when generating 3 month Moving Averages (MA), we would use the following formula.

Forecast during period n = Yn-3+Yn-2+Yn-13

 

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