# Forecasting: Weighted Moving Averages, MAD

Welcome to this Forecasting tutorial on Weighted

Moving Averages. We will be calculating Weighted Moving Averages.

We will also be comparing error measures using the Mean Absolute Deviation, MAD. We will be using these times series data from

7 weeks of sales. And we want to forecast sales using 4-week

weighted moving averages with weights 0.4, 0.3, 0.2, and 0.1.

In practice, the weighted moving average is usually employed when there is a need to place

more importance on some periods over others. In most cases, we place more importance on

more recent data. Therefore in this exercise, the 0.4 weight

will be placed on the most recent value, the 0.3 on the next most recent, and so on.

Let’s now calculate 4-week weighted moving averages using the given weights .4, .3, .2,

and .1. Since we’re computing 4-week averages, we

start by using data from the first 4 weeks to compute the moving average forecast for

week 5. So F5 (that is, forecast for week 5) equals

0.4 times 45 (notice that 45 is the most recent value)

+ .3 times 40 (the next most recent value) + .2 times 44 + .1 times 39 which gives 42.7.

For week 6, the weighted moving average is F6 which equals 0.4(38) + 0.3(45) + 0.2(40) + 0.1(44) which gives 41.1. For week 7, the weighted moving average is

0.4(43) + 0.3(38) + 0.2(45) + 0.1(40) which gives 41.6.

And the forecast for week 8 is 0.4(39) + 0.3(43) + 0.2(38) + 0.1(45) which

gives 40.6. Next we calculate the Mean Absolute Deviation

for this model. First we calculate the absolute errors. That

is, the positive difference between the actual and forecast values and then average them.

There are no errors for weeks 1 to 4 because there are no forecasts.

For week 5, the absolute error is 4.7. For week 6, it is is 1.9.

For week 7, it is 2.6. The mean absolute deviation MAD is the average

of these errors which gives 3.07. Now, note that in this first example, the

weights .4, .3, .2, and .1 added up to 1. Let’s look at the next example where the

weights do not add up to 1. Forecast sales using 2-week weighted moving

averages with weights 3 and 2. In this example we are calculating 2-week

moving averages where the weights 3 and 2 add up to 5, and not to 1.

So in calculating the weighted moving averages, we multiply the sales values by the weights

as we did before, but in this case, we also divide by the total weight which is 5.

And so the forecast for week 3, F3 is 3(44) + 2(39) divided by 5 which gives 42.

For week 4, it is 3(40) + 2(44) divided by 5 and that gives 41.6.

For week 5, it is 43, It is 40.8 for week 6,

And for week 7 it is 41 And finally for week 8, it is 40.6

Next we calculate the mean absolute deviation. The absolute forecast error for week 3 is

the absolute value of 40 – 42 which is 2. For week 4 it is 3.4

For week 5 it is 5 For week 6 it is 2.2

And for week 7 it is 2. On averaging these 5 values, we obtain a mean

absolute deviation value of 2.92. Now let’s compare the error measures. The MAD was 3.07 using the 4-week moving average

method with weights .4, .3, .2, and .1. And the MAD was 2.92 using the 2-week weighted

moving average with weights 3 and 2. Since the MAD is an error measure, smaller

MADs produce better smoothing of the data. Therefore, using MAD, the 2-week weighted

average method produced a better forecast. Please leave your question or comment below.

Thanks for watching.

well explained! thank you

you are good

Joshua you are the man

Thank You.

good job

In 2-week WMA case, weight 3 and 2, are they just random number? and how to get the optimal weights? thanks

If there three weights in question but two of them are given.

How can I calculate the third weight, since it wasn't given. Thanks

josh that's cool thanks

Nice one.

kindly solve this Ques ..it's taken from one of the prestigious competitive exam of India..so the Ques Is- given the numbers 2,6,1,5,3,7,2. if the weights used are 1,4,1 .then weighted moving average of order 3 are given by?.

Man,

during 3:42, I think that something went wrong. So, for week 5 we should have to calculate (3*45+2*40)/5. 2*40 not 44. Because as seen all other calculations we have done it the first 2 CONSEQUENCE numbers from back to front.

nice one keep it up

Very incredible, wish you include more topic in that video lecture

if i increase number of weeks then error will decrease or increase. if error is increase as shown in ur example that 2wma give better smoothing than 4 wma then it means as number of periods increases the smoothing error get increased.

ur great.thanks a lot . awesome explanation

so finally there are 2 types of method if we got value 1 by calculating all given weight value so we have to have solve from 1st method if we are getting another value like 5 or 7 or 10 by calcuting so we have to do by the second method

great help … thank you

Very helpful, thank you.

understandable

his accent sounds Nigerian

When calculating MAD I thought you would divide by n-1 so we would divide by 4 and not 5 ?

thank you for this amazing explanations 👌

can i forecast week 9?

I don't know who you are, I don't know what you want. If you want ransom, I can tell you I don't have money. But what I do have are a very particular skills I'm working on. Skills I am acquiring taking this QMB course. Skills that make me not a nightmare for people like you. Thank you for your videos. You have saved my ass numerous times.

Can we using the method for seasonal data where the irregularity can be extreme? For example, can we know that next week the sales would be 60, which is very different than the rest of your data?

Thank you !

thanks. This video is great!

forecast sounds like fuckass :3

Hello.. The video is great explained very clearly

But I had a doubt, when "we assume the weights of different values the sum of their weights should be equal to 1", Here It is satisfied for 4week but not in case of 2week??

You are a better Professor than MY professor !!!! more clear and easy to understand!!! 100% GOOD for international students!

Man, good job. It was helpful.

Do you have examples on Moving average ?

hi joshua

could you further evaluate for Normalised weighted Root Mean Squared logarithmatic Error,please

Very helpful

coool

How to find exp entail smoothing regression analysis, Markov chain, simulation. Thank you

How do you determine the weight values – .4, .3 etc? Or are they just a given?

Hello Joshua,I would like to thank you for wonderful explanation.i have a question will the smaller value of m will give good forecast if so then how.

well explained and very helpful, Thank you so much Joshua

can u explain decomposition on your nex video

Well Explained, if i have the Data and i should put the weight values how i can calculate them !

i just have Data for sales last year and want to use this method it's applicable and how !

thank you very much for your support

thanks! i Got great ideas for this videos!

So what happens to the first 4 weeks that are empty? Where do we get that data from?

good job @joshua

Thanks for this simple and straightforward explanation.

I have a question on when do we use MSE vs MAE for error calculation

Very good video thank you

Great vid. Thank you so much!

How do you differentiate Mean absolute deviation vs Median absolute deviation which is also short for MAD

Given the following data, use exponential smoothing with α = 0.2 to develop a demand forecast for period 7. (Forecast for Period 1=10).

# In Python

#Weighted Moving Average 2WMA

sales = [39, 44, 40, 45, 38, 43, 39]

calc = lambda x: 0 if x == 0 else (sales[x] * 3 + sales[x-1] * 2)/5

forecast = [ calc(x) for x in range(0, len(sales) ) ]

print(forecast)

#Weighted Moving Average 4WMA

weight = [0.4, 0.3, 0.2, 0.1]

sales = [39, 44, 40, 45, 38, 43, 39]

calc = lambda x: 0 if x < len(weight) else sales[x-1]*weight[0] + sales[x-2]*weight[1] + sales[x-3]*weight[2] + sales[x-4]*weight[3]

forecast = [ calc(x) for x in range(0, len(sales) ) ]

print(forecast)

what if the ( 4 weeks ) is not given, the question only says find the forecast for a specific month? how can i solve ?

What if the sum of weights is less than 1?

How did u get the weights

My favorite YouTube sir

Hello! I got a question, I was reading about this method, and I saw that all the weights must be equal to 1, I'm a bit confused why did you choose weight 5 on the second example.

Nice work nigga

Very good explanation, thanks

Thank you! I was so confused by this in my textbook. You broke it down to where I can understand the material!

Is Moving average a suitable forecasting tool for short term forecasting. Please recommend

Wonderful

How can you calculate the sales for week 9 and 10.

Good explain

Week 5th 4WMA is 38.8

Thank you Sir

Please Josh how would interpret the 2.92 result?

how do we choose the weights while calculating forecasts?

🙏

Your videos are amazing and really easy to understand, do you have anything about Simple Linear Regression?

Fuck our sales?

thank you

SMOOTH

how to decide of their weights ??