This assignment addresses forecasting each of your selected X variables (independent variables) using an exponential smoothing technique. Submit the forecast for each of the three X variables. Use only one exponential smoothing method for each X — the best that applies. Do not use any other forecasting techniques in this assignment. As a result, I expect to see three good exponential smoothing models — one for each X variable.
a) Tell me why you selected the appropriate exponential smoothing method by commenting on each X variable data characteristics. (you should use a time series plots and autocorrelations to do this).
b) Apply the appropriate exponential smoothing forecast technique to each X variable. Show the X data, fitted values and residuals in excel format in an inserted table in the assignment Word document. Show your exponential smoothing model coefficients. (Find the correct coefficient and not just use the default values.)
c) Evaluate the “Goodness To Fit” using at least two error measures — RMSE and MAPE for each X variable model..
d) Check the “Fit” period residual mean proximity to zero and randomness with a time series plot; check the residual time series plot and autocorrelations (ACFs) for trend, cycle and seasonality.
e) Evaluate the residuals for the “Fit” period by indicating the residual distribution using a histogram (normal or not and random or not) for each X variable model,
f) Comment on the acceptability of each model’s ability to pick up the systematic variation in Fit period actual data.
g) Develop a 2 year (8 quarter) forecast for each X variable using the best model determined above and check the forecast for reasonableness.
Show your work and graphs in a Word document. Make sure that you comment on statistics and graphs relevant to answering the above questions. DO NOT leave statistics and graphs stranded. If you show something write about it. Note that this work will likely become part of your class presentation so do a good job on it. Submit the word document in the assignment 6 dropbox with your first initial, last name and Assignment 6 in the file name.
The bottom line is that you should do the same for each X variable and develop a 2 year forecast for each of the X variables using exponential smoothing. Keep in mind that you may need to use different exponential smoothing models for each variable based on the trend, cycle and seasonal characteristics of the variable data. Do not waste your time running models that do not apply to the data
Perform Time Series Decomposition on each of your three selected project X variables. Show the smoothed Trend Values (Minitab TREN), Smoothed Cycle Values (in Minitab DESE/TREN) and Seasonal Indexes (in Minitab SEAS) for each variable.
Again -note that you can create your own cycle factors for the forecast period and apply them to a multiplicative Minitab result. (in Minitab DESE/TREN)
b) Show the seasonal indices and develop a two year time series plot of them for each variable. Do they indicate strong seasonality? How can you tell?
c) Evaluate the “Goodness To Fit” using RMSE and MAPE error measures.
d) Evaluate the residuals for the “Fit” period by indicating the residual distribution (random or not). Use a fit period residual time series plot, residuals ACFs and a histogram to determine if the Fit period residuals are random. If the residuals are not random state if you detect any trend, cycle and seasonality.
e) Select a cycle factor for the next two forecast years. Adjust the forecast for cycle and check for forecast reasonableness.
f) Develop a two year quarterly forecast using the time series decomposition model you evaluated in c) above for each X. Tell me if you believe the forecast looks reasonable and why.
This assignment is essentially the multiple regression analysis portion of your project and it is worth 20 points. This means that I expect you to develop a good regression model with more than one independent variable (X). Ideally, if you made a good choice of variables in your proposal you should be able to include all three X variable in your regression equation. Be sure to complete each part and write your responses supported by Minitab/excel work. This assignment should be turned in to me as a Word document. You should include excel and Minitab tables and graphs in the Word document as required. Be sure to comment on each of the 10 points below.
1. Run scatter plots and a correlation matrix on your project variables and comment on their values and significance if you have done this earlier you may use that analysis here.
2. Note any seasonality in your Y data with ACF (autocorrelation analysis of Y) You may use ACFs that you previously developed.
3. Determine if any of your variables require transformation. If they do, calculate the transformed values and create a scatter plot with a regression line and run a correlation with Y for each transformed X. Create a table for the Y, X and X transformed values.
4. Determine the dummy variables (e.g. for Y variable seasonality or significant events such as marketing and promotional activities.) and include a table of the dummy variable values for regression analysis. Remember, key off of the past marketing and pricing history of the corporation to derive marketing dummy variables. Work with you marketing counter part to set them over time. Also, make sure that you check with your marketing counterpart to include their corporation marketing plan in the forecast period dummy variables (for the two year forecast in part 12 below).
5. Use regression to evaluate the variable combinations to determine the best regression model. Use R square and F as primary determinants of the best model.
Note the significance of each slope term in the model. Rule– if the coefficient is not significant then you may not use the model to forecast. The Marketing variable may be the one exception to this rule — check with me if the marketing dummy variable is not significant.
7. Investigate your best model using appropriate statistics or graphs to comment on possible:
a. Autocorrelation (Serial correlation) with the DW statistic
b. Heteroscedasticity with a residuals versus order plot (look for a megaphone effect)
c. Multicollinearity with the VIF statistic
6. Evaluate model fit with 2 error measures (RMSE and MAPE).
8. Determine the best remedies for any of the problems identified in 5 above and make the appropriate changes to your regression model if required. Rerun the model and evaluate the fit again including error measures, R adjusted square, F value, slope coefficient significance, DW and VIF.
9. Evaluate the model fit residuals and comment on their randomness using autocorrelation functions (ACFs) , histogram and a normality plot (You may use a four-in-one graph set along with residual ACFs).
10.Develop a two year forecast of Y sales/revenues and check for reasonableness. Use the most reliable and the best goodness to fit forecast for each X variable to forecast Y for the next two years. Make sure that your marketing team member(s) forecast plans for the corporation are included in the dummy variable settings or a marketing expense variable for the 2 year forecast. Submit this work in the appropriate Project Part 4 Dropbox.
11. Prepare a ten minute executive level presentation on the market plans and forecast for the target corporation sales. This will be Project Part 5. Be prepared to defend you results. The forecaster must address the reliability of the best forecast model and forecast results while the Marketing team members must address the historical marketing activities and planned marketing actions over the two year forecast period.
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