b) As a part of an effort to forecast future sales (in 1000's of gallons) given in the following table: \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline Period ($t$) & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Sales ($X_t$) & 12 & 18 & 16 & 24 & 17 & 16 & 25 & 21 & 23 & 14 \\ \hline \end{tabular} i) Compute the forecasting values by using exponential smoothing constant $\alpha = 0.2$. Assume the value of period 1 as a forecast of period 0. ii) Compute mean absolute deviation (MAD) and mean square error (MSE) also.
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Step 1: The exponential smoothing formula is given by: $F_t = αA_{t-1} + (1-α)F_{t-1}$ where: $F_t$ is the forecast for period t $A_{t-1}$ is the actual value for period t-1 $F_{t-1}$ is the forecast for period t-1 $α$ is the smoothing constant Show more…
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Consider the following gasoline sales time series. If needed, round your answers to two-decimal digits. Week Sales (1,000s of gallons) 1 18 2 22 3 15 4 24 5 18 6 15 7 21 8 19 9 21 10 20 11 16 12 22 (a) Show the exponential smoothing forecasts using α = 0.1, and α = 0.2. Exponential Smoothing Week α = 0.1 α = 0.2 13 (b) Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of α = 0.1 smoothing constant provides the more accurate forecast, with an overall MSE of (c) Are the results the same if you apply MAE as the measure of accuracy? An a= 0.1 smoothing constant provides the more accurate forecast, with an overall MAE of (d) What are the results if MAPE is used? An a=0.1 smoothing constant provides the more accurate forecast, with an overall MAPE of =
Dominador T.
With the gasoline time series data from the given table, show the exponential smoothing forecasts using α = 0.1. Gasoline Sales Times Series Week sales (1000s of gallons) 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22 Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of α = 0.1 or α = 0.2 for the gasoline sales time series? Do not round your interim computations and round your final answers to three decimal places. α = 0.1 α = 0.2 MSE Prefer: 0.2 Are the results the same if you apply MAE as the measure of accuracy? Do not round your interim computations and round your final answers to three decimal places. α = 0.1 α = 0.2 MAE Prefer: 0.1 What are the results if MAPE is used? Do not round your interim computations and round your final answers to two decimal places. α = 0.1 α = 0.2 MAPE % % Prefer: 0.1
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Consider the following gasoline sales time series. If needed, round your answers to two-decimal digits. Week Sales (1,000s of gallons) 1 17 2 23 3 14 4 25 5 17 6 16 7 22 8 19 9 21 10 19 11 17 12 23 (a) Show the exponential smoothing forecasts using a = 0.1 and a = 0.2. Exponential Smoothing Week a = 0.1 a = 0.2 13 (b) Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of a = 0.1 or a = 0.2 for the gasoline sales time series? Answer: ____ smoothing constant provides the more accurate forecast, with an overall MSE of ____ (c) Are the results the same if you apply MAE as the measure of accuracy? Answer: ____ smoothing constant provides the more accurate forecast, with an overall MAE of ____ (d) What are the results if MAPE is used? Answer: ____ smoothing constant provides the more accurate forecast, with an overall MAPE of ____
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