WEBVTT
00:19.060 --> 00:25.340
so welcome back in the previous session we
were discussing about time series analysis
00:25.340 --> 00:32.580
and we discussed one of the simplest method
of time series that is moving average methods
00:32.580 --> 00:38.020
we discussed 2 methods of moving average the
simple moving average method and the weighted
00:38.020 --> 00:45.130
moving average method then we will also discuss
that limitations of this moving average methods
00:45.130 --> 00:51.450
are responsible for their limited application
into the real field of
00:51.450 --> 00:59.150
demand forecasting so we have improved method
which is known as exponential smoothing method
00:59.150 --> 01:05.170
we also discussed in our previous session
different types of models incorporating various
01:05.170 --> 01:12.130
types of trends and various types of seasonality
component in to the demand data and now we
01:12.130 --> 01:19.650
will move further to see how we can use the
exponential smoothing method for those different
01:19.650 --> 01:25.399
types of components in our demand data for
an example we have
01:25.399 --> 01:33.200
this simple data with us and we will go with
the method of exponential smoothing for this
01:33.200 --> 01:45.600
simple data now to understand the exponential
smoothing method whether we have only horizontal
01:45.600 --> 01:57.720
component in our demand data and there is
no other component in the data what is happening
01:57.720 --> 02:09.660
actually we are right now in the month of
January and February is approaching and in
02:09.660 --> 02:19.040
the month of January we have some level or
you can say the forecasted
02:19.040 --> 02:32.569
demand at on the basis of their forecast you
are doing the forecast for the February now
02:32.569 --> 02:39.000
in the forecast of February there will be
some errors and the actual demand will be
02:39.000 --> 02:50.950
dt now on the basis of this actual demand
of for February we will determined the level
02:50.950 --> 03:03.490
of February and this level of February is
the forecast of march so this is how the system
03:03.490 --> 03:12.550
will work now it is up to us that how much
uncertainties how much variations of a particular
03:12.550 --> 03:15.819
period we want to include
03:15.819 --> 03:23.290
in getting the forecast or the next period
and therefore if we see that there are certain
03:23.290 --> 03:29.240
changes in the external environment which
are at permanent nature we will incorporate
03:29.240 --> 03:35.180
more deviations in to our forecast and if
you see that there are certain temporary changes
03:35.180 --> 03:40.829
in the forecast then we will not incorporate
those changes in to the forecasting model
03:40.829 --> 03:48.989
and therefore this exponential smoothing method
gives us that flexibility that how much variations
03:48.989 --> 03:49.989
you
03:49.989 --> 03:58.290
want to include into the forecasting method
actually as we have discussed in last sessions
03:58.290 --> 04:04.340
that we have 2 components of forecast one
is level and another is the random variation
04:04.340 --> 04:11.530
so basic exponential method we are only interested
in determining the level component and the
04:11.530 --> 04:19.530
random component cannot be determined in viable
mathematical model so whatever is the level
04:19.530 --> 04:25.460
of the current period that is actually the
forecast for the next period? so in the basic
04:25.460 --> 04:33.060
exponential method as i mentioned that the
level of February is the forecast of the march
04:33.060 --> 04:45.039
so if i say if i represent label wise st the
current level i am representing st for this
04:45.039 --> 04:53.220
current level is actually the forecast for
the next period this is the forecast for the
04:53.220 --> 05:09.040
next period so now how do we determined the
current level that is the issue because if
05:09.040 --> 05:17.200
i pick a point in the current level that is
the forecast for the next period now the current
05:17.200 --> 05:25.660
level actually when i am taking this exponential
smoothing method so what i am trying to do
05:25.660 --> 05:32.849
that i will take in to account some of the
fluctuations of my the demand and for that
05:32.849 --> 05:42.889
purpose this is the current level and therefore
st-1 represents the previous base previous
05:42.889 --> 05:56.139
level and some of the fluctuations of my current
period i will like to incorporate and if this
05:56.139 --> 06:09.470
is the new demand - old base this becomes
my expression to calculate my updated base
06:09.470 --> 06:21.520
value or which i can also write as alpha x
dt-st-1 st-1
06:21.520 --> 06:38.320
or you can write it as alpha dt+1-alpha x
st-1 so this becomes the expression for my
06:38.320 --> 06:50.090
new base and now let us see that how do we
use this for our this type of data this data
06:50.090 --> 07:00.900
is there and let us try to use this formula
in this data here we have a data of actual
07:00.900 --> 07:15.759
demand for the first quarter of 2017 as 41000
so my current dt is 41000 the forecast i am
07:15.759 --> 07:23.500
assuming the forecast i am assuming for this
period where i was in the fourth quarter of
07:23.500 --> 07:25.669
2016 i did a
07:25.669 --> 07:39.610
forecast of 40000 for the first quarter of
2017 so let us say my st-1 is 40000 so now
07:39.610 --> 07:46.730
if i determined if i determine the base for
this period if i determine the base for this
07:46.730 --> 07:54.599
period if i determine the s1 2017 that is
actually the forecast for second quarter of
07:54.599 --> 08:04.150
2017 and be please into sure that i am not
taking consideration any kind of trans speciality
08:04.150 --> 08:12.470
in this data though this data exhibits some
kind of seasonalities but for the say for
08:12.470 --> 08:14.849
example i just considering that
08:14.849 --> 08:29.879
seasonality in to this data right now so now
i am determining s1 2017 which i is if i go
08:29.879 --> 08:49.860
by this expressions is alpha x dt dt is d
of first of 2017+1-alpha x st-1 that s of
08:49.860 --> 09:03.440
fourth of 2016 so if i go with this expression
i can calculate s1 2017 and s1 2017 is nothing
09:03.440 --> 09:12.480
but the forecast for the second period of
2017 so i get the forecast of second quarter
09:12.480 --> 09:23.079
of 2017 using this method now here the importance
is that what should be the value of this alpha
09:23.079 --> 09:24.079
what should be the value of
09:24.079 --> 09:33.120
this alpha theoretically speaking the value
of alpha can lie between 0 to 1 value of alpha
09:33.120 --> 09:41.250
can lie between 0 to 1 but practically the
common values of alpha which we used are from
09:41.250 --> 09:48.490
point 05 to point 30 these are the common
values of alpha point 05 to point 30 but it
09:48.490 --> 09:56.470
can be zero or it can 1 also now the meaning
of taking different value of alpha let us
09:56.470 --> 10:04.430
say if i take alpha equals to point 1 if i
take alpha equals to point 1 what does it
10:04.430 --> 10:06.720
mean if i take alpha equals to
10:06.720 --> 10:18.170
point 1the meaning of this alpha is that i
am taking only 10 % i am taking only 10% of
10:18.170 --> 10:25.930
my current demand i am taking only 10% of
my current demand and i am discounting 90%
10:25.930 --> 10:34.070
deviations i am discounting 90% deviations
and i am 90% of my previous base so that is
10:34.070 --> 10:41.760
the meaning of alpha equals to point 1 this
means that a smaller values of alpha is also
10:41.760 --> 10:49.340
means that the smaller values of alpha has
more smoothening effect if you have a smaller
10:49.340 --> 10:50.340
value of alpha
10:50.340 --> 10:57.740
it gives to more smoothening effect and larger
values of alpha larger values of alpha should
10:57.740 --> 11:03.960
only be taken in that case when you have a
shifting base when you feel that there is
11:03.960 --> 11:09.630
a change which is of permanent nature and
you want to improve the change in your forecasting
11:09.630 --> 11:15.589
model then you should go for higher values
of alpha for an example as we have in discussed
11:15.589 --> 11:21.570
in previous session also that when a new pay
commission is coming and purchasing power
11:21.570 --> 11:22.570
of
11:22.570 --> 11:27.019
people are increasing so this is the kind
of permanent kind of change and as a result
11:27.019 --> 11:33.110
of permanent changing you have purchasing
power your value of alpha met permanently
11:33.110 --> 11:39.700
shifted so in that case you can go for higher
values of alpha and when you take lower value
11:39.700 --> 11:47.139
of alpha you are having more smothering effect
now if you take for an example two extreme
11:47.139 --> 11:54.480
cases you take extreme cases when alpha is
equals to 0 and alpha equals to 1 so if you
11:54.480 --> 11:55.480
substitute in this
11:55.480 --> 12:05.160
equation in this case where alpha equals to
0 so it means your current base is equals
12:05.160 --> 12:13.790
to old base the meaning is that you do not
want to include any deviation of the current
12:13.790 --> 12:24.279
period in to your current base like the issue
of a smog during October and November an NCR
12:24.279 --> 12:30.709
area that is a temporary type of phenomena
so because of that whatever fluctuations in
12:30.709 --> 12:31.709
demand has taken
12:31.709 --> 12:37.449
place you do not want include the fluctuations
permanently in to your model and as a result
12:37.449 --> 12:42.170
of that you will take the small values of
alpha and maybe you can take alpha equals
12:42.170 --> 12:52.470
to 0 in some cases then alpha equals to 1
this will lead alpha equals to 1 will lead
12:52.470 --> 13:00.410
to st = dt now st equals to dt in this particular
case you see that you have totally shifted
13:00.410 --> 13:07.519
your base you have taken a new base a new
demand is your new base so you do not want
13:07.519 --> 13:09.930
to take your old base at
13:09.930 --> 13:17.440
all into your consideration so it is a jumping
base type of scenario and maybe in case of
13:17.440 --> 13:23.610
pay commissions may be in case of rehabilitizations
large level of rehabilitation or something
13:23.610 --> 13:29.779
of that is all whenever happens so you can
have every high value of alpha so these are
13:29.779 --> 13:42.399
the extreme cases but normally alpha lies
normally alpha lies between 0 05 to 0 30 so
13:42.399 --> 13:53.089
0 1 0 2 0 25 0 15 these are very popular values
of alpha and on the basis of that you can
13:53.089 --> 13:54.089
do this
13:54.089 --> 14:01.410
calculation and you can get the new base for
this period of 201 and that will automatically
14:01.410 --> 14:07.920
become the forecast for the next period so
this is our simple method of basic exponential
14:07.920 --> 14:15.339
method now as we discussed in the case of
moving average method for better forecast
14:15.339 --> 14:21.600
you need to have long historical data now
that requirement is reduced here you only
14:21.600 --> 14:30.430
need data you do not require this long data
with you you only require data of just last
14:30.430 --> 14:31.730
2 periods and that
14:31.730 --> 14:39.709
current data helps you in getting the forecast
so you are getting forecast with less data
14:39.709 --> 14:47.490
and which is more accurate which is more adoptive
which is more you can say customised as per
14:47.490 --> 14:54.949
the situation whichever is happening in the
market now once we have understood the simplest
14:54.949 --> 15:02.779
form of exponential smoothing method now we
go to different form of smoothing method where
15:02.779 --> 15:10.160
we will see that how you can customise your
model to suit the requirement of trend
15:10.160 --> 15:17.339
and seasonality component in to the demand
data and here we are using only single smothering
15:17.339 --> 15:23.640
constant alpha in those cases you may use
more than one smothering constant because
15:23.640 --> 15:31.070
this smothering constant is only smothering
the fluctuations of your level data but when
15:31.070 --> 15:37.870
you have trend so you require one smothering
constant to smoothen the fluctuations of your
15:37.870 --> 15:43.690
base data and one to smoothen the fluctuations
of your trend data when you have
15:43.690 --> 15:49.850
seasonality in to your demand data then you
require 1 smothering constant to smoothen
15:49.850 --> 15:55.550
the fluctuations of your seasonality component
also so depending upon the type of the characteristic
15:55.550 --> 16:01.320
of your demand data you will require as many
number of a smothering constant so now let
16:01.320 --> 16:15.671
us move to second of smothering method where
we have the trend also in our data now trend
16:15.671 --> 16:28.220
can also be of two types one is linear trend
or additive trend
16:28.220 --> 16:36.139
and the second is ratio trend or multiplicative
trend these are the two types of trends which
16:36.139 --> 16:47.740
are possible the meaning i show you if i have
the historical data with being in that case
16:47.740 --> 16:56.209
you can see this for this is period this is
column a this is column b and let me have
16:56.209 --> 17:11.940
the data for some past periods now here i
am starting with 20 22 26 27 29 31 like that
17:11.940 --> 17:30.501
and in this case we have 20 24 29 34 39 44
so you will see that in both these cases you
17:30.501 --> 17:32.560
have a trend but here in
17:32.560 --> 17:39.420
the first case here the demand is increased
by two units then by 4 then by 1 then by 2
17:39.420 --> 17:45.660
by 2 so you are having a kind of additive
some constant figure or a fluctuating figure
17:45.660 --> 17:52.580
is added in to the demand of previous median
so it is more like a linear trend some almost
17:52.580 --> 18:00.950
constant thing is being added here demand
increase by 4 then 5 then 5 then 5 then again
18:00.950 --> 18:10.330
5 so here the demand is increased in a more
ratio type of field that it is multiply to
18:10.330 --> 18:12.600
the previous periods so finally
18:12.600 --> 18:20.140
from 20 to 44 it has just gambled so that
it is kind of ratio you are getting over period
18:20.140 --> 18:26.430
of time so it is multiplying effect and here
it is additive effect so depending upon what
18:26.430 --> 18:33.740
type of trend you have you can suit make
changes in your model which we are going to
18:33.740 --> 18:42.150
discuss now going for there into the calculation
part of this since we have in our component
18:42.150 --> 18:52.700
trend also and already that linear part is
very much present so two soles type of cases
18:52.700 --> 18:53.700
let
18:53.700 --> 18:58.170
us see if i take the first data with us first
data with us if i take the first data with
18:58.170 --> 19:12.180
us so you have this trend component initially
there is no trend and then you have the trend
19:12.180 --> 19:23.420
of +2 +4 you have +1 +2 and you have again
+2 so these are the trend data which you have
19:23.420 --> 19:38.780
when we are the developing the forecast in
this particular case so now the f2 107 will
19:38.780 --> 19:49.950
be the updated base of the current period
that is s1 2017 + the updated trend of current
19:49.950 --> 19:52.830
period that will make the
19:52.830 --> 19:59.300
forecast for the next period so i need to
make updated base for the current period and
19:59.300 --> 20:04.840
i have to make the updated trend of the current
period and when i add both this things i will
20:04.840 --> 20:10.030
get the forecast for the next period so if
i generalised this relationship so i will
20:10.030 --> 20:22.370
say that ft 1 is nothing but st + tt that
is the forecast for the next period is the
20:22.370 --> 20:28.400
updated base for the current period and the
updated trend for the current period sometime
20:28.400 --> 20:33.430
it is possible but in case of trend data i
will
20:33.430 --> 20:41.690
like to forecast for two three periods ahead
from the current period so in that case if
20:41.690 --> 20:50.650
i want to forecast for m period ahead so in
that case this value of trend is consider
20:50.650 --> 20:59.080
as constant value and then i will do like
this i am taking a particular case of linear
20:59.080 --> 21:06.160
trend that is why i am just adding up these
things if it is a ratio trend then the multiplying
21:06.160 --> 21:12.910
effect will come into picture accordingly
now let us see how do we do that so first
21:12.910 --> 21:18.480
we need to calculate
21:18.480 --> 21:26.030
the updated base and then with the help of
updated base we will determine the updated
21:26.030 --> 21:41.630
trend also so the updated base st we already
know how we determine the alpha dt+1 minus
21:41.630 --> 21:52.480
alpha st minus 1 that is in the simple exponential
method now with the trend it will become alpha
21:52.480 --> 22:06.710
dt+1 minus alpha into st minus 1+ tt minus
1 that is the previous forecast and that is
22:06.710 --> 22:15.470
the current demand and now i also need to
do the updation in the trend data and for
22:15.470 --> 22:16.780
that purpose i
22:16.780 --> 22:27.380
need to calculate the tt and tt is nothing
but the difference of my current base and
22:27.380 --> 22:44.340
the previous base so tt is st -st -1 and this
is beta+ 1 minus beta because i am taking
22:44.340 --> 22:52.490
the second sufficient of a smothering of beta
which is for the trend purpose 1 minus beta
22:52.490 --> 23:02.910
into tt minus 1 so this is the updated trend
value and then finally the forecast ft 1will
23:02.910 --> 23:16.020
be st +tt so this is how we will do the forecast
when trend is available the calculation of
23:16.020 --> 23:19.780
linear trend the additive trend is then
23:19.780 --> 23:27.650
st-st-1 and if it is to be multiple trend
if it is to b e ratio trend it will be st
23:27.650 --> 23:36.900
upon st-1 please be careful that if it is
a ratio trend it will be st upon st-1 and
23:36.900 --> 23:46.470
since i am considering the case of linear
trend it is st-st-1 and this is the old trend
23:46.470 --> 23:54.640
then i update the st + dt and i get the forecast
for the next period and if i want to use this
23:54.640 --> 24:00.990
trend value for getting the forecast for 2
3 4 periods ahead then this expression will
24:00.990 --> 24:06.800
work at ft + mt and now this model is ready
and now i
24:06.800 --> 24:16.340
can use this model for getting my values for
next period here as i discuss about alpha
24:16.340 --> 24:23.900
the same discussion apply for the beta also
the values of beta also varies between 0 to
24:23.900 --> 24:33.160
1 the popular values of beta are from 0 05
to 0 20 because the fluctuations in trend
24:33.160 --> 24:41.880
are not much so we use lesser values of beta
and we want to discount maximum fluctuations
24:41.880 --> 24:48.920
of trend values and it is very rare it is
very rare that you use very extreme values
24:48.920 --> 24:50.930
of beta so normally beta
24:50.930 --> 24:57.890
values are less than alpha values but since
both these are smothering constant so academically
24:57.890 --> 25:05.670
theoretically their values can vary 0 to 1
so beta can also 0 to 1 buth the popular
25:05.670 --> 25:14.810
values are from point 05 to point 20 so now
if i apply this equation these two equations
25:14.810 --> 25:25.590
on this piece of data so you can see that
for seventh period for f7 i need to apply
25:25.590 --> 25:37.910
s6+t6 i need to calculate s6 and t6 and with
the help of s6 and t6 i can directly get the
25:37.910 --> 25:41.880
value of f7 and s6 will come
25:41.880 --> 25:51.490
from this equation for s6 i require s5 and
for t6 i require t5 and when i use these expressions
25:51.490 --> 26:00.720
i can directly get the values of my required
uhhh forecast for the next period then in
26:00.720 --> 26:08.060
case of ratio the only thing which i just
told you this value will change this will
26:08.060 --> 26:23.100
become st upon st-1 in case of ratio this
calculation will change to st in to tt and
26:23.100 --> 26:33.290
this calculation will also change to st-1
in to tt-1 rest of the model will remain as
26:33.290 --> 26:37.710
it is there will not be any change in any
other
26:37.710 --> 26:44.900
component with this model so with this you
can handle both this types of trend you can
26:44.900 --> 26:53.390
handle the linear trend you can handle the
ratio trend but now just by seeing nobody
26:53.390 --> 27:03.570
can give you the answer whether this a has
linear trend or whether b has this linear
27:03.570 --> 27:12.080
trend you were thinking your mind that how
do you can say that here you have 20 to 31
27:12.080 --> 27:18.400
you can have a ratio of one point 5 something
like that here you are moving from 20 to 44
27:18.400 --> 27:19.400
you have ratio of
27:19.400 --> 27:26.780
somewhere around 2 point 2 so why cannot we
apply a ratio model in this case or why cannot
27:26.780 --> 27:34.470
we apply a linear model in this second case
because each time 24 to 29 29 to 34 34 to
27:34.470 --> 27:45.130
39 39 to 44 demand is increasing by very constant
value 5 so why cannot we apply a linear model
27:45.130 --> 27:51.340
in second case and why cannot we apply a ratio
model in the first case practically speaking
27:51.340 --> 27:58.090
theoretically speaking i do not have any answer
for that only my model will tell the answer
27:58.090 --> 28:06.980
only my model will tell the answer model means
whether i am calculating using st-st-1or st
28:06.980 --> 28:19.100
upon st-1 and after determining the forecast
i will calculate the forecasting errors and
28:19.100 --> 28:25.720
whichever model whichever model will give
me minimum forecasting errors whichever model
28:25.720 --> 28:32.740
will give me minimum forecasting error that
is suitable model for my particular case so
28:32.740 --> 28:40.170
now our next topic of discussion is the forecasting
error so that we can understand the
28:40.170 --> 28:45.300
meaning of selection of different type of
models without understanding the forecasting
28:45.300 --> 28:51.580
model it is almost impossible to select the
right kind of model because once you select
28:51.580 --> 28:58.530
the model the appropriateness of that model
will also depend on proper selection of values
28:58.530 --> 29:07.150
of alpha and beta so all these things are
very much you can say in a family the kind
29:07.150 --> 29:13.970
of model the selection of alpha and beta and
these models should produce minimum forecasting
29:13.970 --> 29:15.320
error so in our next
29:15.320 --> 29:23.730
class we will discuss more about forecasting
error and then we will take a case of third
29:23.730 --> 29:28.750
type of component that is the seasonal component
in our demand data and how to handle that
29:28.750 --> 29:35.050
seasonal component in the data so that case
will also take and this data will be useful
29:35.050 --> 29:40.820
in that case also the because here you can
see we have the seasonality in our demand
29:40.820 --> 29:46.460
data present so how to handle the seasonal
component in the demand data and then we can
29:46.460 --> 29:47.980
move the most
29:47.980 --> 29:53.270
complex case where we have seasonality as
well as trend both these things in our demand
29:53.270 --> 29:58.730
data so how to handle such type of cases that
we will see in our next lecture thank you
29:58.730 --> 29:59.190
very much