forecasting (test one study)

What forecasting methods are we going to learn in the course? 

Time-series forecasting 

If you like to predict future demands in 2022, a dataset you need is _____. 

past __***demand***__ data in 2021, 2020, 2019, and so on

What are the three steps in time-series forecasting? 

Plot the data, Make forecast using the techniques suitable for the data pattern,  pick the best forecast. 

What drives the choice of techniques?

The pattern of the data 

What are the techniques suitable for a stationary pattern? 

Exponential smoothing, moving averages 

What are the techniques suitable for a trendy pattern? 

Regression, double exponential smoothing 

What are the techniques suitable for a seasonal pattern? 

Triple exponential smoothing 

What are the common performance measures?

MAE, MAPE, RMSE, R2 

Why do we need to check the performances of the techniques we tried? 

To find the most accurate future prediction 

All performance measures are based on ______ of some forms of errors. 

Averages 

MAE stands for _____. 

Mean Absolute Errors 

RMSE stands for _____. 

Root Mean Squared Errors 

Describe how MAE is calculated.

First, calculate errors by subtracting forecasts from the actual values. Then, convert them to absolute values, which are called absolute errors. Then, average the absolute errors to get MAE. 

A scatterplot is generated by _____ in Excel on a Windows computer. 

Data – Forecast Sheet. 

A scatterplot is generated by _____ in Excel on an Apple computer. 

Insert – Scatter  

How do you run exponential smoothing in Excel? 

Using the "Data - Forecast" menu. 

If you have a mac, how do you run exponential smoothing? 

By manual calculation using FORECAST.ETS(), FORECAST.ETS.CONFINT(), and FORECAST.ETS.STAT(). 

Double exponential smoothing is for ____ data.

Trendy 

Triple exponential smoothing is for ____ data. 

Seasonal 

When is regression used? 

When the data shows a trend.

Given the following scatterplots, which is/are suitable for regression?

(You should be able to identify scatterplots showing a trend) 

Can an exponential smoothing method be used for a trendy data? 

Yes

What are the three regression methods covered in the course?  \n

Linear, exponential, and logarithmic. 

Can a forecast for the first period in the dataset be made by a regression method? 

Yes. 

If the data is trendy, the best forecasting method among the following is 

\
moving average

regression

classical decomposition

regression

If the data is stationary, the best forecasting method among the following is 

\
moving average

regression

classical decomposition

moving average

The three steps in the forecasting are

1. Plot the data (by running exponential smoothing in Excel)
2. Choose the method
3. Evaluate the performance and pick the best forecast

In time-series forecasting, to predict "sales" in 2021, ___ is needed.

past sales

regression steps

1. plot the data using a scatterplot
2. get the regression equation
3. make forecasts using the equation
4. calculate the performance measures
5. calculate the confidence intervals

error =

actual - forecast (B2-C2)

A. Error

= ABS(Error)

ABS(D2)

A.P. Error

= A. Error/Actual

= E2/F2

S. Error=

Error^2

Bias

= AVERAGE(error)

MAE

=AVERAGE(A. Error)

MAPE

=AVERAGE(A.P. Error)

RMSE

=sqrt(AVERAGE(S.Error))

How do you run exponential smoothing in Excel? 

Using the "Data - Forecast" menu.

If you have a mac, how do you run exponential smoothing? 

By manual calculation using FORECAST.ETS(), FORECAST.ETS.CONFINT(), and FORECAST.ETS.STAT(). 

Double exponential smoothing is for ____ data, and Triple exponential smoothing is for ____ data.

Trendy; seasonal

how to calculate exp smoothing forecast on mac

=FORECAST.ETS(A12, $B$2:$B$11,$A$2:$A$11,1,1)

lower limit function for exp smoothing

=C12-FORECAST.ETS.CONFINIT(A12,$B$2:$B$11,$A$2:$A$11,0.95,1,1)

upper limit function for exp smoothing

=C12+FORECAST.ETS.CONFINIT(A12,$B$2:$B$11,$A$2:$A$11,0.95,1,1)

SMAPE (MAPE) forecast for exp smoothing

=FORECAST.ETS.STAT($B$2:$B$11,$A$2:$A$11,5,1,1)

MAE function forecast for exp smoothing

=FORECAST.ETS.STAT($B$2:$B$11,$A$2:$A$11,6,1,1)

RMSE function forecast for exp smoothing

=FORECAST.ETS.STAT($B$2:$B$11,$A$2:$A$11,7,1,1)

What are the two methods for stationary data?

Simple exponential smoothing and moving average 

What are heuristics methods? 

Forecasting methods used for stationary data

If 1/1, 1/2, and 1/3 sales are 3, 3, and 6, respectively, what is the forecasted sales for 1/4 by 2-day moving average? 

4\.5 ( = 3+6/2)

What is a span? 

The number of periods that will be averaged to calculate a forecast 

steps of moving averages

1. Decide the span (that is, *n*). That is, how many past data points will be used to predict today's (this month's, this quarter's, etc.) value. 
2. Calculate the average of the past data points of the span and use it as the forecast. 
3. Calculate performance measures, such as MAE, MAPE, and RMSE. 
4. Calculate a confidence interval, which is typically "forecast ± 2\*RMSE." 

how to calculate 2-week moving average

Calculate the average 2 weeks for week 3. Then, copy the formula to weeks 4 to 11.

(with two week moving average) since there are errors in weeks 13 and 14, how do you fix it?

copy B12 to B13:B14

what is errors?

actual - forecast

what are absolute errors?

absolute values of the raw errors

what are absolute percentage errors?

Percentages of absolute errors based on the actual values. 

what are squared errors?

Squared values of the raw (or absolute) errors. 

what is BIAS?

average of error

what is MAE?

average of A. error

what is MAPE?

average of A.P. Error

what is RMSE?

root mean square error

**When comparing multiple methods, we choose the method with the ______ error. For this task, we choose one of MAE, MAPE, and RMSE, and compare its value across the methods. Then, pick the method with the smallest value of the chosen performance measure.**  

**smallest**

formula for lower limit for moving average

=C12-2*RMSE; for RMSE put the cell! like =C12-2*\*$G$12

formula for upper limit for moving average

=C12+2*RMSE; for RMSE put the cell! like =C12+2*$G$12

what does BIAS tell us?

if the method over-forecasts or under-forecasts on average

If the value of BIAS is positive, it means most errors are

positive, which in turn means forecasts are on average is smaller than the actual values. In this case, we say the method **under-forecasts on average**.

If the value of BIAS is negative, on the other hand, the forecasts are on average is

greater than the actual values and the method **over-forecasts on average**. 

Note that BIAS cannot capture the magnitude of average errors because positive and negative errors will be canceled out each other when they are averaged. Therefore, we do not use BIAS for

performance comparison.  

 

what do MAD, MAPE, and RMSE capture?

the magnitude of average errors, so the closer to zero the better

what is a confidence interval?

collection of possible true future values

A more accurate method will produce a tighter range. That is, if a confidence interval of Method A is (150, 170) and that of Method B is (140, 180), it is likely that ______ _ is more accurate. 

Method A

How is an error calculated?  

Actual - Forecast 

If BIAS of a certain method is 1.5, the method (under-/over-) forecasts

under

If BIAS is 2, and forecast of Q2, 2021 is 100, the unbiased forecast for Q2, 2021 is ___. 

102 

Method A has BIAS of 2, and Method B has BIAS of 1. Therefore, Method B is more accurate. (True/False/Uncertain)

Uncertain (Need to use MAD, MAPE, or RMSE) 

MAD of Method A is 1.5 and that of Method B is 2. Which method is more accurate? 

Method A. 

MAD of Method C is 1.5 and RMSE of Method D is 0.9. Which method is more accurate?  \n

Cannot tell. MAD of Method A should be compared with MAD of Method B or RMSE of Method A should be compared with RMSE of Method B. 

If a confidence interval for Sales in Q3, 2021 is ($300,000, $350,000), the true sales in Q3, 2021 can be as big as ____. 

$350,000 

For a trendy dataset, you can use

**double exponential smoothing** and **regression**

When is regression used? 

When the data shows a trend.  

Can an exponential smoothing method be used for a trendy data?  \n  

yes

What are the three regression methods covered in the course?  \n

Linear, exponential, and logarithmic. 

Can a forecast for the first period in the dataset be made by a regression method? 

yes

Linear regression is used when

a trend in the data is relatively a straight line

regression steps

1. plot the data using a scatterplot
2. get the regression equation
3. make forecasts using the equation
4. calculate the performance measures
5. calculate the confidence intervals

A linear regression equation can be written as 

**Y = Coefficient*X + Intercept;** where X is typically time (such as month, quarter, or year) and Y is a variable you wish 

to predict (such as sales or demand). 

**Demand = 1.3939*Week + 47.333; what does each number represent?**

* Y = Demand 
* X = Week 
* X-coefficient = 1.3939 
* Intercept = 47.333 

In linear regression, an **X-coefficient (or simply coefficient or slope) represents the change in Y when X increases by**

1

What is the value of X-coefficient?   \n         Demand =  100 + 2 \* Month 

2

Regression equation: Sales (in $) = 20\*Month + ▢ 

 


2. If month changes from 10 to 11, Sales will (increase or decrease) by ____. 
3. If month changes from 20 to 25, Sales will (increase or decrease) by ____. 
4. If month changes from 20 to 17, Sales will (increase or decrease) by ____. 
5. If Sales in month 9 is $200, Sales in month 12 will be $____. 

1. Increase, 20 
2. Increase, 100 ( = 20 \* 5) 
3. Decrease, 60 (= 20 \* 3) 
4. 260 (Since the time increases by 3, sales will increase by 60. Therefore, the sales in month 12 will be greater than the sales in month 9 by 60.) 

Regression equation: Sales (in $) = -20\*Month + ▢ 

 


6. If month changes from 10 to 11, Sales will (increase or decrease) by ____. 
7. If month changes from 20 to 25, Sales will (increase or decrease) by ____. 
8. If month changes from 20 to 17, Sales will (increase or decrease) by ____. 
9. If Sales in month 9 is $200, Sales in month 12 will be $____. 

1. Decrease, 20 
2. Decrease, 100 
3. Increase, 60 
4. 140 

Exponential regression is used if a trend line in the data becomes

more vertical when increasing or flatter when decreasing as the time goes by.  

example of exponential regression formula

=47.685\**exp(0.0254**A2) **note that “e” changes to exp and you use * for the multiplacation**

An exponential regression equation can be written by 

**Y = Intercept*exp(Coefficient*X),** 

 

where X is typically time (such as month, quarter, or year) and Y is a variable you wish to predict (such as sales or demand). 

what does each part of **Demand = 47.685*exp(0.0254*week).**  mean?

* Y = Demand 
* X = Week 
* X-coefficient = 0.0254 
* Intercept = 47.685 

 

In exponential regression, an **X-coefficient (or simply coefficient) represents**

**the** __**approximate**__ **% change in Y when X increases by 1 if the coefficient is positive**.  

**Demand = 47.685*exp(0.0254*week).** ; what does the 0.0254 represent?

**the approximate % change in Demand when Week increases by 1**. That is, for each week, the demand increases by around 2.5% (0.0254). The increase % in two weeks is NOT 5%. The correct calculation is (1+0.0254)² - 1 = 0.0514 = 5.14%; The increase % in three weeks is then 7.82% (=(1+0.0254)³ - 1 = 0.0782); and so on.   

(exp regression) If the coefficient is negative, demand

decreases; For example, if the coefficient is -0.05, it means demand decreases by around 5% each week. The decrease in two weeks is -9.75% (=(1-0.05)² - 1 = -0.0975); The increase in three weeks is -14.26% (=(1-0.05)³ - 1 = -1 -0.1426); and so on. 

Note that if the value of the coefficient is too big (>= 0.20) or too small (

not work. Therefore, you need to calculate the accurate percent change by  

\
ecofficient∗∆X−1,

 

where

∆X

is a change in X. For a unit change,

∆X

is 1

What is the value of X-coefficient?   \n         Demand =  100 \* exp(2 \* Month) 

2