Exponential Smoothing in Excel (Find α) | Use Solver to find smoothing constant alpha

1. Diagram
   Observation

   Cell C1 is labeled α and cell C2 contains 0.4.

2. Audio
   Observation

   The narrator says he has chosen a random value for alpha, which is 0.4 here.

$\alpha$

Smoothing constant used in the exponential smoothing forecast formula.

In this clip it is set to 0.4; the video does not state the general admissible range.

1. Diagram
   Observation

   Cell D1 is labeled 1 - α and cell D2 contains 0.6.

2. Formula
   Observation

   The displayed forecast formula uses the term (1-α).

$1-\alpha$

Complement of the smoothing constant, multiplying the previous forecast in the exponential smoothing update.

Here it equals 0.6 because $α=0.4$.

1. Diagram
   Observation

   Column C is headed Demand and lists 48, 44, 40, 50, 37, 42, 43 for months 1 through 7.

2. Audio
   Observation

   The narrator refers to these as time series data and later as actual values.

$\text{Demand}$

Actual observed time-series value for each month.

Seven monthly observations are shown in the worksheet.

1. Diagram
   Observation

   Column D is headed Forecast.

2. Audio
   Observation

   The narrator explains how to compute forecasts for periods 2 through 7.

$\text{Forecast}$

Exponentially smoothed forecast value for a period.

In this clip, forecasts are filled from period 2 onward.

1. Diagram
   Observation

   Column E is headed |Error|.

2. Formula
   Observation

   The entered formula is =ABS(C6-D6).

|$\text{Error}$|

Absolute forecast error, the magnitude of the difference between actual demand and forecast.

Computed for periods with both demand and forecast values.

1. Diagram
   Observation

   Column F is headed Error².

2. Formula
   Observation

   The entered formula is =$E6^2$.

$\text{Error}^2$

Squared forecast error, obtained by squaring the absolute error column.

Computed rowwise after |Error| is available.

1. Diagram
   Observation

   Column G is headed APE.

2. Audio
   Observation

   The narrator says he will calculate absolute percent errors.

1. No APE formula or numeric APE values are shown within this 120-second clip.

$\text{APE}$

Absolute percent error column introduced in the worksheet layout.

Header is visible, but calculation is not demonstrated before the clip ends.

1. Diagram
   Observation

   Summary labels MAD, MSE, and MAPE appear below the table.

2. Audio
   Observation

   The narrator mentions calculating absolute errors, squared errors, and absolute percent errors.

1. The clip shows only the labels; no formulas or values for MAD are entered before 120 seconds.

$\text{MAD}$

Mean absolute deviation summary metric label in the worksheet.

Label only in this clip.

1. Diagram
   Observation

   Summary labels MAD, MSE, and MAPE appear below the table.

1. The clip shows only the label; no formula or value for MSE is entered before 120 seconds.

$\text{MSE}$

Mean squared error summary metric label in the worksheet.

Label only in this clip.

1. Diagram
   Observation

   Summary labels MAD, MSE, and MAPE appear below the table.

1. The clip shows only the label; no formula or value for MAPE is entered before 120 seconds.

$\text{MAPE}$

Mean absolute percentage error summary metric label in the worksheet.

Label only in this clip.

1. Diagram
   Observation

   Cell C1 is labeled α and cell C2 contains 0.4.

2. Audio
   Observation

   The narration says the variable value we want to change is alpha and that alpha needs to be between 0 and 1.

$\alpha$

Smoothing constant used as the decision variable in the exponential-smoothing worksheet.

Constrained to $0 \le \alpha \le 1$ in the Solver setup.

1. Diagram
   Observation

   Cell D1 is labeled $1 - \alpha$ and cell D2 contains 0.6.

$1-\alpha$

Complement of the smoothing constant shown beside $\alpha$ in the worksheet header.

1. Audio
   Observation

   The narrator states: alpha times actual in the last period plus one minus alpha times forecast in the last period.

2. Diagram
   Observation

   On-screen text reads: Forecast = α × Actual (in the last period) + (1-α) × Forecast (in the last period).

3. Formula
   Observation

   Excel formula entered in D7 is =$C$$2*C6$+$D$$2*D6$.

The clip presents the standard simple exponential smoothing update: the next forecast is a weighted average of the most recent actual observation and the most recent forecast. In the worksheet, the weights are stored in fixed cells so the same formula can be copied downward.

1. Uses the immediately preceding actual value and preceding forecast value.

2. In this example α is taken from cell C2 and 1-α from cell D2.

1. Initialization rule when no prior forecast is supplied
2. Using absolute references for parameters in Excel

1. Audio
   Observation

   The narrator says that if you are not given a forecast for the first period, then the forecast is the actual value for the first period, and consequently it will be the forecast for the second period as well.

2. Diagram
   Observation

   Blue overlays show $F1 = A1$ and $F2 = A1$.

3. Formula
   Observation

   Cell D6 is filled with =C5, giving forecast 48 for period 2.

Because no earlier forecast is provided for period 1, the video sets the starting forecast equal to the first actual demand. The same value is then carried into period 2, so the first recursive forecast calculation begins at period 3.

1. Applies when the problem does not provide an exogenous initial forecast.

2. Demonstrated on a seven-period monthly demand series.

1. Audio
   Observation

   The narrator says to press F4 to make it absolute and explains that the dollar signs ensure the alpha cell is locked down when copying the formula to other cells.

2. Formula
   Observation

   Formula bar shows =$C$$2*C6$+$D$$2*D6$.

3. Diagram
   Observation

   An on-screen key overlay shows F4 while the reference is edited.

The parameter cells for α and 1-α are written with dollar signs so they remain fixed when the forecast formula is copied to lower rows. By contrast, the demand and forecast references are relative so they shift row by row.

1. Needed when a formula will be copied across multiple rows or columns.

2. Used here to keep the smoothing constants fixed while updating period-specific inputs.

1. Audio
   Observation

   The narrator says: For the absolute errors we type equals ABS and then actual minus forecast value.

2. Formula
   Observation

   Cell E6 contains =ABS(C6-D6).

3. Diagram
   Observation

   Column E is headed |Error| and fills downward with 4, 6.4, 6.16, 9.304, 0.5824, 0.65056.

The worksheet computes the magnitude of each period’s forecast error by subtracting the forecast from the actual demand and applying ABS. This produces a nonnegative error measure for each row.

1. Requires both an actual value and a forecast value in the same row.

1. Initialization rule when no prior forecast is supplied
2. One-step exponential smoothing forecast formula

1. Audio
   Observation

   The narrator says: For the squared error, square the absolute error and double click the handle to copy it down.

2. Formula
   Observation

   Cell F6 contains =$E6^2$.

3. Diagram
   Observation

   Column F is headed Error² and fills with 16, 40.96, 37.9456, 86.56442, 0.33919, 0.423228.

1. The final copied values are visible only near the end of the clip; the last row fill completes right at the boundary.

After the absolute errors are computed, the video squares those values to create the Error² column. Because squaring removes sign, using the absolute error or the raw error gives the same squared result.

1. The |Error| column must already be populated.

1. Absolute forecast error in Excel

1. Audio
   Observation

   For absolute percent error, divide the absolute error by the actual value and multiply by 100.

2. Formula
   Observation

   Cell G6 is filled with =$E6/C6*100$.

3. Animation
   Observation

   The formula is entered in G6 and then copied down through the APE column.

The video defines APE for each month as the absolute forecast error divided by the actual demand, then multiplied by 100. In the worksheet this is implemented as =$E6/C6*100$ and copied downward, producing percentage values such as 9.090909 for month 2.

1. Use the absolute error, not the signed error.

2. Divide by the actual demand value for the same period.

3. Multiply by 100 to express the result as a percentage.

1. |$\text{Error}$|
2. $\text{Demand}$
3. $\text{APE}$

1. Audio
   Observation

   To find MAD, we use equals average to find the mean of the absolute errors.

2. Formula
   Observation

   Cell E12 is filled with =AVERAGE(E6:E11).

3. Diagram
   Observation

   The resulting MAD value shown is 4.51616.

MAD is presented as the mean of the absolute errors. The spreadsheet computes it with =AVERAGE(E6:E11), averaging the |Error| column over months 2 through 7.

1. Average the absolute errors over the chosen set of periods.

2. In this clip the averaged range is E6:E11.

1. |$\text{Error}$|
2. $\text{MAD}$

1. Audio
   Observation

   Then drag to copy the formula for MSE and MAPE.

2. Animation
   Observation

   The average formula from E12 is dragged across to F12 and G12.

3. Diagram
   Observation

   F12 becomes 30.37207 and G12 becomes 10.90941.

After MAD is computed as an average of |Error|, the same averaging method is copied horizontally to the Error^2 and APE columns. This yields MSE as the average of squared errors and MAPE as the average of absolute percentage errors.

1. The copied formula must reference the corresponding column range.

2. In this worksheet the displayed results are MSE = 30.37207 and MAPE = 10.90941.

1. Mean Absolute Deviation (MAD)
2. $\text{Error}^2$
3. $\text{APE}$
4. $\text{MSE}$
5. $\text{MAPE}$

1. Audio
   Observation

   Now suppose we want the best alpha that minimizes MAD. For set objective, we click on the MAD value. Click Min for minimization. The variable value we want to change is alpha, so we click the alpha value for the changing variable cells.

2. Diagram
   Observation

   Solver Parameters shows Set Objective: $E$12, To: Min, By Changing Variable Cells: $C$2.

The video configures Excel Solver to choose the smoothing constant alpha that gives the smallest MAD. The objective cell is the MAD cell E12, the direction is Min, and the changing cell is the alpha cell C2.

1. Objective cell is $E$12 (MAD).

2. Changing variable cell is $C$$2 (\alpha)$.

3. Optimization direction is Min.

1. Mean Absolute Deviation (MAD)
2. $\alpha$
3. $\text{MAD}$

1. Audio
   Observation

   Now, alpha needs to be between zero and one. This checked box here says make unconstrained variable non-negative. That is, we'll leave this box checked if we want alpha to be greater than or equal to zero. To ensure alpha is less than or equal to one, we click Add here to add the constraint. For cell reference, we select the alpha value. Make sure the less than or equal sign is selected, then input one on the right here. Click OK.

2. Diagram
   Observation

   Solver Parameters shows Make Unconstrained Variables Non-Negative checked and Subject to the Constraints: $C$2 <= 1.

3. Animation
   Observation

   An overlay displays $0 \leq \alpha \leq 1$ while the constraint is being explained.

The smoothing constant is restricted to the interval from 0 to 1. The lower bound is enforced by leaving Make Unconstrained Variables Non-Negative checked, and the upper bound is added explicitly as $C$2 <= 1.

1. Keep Make Unconstrained Variables Non-Negative checked for $\alpha \ge 0$.

2. Add the explicit constraint $C$2 <= 1 for $\alpha \le 1$.

1. $\alpha$
2. Solver setup for minimizing MAD with respect to alpha

1. Audio
   Observation

   The narrator concludes: 'And that's how to use Solver to find the best alpha for exponential smoothing.'

2. Formula
   Observation

   The worksheet contains α, 1 - α, Demand, Forecast, |Error|, Error², APE, MAD, MSE, and MAPE.

1. The explicit recurrence formula for exponential smoothing is not shown in this clip.

This clip demonstrates choosing the smoothing constant $\alpha$ in an exponential smoothing model by minimizing forecast error measures computed in Excel. The spreadsheet stores $\alpha$ in cell C3 and its complement $1-\alpha$ in D3, then updates forecasts and error summaries whenever $\alpha$ changes.

1. The model is being tuned on a fixed historical demand series.

2. $\alpha$ is treated as the optimization variable.

3. Error metrics are recomputed automatically from the current $\alpha$.

1. Formula
   Observation

   Columns E, F, and G are labeled |Error|, Error², and APE; row 12 labels the averages as MAD, MSE, and MAPE.

2. Audio
   Observation

   The narrator explicitly names MAD, MSE, and MAPE as the criteria being minimized.

The video uses three aggregate error measures to evaluate a chosen $\alpha$: MAD from the absolute errors, MSE from the squared errors, and MAPE from the absolute percentage errors. These are displayed as single summary cells E12, F12, and G12.

1. $e_i$ denotes forecast error for period $i$.

2. $y_i$ denotes actual demand for period $i$.

3. The formulas shown here are the standard interpretations consistent with the displayed columns; the clip itself only shows the column headings and summary labels.

1. Exponential smoothing parameter selection context

1. Audio
   Observation

   The narrator explicitly states the rule for exponential smoothing when no first-period forecast is given.

2. Diagram
   Observation

   Overlays $F1 = A1$ and $F2 = A1$ visually restate the same rule.

If no forecast is given for the first period, then the first-period forecast is taken to be the first actual value, and that same value is also used as the forecast for the second period.

1. The method being applied is exponential smoothing.

2. No external initial forecast is supplied for period 1.

For the demonstrated time series in this worksheet.

1. Audio
   Observation

   Note that the best alpha that will minimize MAD may differ from the one that will minimize MSE.

The value of $\alpha$ that minimizes MAD need not be the same as the value of $\alpha$ that minimizes MSE.

1. The forecasts depend on $\alpha$.

2. MAD and MSE are both being used as optimization criteria.

There exist cases in which the minimizer of MAD differs from the minimizer of MSE.

1. Diagram
   Observation

   Solver Results states: Solver has converged to the current solution. All Constraints are satisfied.

2. Diagram
   Observation

   After solving, C2 changes from 0.4 to 0.30841 and D2 changes from 0.6 to 0.69159.

3. Diagram
   Observation

   The updated summary row shows MAD = 4.47553, MSE = 29.84198, MAPE = 10.88013.

Using the configured Solver model, the reported solution is $\alpha = 0.30841$ with MAD = 4.47553, and all constraints are satisfied.

1. Set Objective is $E$12.

2. To is Min.

3. By Changing Variable Cells is $C$2.

4. Make Unconstrained Variables Non-Negative is checked.

5. Constraint $C$2 <= 1 is imposed.

6. Solving Method is GRG Nonlinear.

For the displayed worksheet and Solver settings, the returned solution satisfies the stated constraints.

1. Audio
   Observation

   The narrator says: 'You can see here that the optimal alpha value is point three zero eight four. That is, to obtain the smallest MAD possible, we should set alpha to about point three zero eight four.'

2. Formula
   Observation

   Solver Results is open with $α=0.30841$ in C3 and MAD=4.47553 in E12.

For the displayed dataset and spreadsheet setup, the Solver result identifies $\alpha \approx 0.3084$ as the value that minimizes MAD.

1. The demand series and forecast-error calculations are those shown in the worksheet.

2. Solver is minimizing cell E12 (MAD).

3. The changing cell is C3 ($\alpha$).

4. The constraint $C3 \le 1$ is in force.

For the specific worksheet example shown in the clip.

1. Audio
   Observation

   The narrator says: 'Now let's determine the best alpha that will minimize MSE... And we can see here that the best alpha that minimizes MSE is point three one four four.'

2. Formula
   Observation

   Solver Parameters shows objective $F$12, Min, changing cell $C$3, constraint $C$3 <= 1; after Solve, $C3=0.3144$ and $F12=29.83905$.

For the same worksheet example, changing the Solver objective to MSE yields an optimal smoothing constant $\alpha \approx 0.3144$.

1. Solver objective cell is F12 (MSE).

2. Changing variable cell remains C3 ($\alpha$).

3. Constraint $C3 \le 1$ remains active.

4. GRG Nonlinear method is used.

For the specific worksheet example shown in the clip.

1. Audio
   Observation

   The narrator says: 'Doing the same for MAPE, we obtain point three zero eight four, just like with MAD.'

2. Formula
   Observation

   Solver Parameters shows objective $G$12, Min, changing cell $C$3, constraint $C$3 <= 1; Solver Results then shows $C3=0.30841$.

1. The final MAPE value after the MAPE run is not clearly emphasized in audio, though the worksheet shows 10.88013 in G12.

For the same worksheet example, minimizing MAPE gives $\alpha \approx 0.3084$, matching the MAD result reported by the narrator.

1. Solver objective cell is G12 (MAPE).

2. Changing variable cell remains C3 ($\alpha$).

3. Constraint $C3 \le 1$ remains active.

4. GRG Nonlinear method is used.

For the specific worksheet example shown in the clip.

1. Formula
   Observation

   D7 is entered as =$C$$2*C6$+$D$$2*D6$.

2. Diagram
   Observation

   After entry, D7 displays 46.4.

3. Audio
   Observation

   The narrator describes the formula and then drags the handle down to period 7.

1. Expression

   $$F_2=A_1=48$$
   Explanation

   Period 2 is initialized directly from the first actual demand because no prior forecast is supplied.

   Justification

   Initialization rule stated in the video.

   Shown in the video
2. Expression

   $$F_3=\alpha A_2+(1-\alpha)F_2$$
   Explanation

   The period-3 forecast is formed from the period-2 actual and the period-2 forecast.

   Justification

   Exponential smoothing update formula shown on screen.

   Shown in the video
3. Expression

   $$F_3=0.4\times 44+0.6\times 48$$
   Explanation

   Substitute $α=0.4$, $A_2=44$, and $F_2=48$ into the update formula.

   Justification

   Values are read from cells C2, D2, C6, and D6 in the worksheet.

   Derived from the video
4. Expression

   $$F_3=17.6+28.8=46.4$$
   Explanation

   The arithmetic yields the displayed forecast in cell D7.

   Justification

   Direct numerical evaluation matches the worksheet output.

   Derived from the video
5. Expression$\text{Copy }$ =$C$$2*C6$+$D$$2*D6 \text{ down to row 11}$
   Explanation

   Dragging the fill handle applies the same recurrence to periods 4 through 7, producing 43.84, 46.304, 42.5824, and 42.34944.

   Justification

   Relative references advance row by row while absolute references keep the parameters fixed.

   Shown in the video

The worksheet generates forecasts $F_3$ through $F_7$ by repeated application of the exponential smoothing recurrence after initializing $F_2=48$.

1. Formula
   Observation

   E6 is =ABS(C6-D6) and F6 is =$E6^2$.

2. Diagram
   Observation

   Filled columns show |Error| values 4, 6.4, 6.16, 9.304, 0.5824, 0.65056 and Error² values 16, 40.96, 37.9456, 86.56442, 0.33919, 0.423228.

1. The exact completion instant of the last Error² fill is at the clip boundary.

1. Expression

   $$|e_2|=|44-48|=4$$
   Explanation

   For period 2, subtract the forecast from demand and take absolute value.

   Justification

   Formula =ABS(C6-D6) entered in the worksheet.

   Shown in the video
2. Expression

   $$|e_3|=|40-46.4|=6.4$$
   Explanation

   The same rowwise operation is applied to period 3.

   Justification

   Copied formula down column E.

   Shown in the video
3. Expression

   $$e_2^2=4^2=16$$
   Explanation

   Square the period-2 absolute error to populate the Error² column.

   Justification

   Formula =$E6^2$ entered in the worksheet.

   Shown in the video
4. Expression

   $$e_3^2=6.4^2=40.96$$
   Explanation

   Square the period-3 absolute error similarly.

   Justification

   Copied formula down column F.

   Shown in the video
5. Expression

   $$\text{Continue down rows 8--11}$$
   Explanation

   The remaining displayed values follow the same pattern for periods 4 through 7.

   Justification

   Fill-handle copying demonstrated on screen.

   Shown in the video

The error diagnostics are built rowwise from the demand and forecast columns, first as absolute errors and then as squared errors.

1. Audio
   Observation

   For absolute percent error, divide the absolute error by the actual value and multiply by 100. Then double-click to copy it down.

2. Formula
   Observation

   =$E6/C6*100$ appears in G6.

3. Animation
   Observation

   The formula is copied down the APE column.

1. Expression

   $$\text{APE}_i=\frac{|\text{Error}_i|}{\text{Demand}_i}\times 100$$
   Explanation

   The narrator states the rule for absolute percent error.

   Justification

   Audio definition at 00:00:02-00:00:09.

   Shown in the video
2. Expression

   $$=E6/C6*100$$
   Explanation

   This is the spreadsheet implementation of the rule for month 2.

   Justification

   Formula bar and cell G6 content visible at 00:00:06-00:00:12.

   Shown in the video
3. Expression

   $$\text{G6:G11 filled by copying down}$$
   Explanation

   The same relative formula is applied to the remaining rows.

   Justification

   Animation of copying the formula down at 00:00:13-00:00:16.

   Shown in the video

The APE column is obtained by dividing each absolute error by the corresponding demand and multiplying by 100.

1. Audio
   Observation

   To find MAD, we use equals average to find the mean of the absolute errors. Then drag to copy the formula for MSE and MAPE.

2. Formula
   Observation

   =AVERAGE(E6:E11) is entered in E12.

3. Diagram
   Observation

   E12, F12, and G12 display 4.51616, 30.37207, and 10.90941.

1. Expression

   $$\text{MAD}=\operatorname{AVERAGE}(E6:E11)$$
   Explanation

   The MAD cell averages the absolute-error column.

   Justification

   Audio plus formula bar at 00:00:17-00:00:23.

   Shown in the video
2. Expression

   $$\text{MSE}=\operatorname{AVERAGE}(F6:F11)$$
   Explanation

   Copying the average formula to the Error^2 column gives the mean squared error.

   Justification

   Drag-copy animation and displayed F12 value at 00:00:23-00:00:29.

   Derived from the video
3. Expression

   $$\text{MAPE}=\operatorname{AVERAGE}(G6:G11)$$
   Explanation

   Copying the average formula to the APE column gives the mean absolute percentage error.

   Justification

   Drag-copy animation and displayed G12 value at 00:00:23-00:00:29.

   Derived from the video

The three summary error measures are the columnwise averages of |Error|, Error^2, and APE.

1. Audio
   Observation

   Now suppose we want the best alpha that minimizes MAD... Click Min... The variable value we want to change is alpha... alpha needs to be between zero and one... Leave this method here as nonlinear. And click solve.

2. Diagram
   Observation

   Solver Parameters shows Set Objective $E$12, To Min, By Changing Variable Cells $C$2, constraint $C$2 <= 1, Make Unconstrained Variables Non-Negative checked, GRG Nonlinear selected.

3. Diagram
   Observation

   Solver Results reports convergence and all constraints satisfied; C2 becomes 0.30841 and E12 becomes 4.47553.

1. Expression

   $$\min \ \text{MAD}(\alpha)$$
   Explanation

   Choose MAD as the objective to be minimized.

   Justification

   Audio at 00:00:52-00:01:04 and Set Objective $E$12 with To: Min.

   Shown in the video
2. Expression

   $$\alpha \leftarrow C2$$
   Explanation

   Identify the alpha cell as the changing variable.

   Justification

   Audio at 00:01:05-00:01:13 and By Changing Variable Cells $C$2.

   Shown in the video
3. Expression

   $$\alpha \ge 0$$
   Explanation

   Retain the non-negativity option for unconstrained variables.

   Justification

   Audio at 00:01:13-00:01:29 and checked Make Unconstrained Variables Non-Negative box.

   Shown in the video
4. Expression

   $$\alpha \le 1$$
   Explanation

   Add the explicit upper-bound constraint on the alpha cell.

   Justification

   Audio at 00:01:30-00:01:52 and constraint list showing $C$2 <= 1.

   Shown in the video
5. Expression

   $$\text{Method: GRG Nonlinear}$$
   Explanation

   Leave the solving method set to nonlinear.

   Justification

   Audio at 00:01:53-00:01:56 and dropdown display.

   Shown in the video
6. Expression

   $$\alpha^*=0.30841,\ \text{MAD}^*=4.47553$$
   Explanation

   Run Solve and read the converged solution from the worksheet.

   Justification

   Solver Results dialog and updated cells at 00:01:57-00:01:59.

   Shown in the video

With the stated setup, Solver converges to $\alpha = 0.30841$ as the feasible value minimizing MAD in this worksheet.

1. Formula
   Observation

   Solver Parameters displays Set Objective: $F$12, To: Min, By Changing Variable Cells: $C$3, Subject to the Constraints: $C$3 <= 1, Solving Method: GRG Nonlinear.

2. Audio
   Observation

   The narrator says the objective is set to MSE, other settings remain valid, and then Solve is clicked.

3. Formula
   Observation

   After solving, C3 changes to 0.3144 and F12 changes to 29.83905.

1. Expression

   $$\text{Initial state: } C3=0.4,\; F12=30.37207$$
   Explanation

   Before rerunning Solver for MSE, the worksheet shows $α=0.4$ and the corresponding MSE value.

   Justification

   Directly visible in the spreadsheet at about 13–15 seconds.

   Shown in the video
2. Expression

   $$\text{Set Objective: } F12,\quad \text{To: Min},\quad \text{By Changing Variable Cells: } C3$$
   Explanation

   The optimization target is changed to the MSE cell while keeping α as the decision variable.

   Justification

   Visible in the Solver Parameters dialog and stated in the narration.

   Shown in the video
3. Expression

   $$C3 \le 1$$
   Explanation

   The upper-bound constraint on α is retained from the previous setup.

   Justification

   Visible in Solver Parameters under Subject to the Constraints.

   Shown in the video
4. Expression

   $$\text{Solving Method: GRG Nonlinear}$$
   Explanation

   The nonlinear solver engine is selected for this optimization.

   Justification

   Visible in the Solver Parameters dialog.

   Shown in the video
5. Expression

   $$\text{Result: } C3=0.3144,\; F12=29.83905$$
   Explanation

   After clicking Solve, the worksheet updates to the reported optimum for MSE.

   Justification

   Visible in Solver Results and the updated spreadsheet cells.

   Shown in the video

The numerical Solver run demonstrates that, for this dataset and spreadsheet formulation, the MSE-minimizing smoothing constant is approximately $\alpha=0.3144$.

1. Formula
   Observation

   Solver Parameters displays Set Objective: $G$12, To: Min, By Changing Variable Cells: $C$3, Subject to the Constraints: $C$3 <= 1, Solving Method: GRG Nonlinear.

2. Audio
   Observation

   The narrator says: 'Doing the same for MAPE, we obtain point three zero eight four, just like with MAD.'

3. Formula
   Observation

   Solver Results then shows $C3=0.30841$.

1. The intermediate click sequence is brief, but the objective change to G12 and the resulting α value are visible.

1. Expression

   $$\text{Reset state before MAPE run: } C3=0.4,\; G12=10.90941$$
   Explanation

   Before optimizing MAPE, the worksheet again shows $α=0.4$ and the corresponding MAPE.

   Justification

   Visible in the spreadsheet around 33–35 seconds.

   Shown in the video
2. Expression

   $$\text{Set Objective: } G12,\quad \text{To: Min},\quad \text{By Changing Variable Cells: } C3$$
   Explanation

   The objective cell is switched to MAPE while the same changing cell is used.

   Justification

   Visible in Solver Parameters.

   Shown in the video
3. Expression

   $$C3 \le 1$$
   Explanation

   The same upper-bound constraint on α is kept.

   Justification

   Visible in Solver Parameters.

   Shown in the video
4. Expression

   $$\text{Result: } C3=0.30841$$
   Explanation

   After solving, α returns to the value previously associated with the MAD optimum.

   Justification

   Visible in Solver Results and the updated C3 cell.

   Shown in the video

The numerical Solver run shows that minimizing MAPE for this example gives $\alpha \approx 0.3084$, which the narrator notes is the same as for MAD.

1. Diagram
   Observation

   The worksheet lists Month 1 through 7 with Demand values 48, 44, 40, 50, 37, 42, 43.

2. Audio
   Observation

   The narrator says he will calculate exponential smoothing forecasts for this time series data in Excel.

Given monthly demand values 48, 44, 40, 50, 37, 42, 43 and $α=0.4$, compute exponential smoothing forecasts and the associated absolute and squared errors in Excel.

1. Months 1 through 7 are listed.

2. Demand values are 48, 44, 40, 50, 37, 42, 43.

3. α is set to 0.4 and 1-α to 0.6.

4. No initial forecast is supplied for period 1.

Populate the Forecast, |Error|, and Error² columns for the example dataset.

1. Expression

   $$F_2=A_1=48$$
   Explanation

   Initialize the second-period forecast with the first actual value.

   Justification

   Stated initialization rule in the video.

   Shown in the video
2. Expression

   $$F_t=0.4A_{t-1}+0.6F_{t-1}\quad(t=3,\dots,7)$$
   Explanation

   Apply the exponential smoothing recurrence to obtain later forecasts.

   Justification

   Displayed formula and entered Excel formula.

   Shown in the video
3. Expression

   $$(F_3,F_4,F_5,F_6,F_7)=(46.4,43.84,46.304,42.5824,42.34944)$$
   Explanation

   These are the forecast values shown after filling the column.

   Justification

   Visible worksheet outputs.

   Shown in the video
4. Expression

   $$|e_t|=|A_t-F_t|\quad(t=2,\dots,7)$$
   Explanation

   Compute absolute errors row by row.

   Justification

   Formula =ABS(C6-D6) entered in Excel.

   Shown in the video
5. Expression

   $$(|e_2|,\dots,|e_7|)=(4,6.4,6.16,9.304,0.5824,0.65056)$$
   Explanation

   These are the displayed absolute error values.

   Justification

   Visible worksheet outputs.

   Shown in the video
6. Expression

   $$e_t^2=(|e_t|)^2\quad(t=2,\dots,7)$$
   Explanation

   Square the absolute errors to form the Error² column.

   Justification

   Formula =$E6^2$ entered in Excel.

   Shown in the video
7. Expression

   $$(e_2^2,\dots,e_7^2)=(16,40.96,37.9456,86.56442,0.33919,0.423228)$$
   Explanation

   These are the displayed squared error values.

   Justification

   Visible worksheet outputs.

   Shown in the video

Forecasts: 48, 46.4, 43.84, 46.304, 42.5824, 42.34944 for periods 2 through 7. Absolute errors: 4, 6.4, 6.16, 9.304, 0.5824, 0.65056. Squared errors: 16, 40.96, 37.9456, 86.56442, 0.33919, 0.423228.

Each displayed number matches direct substitution into the stated formulas using the worksheet’s demand values and $α=0.4$.

1. Diagram
   Observation

   Month 2 row shows Demand = 44, Forecast = 48, |Error| = 4, and the formula =$E6/C6*100$ in the APE cell.

2. Diagram
   Observation

   The resulting APE value displayed is 9.090909.

Compute the absolute percentage error for the month with demand 44 and forecast 48.

1. $\text{Demand}=44$

2. $\text{Forecast}=48$

3. |$\text{Error}$|=4

Find APE for that row.

1. Expression

   $$\text{APE}=\frac{4}{44}\times 100$$
   Explanation

   Apply the stated APE rule using the absolute error and actual demand.

   Justification

   Audio definition plus visible formula =$E6/C6*100$.

   Shown in the video
2. Expression

   $$=9.090909$$
   Explanation

   The spreadsheet displays the evaluated percentage.

   Justification

   Visible result in the APE column.

   Shown in the video

9.090909

The displayed cell value matches the direct calculation $4/44*100$.

1. Diagram
   Observation

   Before optimization, the summary row shows MAD = 4.51616, MSE = 30.37207, MAPE = 10.90941.

2. Formula
   Observation

   =AVERAGE(E6:E11) is used for MAD and then copied across.

Read the initial error summaries after the average formulas are entered.

1. $\alpha=0.4$

2. |Error| column values are present

3. Error^2 column values are present

4. APE column values are present

Determine MAD, MSE, and MAPE for the initial worksheet state.

1. Expression

   $$\text{MAD}=4.51616$$
   Explanation

   Average of the |Error| column is shown in E12.

   Justification

   Visible formula result at 00:00:23.

   Shown in the video
2. Expression

   $$\text{MSE}=30.37207$$
   Explanation

   Average of the Error^2 column is shown in F12 after copying the formula.

   Justification

   Visible result at 00:00:27-00:00:29.

   Shown in the video
3. Expression

   $$\text{MAPE}=10.90941$$
   Explanation

   Average of the APE column is shown in G12 after copying the formula.

   Justification

   Visible result at 00:00:27-00:00:29.

   Shown in the video

MAD = 4.51616, MSE = 30.37207, MAPE = 10.90941

These values are directly displayed in the summary row before Solver is run.

1. Audio
   Observation

   Suppose we want the best alpha that minimizes MAD.

2. Diagram
   Observation

   Solver Parameters are set to minimize $E$12 by changing $C$2 with $C$2 <= 1 and non-negativity enabled.

3. Diagram
   Observation

   After solving, $C2 = 0.30841$, $D2 = 0.69159$, MAD = 4.47553, MSE = 29.84198, MAPE = 10.88013.

Use Excel Solver to determine the alpha value that minimizes MAD subject to $0 \le \alpha \le 1$.

1. Objective cell is MAD in $E$12.

2. Changing cell is alpha in $C$2.

3. Constraints are $\alpha \ge 0$ and $\alpha \le 1$.

4. Solving method is GRG Nonlinear.

Find the optimal alpha and the corresponding minimized MAD.

1. Expression

   $$\min \ \text{MAD}(\alpha)$$
   Explanation

   Set the Solver objective to the MAD cell and choose Min.

   Justification

   Audio and Solver Parameters display.

   Shown in the video
2. Expression

   $$\text{Changing Variable Cells}:\ C2$$
   Explanation

   Tell Solver to vary the alpha cell.

   Justification

   Audio and Solver Parameters display.

   Shown in the video
3. Expression

   $$0 \le \alpha \le 1$$
   Explanation

   Enforce the admissible range for the smoothing constant.

   Justification

   Checked non-negativity box plus explicit $C$2 <= 1 constraint.

   Shown in the video
4. Expression

   $$\alpha^*=0.30841$$
   Explanation

   Solver updates the alpha cell to the reported optimum.

   Justification

   Post-solve worksheet display.

   Shown in the video
5. Expression

   $$\text{MAD}^*=4.47553$$
   Explanation

   The minimized MAD is shown in the objective cell after solving.

   Justification

   Post-solve worksheet display.

   Shown in the video

$\alpha^*=0.30841$,$\quad \text{MAD}^*=4.47553$

Solver Results states that the solution converged and all constraints are satisfied.

1. Formula
   Observation

   The worksheet shows Demand values 48, 44, 40, 50, 37, 42, 43 and summary metrics MAD, MSE, MAPE in row 12.

2. Audio
   Observation

   The narrator walks through finding the best alpha for MAD, MSE, and MAPE using Solver.

1. The underlying forecast recursion is not explicitly written out in the clip.

Given a historical demand series in Excel and an exponential smoothing forecast table, determine the smoothing constant $\alpha$ that minimizes each of MAD, MSE, and MAPE using Solver.

1. Monthly demand values shown in column B: 48, 44, 40, 50, 37, 42, 43.

2. $\alpha$ is stored in cell C3 and $1-\alpha$ in D3.

3. Error columns are |Error|, Error², and APE.

4. Summary cells are E12=MAD, F12=MSE, G12=MAPE.

5. Solver constraint shown: $C3 \le 1$.

6. Make Unconstrained Variables Non-Negative is checked.

7. Solving Method: GRG Nonlinear.

Identify the optimal $\alpha$ for minimizing MAD, then MSE, then MAPE.

1. Expression

   $$\alpha \approx 0.3084 \quad \text{with} \quad \text{MAD}=4.47553$$
   Explanation

   The clip opens on a completed Solver result for MAD, and the narrator states that this alpha gives the smallest MAD.

   Justification

   Audio plus visible Solver Results and spreadsheet values at 0–11 seconds.

   Shown in the video
2. Expression

   $$\text{Set Objective: } F12,\; \text{Min},\; \text{Changing Cell: } C3,\; C3 \le 1$$
   Explanation

   To optimize MSE, the objective cell is changed to F12 while keeping the same decision variable and constraint.

   Justification

   Visible in Solver Parameters at about 15–24 seconds.

   Shown in the video
3. Expression

   $$\alpha = 0.3144 \quad \text{with} \quad \text{MSE}=29.83905$$
   Explanation

   After clicking Solve, the worksheet updates to the MSE-optimal solution.

   Justification

   Visible in Solver Results and updated cells at about 25–33 seconds.

   Shown in the video
4. Expression

   $$\text{Set Objective: } G12,\; \text{Min},\; \text{Changing Cell: } C3,\; C3 \le 1$$
   Explanation

   To optimize MAPE, the objective cell is changed to G12 while retaining the same setup otherwise.

   Justification

   Visible in Solver Parameters at about 35–37 seconds.

   Shown in the video
5. Expression

   $$\alpha \approx 0.3084$$
   Explanation

   The MAPE run returns the same alpha value reported for MAD.

   Justification

   Narration plus visible Solver Results at about 38–43 seconds.

   Shown in the video

For the displayed example: minimizing MAD gives $\alpha \approx 0.3084$; minimizing MSE gives $\alpha \approx 0.3144$; minimizing MAPE gives $\alpha \approx 0.3084$.

Each answer is verified by the corresponding Solver output screen and the updated spreadsheet cells showing the chosen objective value after optimization.

1. Diagram
   Observation

   The screen shows an Excel workbook titled Exponential Smoothing - Excel.xlsx with α and 1-α at the top, a monthly demand table, empty Forecast, |Error|, Error², and APE columns, and summary labels MAD, MSE, MAPE below.

2. Caption evidence
   Observation

   Overlay text reads: Exponential Smoothing in Excel and Finding best α using Solver.

1. Parameter cells C1:C2 and D1:D2

2. Monthly table with Month, Demand, Forecast, |Error|, Error², APE

3. Summary labels MAD, MSE, MAPE

4. Title overlays

1. The title overlay appears over the static worksheet.

2. Red highlight boxes move among the demand column, α cell, and error-related headers as the narrator introduces the task.

1. The underlying demand data remain unchanged during the introduction.

2. α stays at 0.4 and 1-α stays at 0.6.

The visual layout establishes the forecasting problem, the parameter location, and the error metrics that will be computed.

1. Diagram
   Observation

   Blue boxes display $F1 = A1$ and then $F2 = A1$ while the cursor moves around the first two rows of the table.

1. Blue formula overlays

2. Rows for months 1 and 2

3. Demand and Forecast columns

1. The overlay first states $F1 = A1$, then changes to $F2 = A1$.

2. Cell D6 is prepared to receive the value from C5.

1. The demand values in column C do not change.

2. The parameter cells remain fixed at 0.4 and 0.6.

The animation encodes the initialization convention: absent a prior forecast, the first actual value seeds the forecast sequence and is reused for period 2.

1. Animation
   Observation

   After D7 evaluates to 46.4, the fill handle is dragged downward through row 11.

2. Diagram
   Observation

   Forecast values appear sequentially in D8:D11 as 43.84, 46.304, 42.5824, 42.34944.

1. Cell D7 formula

2. Fill handle

3. Forecast column D

1. One manually entered forecast formula is propagated to later periods.

2. New forecast values populate rows 8 through 11 in order.

1. The absolute references $C$2 and $D$2 stay fixed.

2. The relative references to prior demand and forecast shift down one row at a time.

The drag operation demonstrates how a single recurrence relation generates the whole forecast path once the initial condition is set.

1. Animation
   Observation

   The user enters =ABS(C6-D6) in E6, then fills column E downward; next enters =$E6^2$ in F6 and fills column F downward.

2. Diagram
   Observation

   Columns E and F populate with the displayed error and squared-error values.

1. The very last squared-error fill completes at the end boundary of the clip.

1. Column E header |Error|

2. Column F header Error²

3. Formula bars for E6 and F6

1. Column E fills from row 6 to row 11 with absolute errors.

2. Column F then fills from row 6 to row 11 with squared errors.

1. Demand and forecast columns remain unchanged while error columns are computed.

2. The formulas are copied without altering their row-relative structure.

The visual sequence shows the standard diagnostic workflow: first compute forecast deviations, then transform them into squared deviations for later summary measures.

1. Diagram
   Observation

   The worksheet shows headers α and 1-α in row 1, values 0.4 and 0.6 in row 2, and a table with Month, Demand, Forecast, |Error|, Error^2, APE from rows 4-11, with MAD, MSE, MAPE in row 13.

1. Header cells C1:D2

2. Forecast table rows 4-11

3. Summary row 13

1. The table structure remains the same throughout the clip.

2. Column order stays Month, Demand, Forecast, |Error|, Error^2, APE.

The visual layout organizes the data so that each error measure can be computed columnwise and then summarized in one row.

1. Animation
   Observation

   The cursor enters =$E6/C6*100$ in G6 and copies it down the APE column.

2. Diagram
   Observation

   New APE values appear row by row, ending with 9.090909, 16, 12.32, 25.14595, 1.386667, 1.51293.

1. Cell G6

2. APE column G

3. Rows 6-11

1. The APE column changes from blank to filled with percentage values.

2. The formula is replicated downward using relative references.

1. The underlying Demand and |Error| values do not change during this step.

The animation demonstrates that APE is a rowwise transformation of absolute error and demand.

1. Animation
   Observation

   =AVERAGE(E6:E11) is entered in E12, then dragged across to F12 and G12.

2. Diagram
   Observation

   Summary values 4.51616, 30.37207, and 10.90941 appear under MAD, MSE, and MAPE.

1. Cells E12:G12

2. Columns E, F, G

1. The summary row changes from empty to populated with three averages.

2. The same averaging operation is applied across adjacent error columns.

1. The source columns |Error|, Error^2, and APE remain unchanged during this step.

The visual sequence shows that MAD, MSE, and MAPE are obtained by averaging their respective column entries.

1. Diagram
   Observation

   Solver Parameters opens and is filled with Set Objective $E$12, To Min, By Changing Variable Cells $C$2, constraint $C$2 <= 1, Make Unconstrained Variables Non-Negative checked, GRG Nonlinear selected.

2. Animation
   Observation

   Red highlight boxes emphasize the objective, variable cell, constraint area, and solving method as they are discussed.

1. Solver Parameters dialog

2. Cell $E$12

3. Cell $C$2

4. Constraint list

5. Solving Method dropdown

1. The objective field becomes $E$12.

2. The direction changes to Min.

3. The changing-variable field becomes $C$2.

4. The constraint $C$2 <= 1 is added.

5. The solving method remains GRG Nonlinear.

1. The worksheet data behind the dialog stays visible and structurally unchanged.

The dialog visually encodes the mathematical program: minimize MAD over alpha subject to 0 <= alpha <= 1.

1. Diagram
   Observation

   Solver Results appears, then the worksheet updates C2 to 0.30841, D2 to 0.69159, and the summary row to MAD 4.47553, MSE 29.84198, MAPE 10.88013.

1. Cells C2 and D2

2. Summary cells E12:G12

3. Solver Results dialog

1. Alpha changes from 0.4 to 0.30841.

2. 1-alpha changes from 0.6 to 0.69159.

3. MAD changes from 4.51616 to 4.47553.

4. MSE changes from 30.37207 to 29.84198.

5. MAPE changes from 10.90941 to 10.88013.

1. The solver message states that all constraints are satisfied.

The final visual update shows the effect of reoptimizing alpha on both the parameter cells and all downstream error summaries.

1. Animation
   Observation

   A Solver Results dialog overlays the worksheet while $C3=0.30841$ and $E12=4.47553$ are visible.

2. Formula
   Observation

   The word Minimum appears briefly near the MAD area around 5–7 seconds.

1. The brief appearance of the word Minimum is visible but not accompanied by a full explanatory sentence in this clip.

1. Solver Results dialog

2. Cell C3 with $α=0.30841$

3. Cell D3 with $1-α=0.69159$

4. Row 12 summary metrics MAD, MSE, MAPE

1. The dialog confirms convergence to the current solution.

2. The spreadsheet remains on the MAD-optimal state while the narrator explains the result.

1. The demand series in column B does not change.

2. The constraint structure from Solver is implied to remain the same.

This visual establishes the MAD-optimal smoothing constant and links it to the minimized MAD value shown in the worksheet.

1. Animation
   Observation

   The Solver Parameters dialog opens and shows Set Objective $F$12, To: Min, By Changing Variable Cells $C$3, Subject to the Constraints $C$3 <= 1, and GRG Nonlinear.

1. Solver Parameters dialog

2. Objective field

3. Changing Variable Cells field

4. Constraints list

5. Solving Method dropdown

1. The objective cell is set to F12 (MSE).

2. The Min option is selected.

3. The changing cell remains C3.

4. The constraint C3 <= 1 is displayed.

1. The same worksheet data and error table remain in the background.

2. The optimization variable is still α in C3.

The visual demonstrates how to redirect the same Solver model from one error criterion to another by changing only the objective cell.

1. Animation
   Observation

   After Solve is clicked, Solver Results reports a found solution and the worksheet updates to $C3=0.3144$, $D3=0.6856$, $F12=29.83905$.

1. Solver Results dialog

2. Updated cells C3, D3, and F12

1. α changes from 0.4 to 0.3144.

2. MSE changes from 30.37207 to 29.83905.

3. The dialog states that all constraints and optimality conditions are satisfied.

1. The demand data and table layout remain unchanged.

2. The constraint set is the same as in the preceding setup.

This visual confirms the numerical outcome of the MSE minimization run.

1. Audio
   Observation

   The narrator emphasizes pressing F4 and says the dollar signs ensure the alpha cell is locked down when copying the formula to other cells.

When a formula uses a separate parameter cell such as α, one might copy it downward without locking the parameter reference.

The video stresses using $C$2 and $D$2 so the smoothing constants stay fixed while the period-specific demand and forecast references move row by row.

1. Audio
   Observation

   The narrator explains what to do if you are not given a forecast for the first period.

2. Diagram
   Observation

   Overlays show $F1 = A1$ and $F2 = A1$.

Learners may think exponential smoothing cannot start unless an external forecast for period 1 is provided.

This clip demonstrates a common fallback: if no initial forecast is given, use the first actual value as the seed and carry it into period 2.

1. Audio
   Observation

   Note that the best alpha that will minimize MAD may differ from the one that will minimize MSE.

That the alpha minimizing MAD is automatically the same as the alpha minimizing MSE.

The video explicitly warns that different error criteria can lead to different optimal alpha values.

1. Audio
   Observation

   For absolute percent error, divide the absolute error by the actual value and multiply by 100.

2. Formula
   Observation

   The implemented formula is =$E6/C6*100$, using column C (Demand) in the denominator.

That APE should divide the absolute error by the forecast value.

The demonstrated formula divides by the actual demand value in column C, not by the forecast in column D.

1. Audio
   Observation

   The narrator separately finds different optima: 0.3084 for MAD, 0.3144 for MSE, and 0.3084 for MAPE.

2. Formula
   Observation

   The worksheet shows distinct objective cells E12, F12, and G12 being minimized.

One might assume that the same smoothing constant is always optimal regardless of whether MAD, MSE, or MAPE is being minimized.

In this example, MSE produces a slightly different optimal alpha ($0.3144$) than MAD and MAPE ($0.3084$), so the best $\alpha$ depends on the chosen error criterion.

1. Formula
   Observation

   Solver Parameters explicitly shows Solving Method: GRG Nonlinear for these optimization runs.

A viewer might think the problem is handled with a linear programming solver because the interface is simple and tabular.

The clip shows the GRG Nonlinear engine being used, indicating the optimization is treated as a smooth nonlinear problem in Excel Solver.

1. Audio
   Observation

   The narrator first explains the initialization rule and then says the first calculation is therefore in the third period.

2. Formula
   Observation

   D6 is set from C5 before D7 uses the recurrence with row 6 values.

The recurrence can only begin at period 3 after the video’s initialization rule supplies $F_2$ from $A_1$.

1. Formula
   Observation

   The entered formula is =$C$$2*C6$+$D$$2*D6$.

2. Audio
   Observation

   The narrator explains that the dollar signs lock the alpha cell when copying the formula.

Absolute referencing is the Excel mechanism that lets the same exponential smoothing formula be copied down the column without changing the parameter cells.

1. Formula
   Observation

   Column E uses =ABS(C6-D6), directly referencing the demand and forecast columns.

2. Diagram
   Observation

   The |Error| column is filled only after the Forecast column has values.

Absolute error computation requires the forecast series to have been generated first.

1. Formula
   Observation

   Column F uses =$E6^2$, taking the already computed |Error| values as input.

2. Audio
   Observation

   The narrator says to square the absolute error.

The squared-error column is built directly from the absolute-error column in the demonstrated workflow.

1. Diagram
   Observation

   The table includes a rowwise APE column and a separate summary label MAPE below the table.

1. This relationship is not explicitly discussed in the audio within the clip.

Editorial clarification: APE denotes the per-period absolute percentage error column, whereas MAPE is the aggregate mean of such percentages shown only as a summary label here.

1. Diagram
   Observation

   APE is computed rowwise in column G, then MAPE is obtained by averaging column G in cell G12.

MAPE is built from the rowwise APE values, so the APE formula must be established before the average can produce MAPE.

1. Audio
   Observation

   To find MAD, we use equals average to find the mean of the absolute errors.

2. Formula
   Observation

   =AVERAGE(E6:E11) references the |Error| column.

MAD is defined in the video as the average of the absolute errors, so the |Error| column is a direct prerequisite.

1. Diagram
   Observation

   Solver Parameters sets the objective to $E$12, the MAD cell.

2. Audio
   Observation

   Suppose we want the best alpha that minimizes MAD.

The MAD measure computed earlier becomes the objective function minimized by Solver.

1. Audio
   Observation

   Alpha needs to be between zero and one.

2. Diagram
   Observation

   Solver uses non-negativity plus $C$2 <= 1.

The Solver optimization is meaningful only under the stated feasible region 0 <= alpha <= 1 for the smoothing constant.

1. Audio
   Observation

   The best alpha that will minimize MAD may differ from the one that will minimize MSE.

The video contrasts MAD and MSE as alternative optimization criteria that can yield different optimal alpha values.

1. Formula
   Observation

   Changing C3 updates Forecast, |Error|, Error², APE, and the summary cells MAD, MSE, MAPE.

2. Audio
   Observation

   The narrator discusses selecting alpha to minimize each metric.

The smoothing constant $\alpha$ is the input whose value determines the forecast errors summarized by MAD, MSE, and MAPE.

1. Formula
   Observation

   Solver objective cells are set to E12, F12, or G12 depending on the metric being minimized.

Understanding what MAD, MSE, and MAPE measure is required before choosing one of them as the Solver objective.

1. Diagram
   Observation

   Cells C1:C2 show $α=0.4$.

2. Audio
   Observation

   The narrator calls 0.4 the chosen alpha value.

1. $\alpha$
2. One-step exponential smoothing forecast formula

1. Audio
   Observation

   The narrator says the first calculation is therefore in the third period.

2. Diagram
   Observation

   Overlays show $F1 = A1$ and $F2 = A1$.

1. Initialization rule when no prior forecast is supplied
2. One-step exponential smoothing forecast formula