1
00:00:19,060 --> 00:00:31,490
Welcome to the fourth lecture on the subject
Economics Management and Entrepreneurship.
2
00:00:31,490 --> 00:00:40,840
If you recall in the last 3 lectures we were
talking about economics in particular managerial
3
00:00:40,840 --> 00:00:54,470
economics and in which we started discussing
about demand and supply of products and services
4
00:00:54,470 --> 00:01:04,750
and how in the market an equilibrium condition
can exist and how equilibrium demand and equilibrium
5
00:01:04,750 --> 00:01:10,330
supply can be estimated.
6
00:01:10,330 --> 00:01:20,530
In the last lecture we talked about demand
elasticity, how demand changes with different
7
00:01:20,530 --> 00:01:30,229
factors and today we are going to discuss
about demand forecasting.
8
00:01:30,229 --> 00:01:39,560
Demand forecasting is very important, particularly
for an entrepreneur.
9
00:01:39,560 --> 00:01:48,229
To start with let me clarify that demand is
not same as sales.
10
00:01:48,229 --> 00:02:00,399
Sales of an enterprise is the amount that
is delivered to the customers and the amount
11
00:02:00,399 --> 00:02:06,229
of money realized from the customers that
is the sales.
12
00:02:06,229 --> 00:02:17,440
Whereas demand is the potential demand for
the product in the market, therefore demand
13
00:02:17,440 --> 00:02:27,890
is always greater than or in the limit equal
to sales.
14
00:02:27,890 --> 00:02:31,860
Estimating demand is what is forecasting.
15
00:02:31,860 --> 00:02:43,260
Forecasting is basically estimating the future
value of the potential demand of your product
16
00:02:43,260 --> 00:02:48,810
or service that an enterprise offers.
17
00:02:48,810 --> 00:02:54,550
Anything that is to be estimated for the future
is difficult.
18
00:02:54,550 --> 00:03:03,690
In particular if there are large number of
factors, that influence the value of the potential
19
00:03:03,690 --> 00:03:05,470
demand.
20
00:03:05,470 --> 00:03:13,129
Therefore, it is not surprising that there
are a very large number of methods that have
21
00:03:13,129 --> 00:03:17,230
been provided in the literature.
22
00:03:17,230 --> 00:03:28,599
And being practiced by the enterprises, throughout
the world in making estimates of demand.
23
00:03:28,599 --> 00:03:42,459
Now, before I proceed further, let me say
that demand is always difficult to estimate,
24
00:03:42,459 --> 00:03:49,909
because it is very uncertain and because there
are large number of factors as I said, but
25
00:03:49,909 --> 00:03:56,939
whatever may be the accuracy of the demand,
a decision has to be taken because it will
26
00:03:56,939 --> 00:04:03,689
be useful in many ways for many purposes.
27
00:04:03,689 --> 00:04:13,510
So in today's lecture we shall basically study
different types of methods that are used popularly
28
00:04:13,510 --> 00:04:25,720
in academics and in practice and also say
how they are useful in decision making.
29
00:04:25,720 --> 00:04:38,650
So, in this lecture, we shall first of all
focus on uses of forecasts, methods of forecasting,
30
00:04:38,650 --> 00:04:50,210
and in particular, we shall discuss and highlight
certain aspects of qualitative, time series,
31
00:04:50,210 --> 00:04:54,620
and econometric methods.
32
00:04:54,620 --> 00:05:02,410
First, need for demand forecasting or uses
of demand forecasting.
33
00:05:02,410 --> 00:05:10,870
First thing for an entrepreneur particularly
the one who is starting an enterprise newly
34
00:05:10,870 --> 00:05:20,729
capacity planning is very important and for
that a long term projection of the demand
35
00:05:20,729 --> 00:05:32,069
is important and based on that, the capacity
of the company can be planned.
36
00:05:32,069 --> 00:05:41,250
Once capacity is planned, the actual production
plan will depend on the circum forecast.
37
00:05:41,250 --> 00:05:54,979
Also, how much to inventory to hold so that
no sale is lost, no demand is lost, forecast
38
00:05:54,979 --> 00:05:59,410
of demand is quite important.
39
00:05:59,410 --> 00:06:07,759
Once the production is planned, we would like
to also purchase the input materials and services
40
00:06:07,759 --> 00:06:17,410
to actually produce those goods so that we
will also depend on the forecast made.
41
00:06:17,410 --> 00:06:28,370
How many sales force to actually deploy so
that we can sell the amount that we produce
42
00:06:28,370 --> 00:06:35,389
is actually planning distribution network
to which market.
43
00:06:35,389 --> 00:06:43,550
And by which means, by deploying how many
sales persons, we will be able to sale our
44
00:06:43,550 --> 00:06:53,190
products will also depend on the demand forecast
that is made right in the beginning.
45
00:06:53,190 --> 00:07:02,240
Management of working capital to deploy resources
input material, the machines, the power that
46
00:07:02,240 --> 00:07:08,620
is required all that requires money and their
working capital.
47
00:07:08,620 --> 00:07:17,819
Once we know or we can make an estimate of
the demand, we can similarly make an estimate
48
00:07:17,819 --> 00:07:26,159
of the need for working capital to be able
to be sustain in the business.
49
00:07:26,159 --> 00:07:36,680
And finally if we know that our demand is
so much accordingly we can also decide on
50
00:07:36,680 --> 00:07:40,000
the prices that we shall charge for our product.
51
00:07:40,000 --> 00:07:49,740
Now these are only a few areas, which we mention
has the uses of forecasting.
52
00:07:49,740 --> 00:07:58,979
Basically, a forecast is an information for
decision making and decision making for capacity
53
00:07:58,979 --> 00:08:06,580
planning, for production planning, for inventory
building, for distribution etc.
54
00:08:06,580 --> 00:08:12,620
All these decision making requires an important
input of forecasting.
55
00:08:12,620 --> 00:08:20,430
Therefore forecast is important.
56
00:08:20,430 --> 00:08:24,169
Now there are different methods of demand
forecasting.
57
00:08:24,169 --> 00:08:37,440
We would like to categorize them in 3 groups:
Qualitative analysis and quantitative analysis.
58
00:08:37,440 --> 00:08:45,610
Quantitative analysis can be further divided,
subdivided as time series analysis and econometric
59
00:08:45,610 --> 00:08:47,170
models.
60
00:08:47,170 --> 00:08:57,100
Now, there can be different ways in which
the forecasts can be divided or grouped.
61
00:08:57,100 --> 00:09:04,300
This is one way in which I have grouped the
demand forecasting methods.
62
00:09:04,300 --> 00:09:14,300
First, let us talk about qualitative forecasting.
63
00:09:14,300 --> 00:09:23,110
In qualitative forecasting, normally we do
not deal with numbers.
64
00:09:23,110 --> 00:09:28,430
Quantitative forecasting uses numbers.
65
00:09:28,430 --> 00:09:38,820
Qualitative forecasting on the other hand
does not rely so much on or does not use numbers.
66
00:09:38,820 --> 00:09:48,320
We divide qualitative forecasting methods
into groups: Expert-opinion survey and consumer
67
00:09:48,320 --> 00:09:51,780
survey.
68
00:09:51,780 --> 00:10:03,950
Expert opinion survey can be further subdivided
into 3 individual items: Personal insights,
69
00:10:03,950 --> 00:10:13,250
panel consensus, and Delphi method, and the
consumer survey method can be divided as sample
70
00:10:13,250 --> 00:10:16,870
survey method and end-use method.
71
00:10:16,870 --> 00:10:26,200
Now let us study these 2 each one of these
in more detail.
72
00:10:26,200 --> 00:10:35,420
To start with we talk about the personal insight.
73
00:10:35,420 --> 00:10:46,290
Basically, it depends on an individual an
expert who is extremely wise, highly experienced,
74
00:10:46,290 --> 00:10:58,690
he has lot of ideas, and the person can make
a judicious estimate of the demand for the
75
00:10:58,690 --> 00:11:00,890
product in the market.
76
00:11:00,890 --> 00:11:13,779
So, naturally is very very difficult to get
hold of such a wise, knowledgeable, insightful,
77
00:11:13,779 --> 00:11:23,180
and experienced person to be able to make
a good estimate of demand.
78
00:11:23,180 --> 00:11:29,430
He can be totally incorrect or he can be totally
correct.
79
00:11:29,430 --> 00:11:40,130
It is very difficult to say to what extent
the experts estimate is going to be accurate.
80
00:11:40,130 --> 00:11:54,910
Therefore, in normal practice is to get a
panel of experts, a group of experts and try
81
00:11:54,910 --> 00:12:04,700
to have an interaction among the panel experts,
so that a consensus among them emerges.
82
00:12:04,700 --> 00:12:15,560
At that consensus would probably possibly
would be more accurate than an individual
83
00:12:15,560 --> 00:12:18,839
expertâ€™s opinion.
84
00:12:18,839 --> 00:12:31,100
Now, there are different ways by which the
panel of expertâ€™s ideas can be obtained
85
00:12:31,100 --> 00:12:37,470
and an interaction among them can be conducted.
86
00:12:37,470 --> 00:12:42,200
One is based on interview.
87
00:12:42,200 --> 00:12:50,990
Now if it is a personal interview, then naturally
no interaction is possible.
88
00:12:50,990 --> 00:12:58,440
Personal interview could be face-to-face interview
or it could be even a telephonic interview.
89
00:12:58,440 --> 00:13:10,940
Now in such cases, because there are more
than 1 expert, it is expected that different
90
00:13:10,940 --> 00:13:18,829
factors that one might overlook will surface
and the effect of those factors on the estimates
91
00:13:18,829 --> 00:13:26,339
of the demand can actually be understood,
estimated, and projected.
92
00:13:26,339 --> 00:13:33,459
Therefore it is expected that there is a greater
degree of confidence that we can have on the
93
00:13:33,459 --> 00:13:37,630
estimate made by this panel of experts.
94
00:13:37,630 --> 00:13:51,310
Now, sometimes the panels are brought to a
meeting, where
95
00:13:51,310 --> 00:13:53,470
its expert's opinion is collected.
96
00:13:53,470 --> 00:14:03,600
Now, the panel therefore, face each other
and interact among themselves face to face.
97
00:14:03,600 --> 00:14:15,320
In such a case, also a consensus can come,
but it can lead to a lot of difficulty.
98
00:14:15,320 --> 00:14:25,529
Particularly, if there is a senior person
who publically makes his or her opinion then
99
00:14:25,529 --> 00:14:31,190
it is difficult for him or her to retrace
it or to change it.
100
00:14:31,190 --> 00:14:40,450
Similarly, if a powerful personality holding
a senior position makes a statement is not
101
00:14:40,450 --> 00:14:49,300
impossible that the juniors will keep quite
although they do not really a quiet agree
102
00:14:49,300 --> 00:14:55,390
with the statements or opinion made by the
senior member.
103
00:14:55,390 --> 00:15:05,529
Like this, there are quite a lot of difficulties
if meetings of experts take place and through
104
00:15:05,529 --> 00:15:13,920
a meeting the estimates are made.
105
00:15:13,920 --> 00:15:20,160
Because of this difficulties there are various
other methods and in particular.
106
00:15:20,160 --> 00:15:32,130
A method that has emerged in the last few
years 2 to 3 decades in the Delphi technique.
107
00:15:32,130 --> 00:15:40,899
Delphi technique is basically a series of
questionnaire surveys among panel members
108
00:15:40,899 --> 00:15:47,569
not 1 questionnaire survey, but a series of
questionnaire surveys among the selected panel
109
00:15:47,569 --> 00:16:03,819
experts and the responses obtained in every
round from the experts are summarized and
110
00:16:03,819 --> 00:16:13,410
the summary response is sent back to each
individual member of the panel.
111
00:16:13,410 --> 00:16:26,600
So that he or she can actually change his
or her opinion on the basis of the group opinion
112
00:16:26,600 --> 00:16:35,009
that is available with him or her in the form
of summary response of the previous round.
113
00:16:35,009 --> 00:16:47,311
Normally, in the second round or in the third
round we have quantitative responses and in
114
00:16:47,311 --> 00:16:59,029
that case, what normally Delphi technique
does is to find out the median of the responses
115
00:16:59,029 --> 00:17:01,370
and the inter-quartile range.
116
00:17:01,370 --> 00:17:13,890
So median like mean is a measure of the central
tendency and inter-quartile range is like
117
00:17:13,890 --> 00:17:17,040
standard deviation.
118
00:17:17,040 --> 00:17:27,800
So when a summary response is fed back to
the members of the panel, the group response
119
00:17:27,800 --> 00:17:34,850
is made available to each one of them in the
form of the median value and the inter-quartile
120
00:17:34,850 --> 00:17:43,810
range value of the group responses and finally
the reduction in the inter-quartile range
121
00:17:43,810 --> 00:17:57,460
as the number of rounds progresses is a measure
of the extent to which consensus among the
122
00:17:57,460 --> 00:18:03,059
members of the panel takes place.
123
00:18:03,059 --> 00:18:05,950
This in short is the Delphi technique.
124
00:18:05,950 --> 00:18:17,040
It has the advantage that a senior member
of a panel cannot influence or buy as the
125
00:18:17,040 --> 00:18:19,780
opinion of a junior member.
126
00:18:19,780 --> 00:18:22,830
Yet they can have interaction.
127
00:18:22,830 --> 00:18:33,930
They have a chance to change their opinion,
because of the multiple rounds of questionnaire
128
00:18:33,930 --> 00:18:36,600
survey anonymity is maintained.
129
00:18:36,600 --> 00:18:44,680
Nobody knows who the other members are therefore
the estimates are unlikely to be biased.
130
00:18:44,680 --> 00:18:51,800
And now we take the case of the sample survey
method.
131
00:18:51,800 --> 00:19:04,080
This is a very popular method used by enterprises
to make forecast of demand.
132
00:19:04,080 --> 00:19:10,670
Here what is done is the number of potential
customers is first estimated.
133
00:19:10,670 --> 00:19:25,760
Let the number be N. Then, randomly a sample
of such potential customers is selected and
134
00:19:25,760 --> 00:19:40,830
let the size of these samples be n and then
through a method of interview or a questionnaire
135
00:19:40,830 --> 00:19:50,970
survey their individual requirements is obtained
to the survey method by meeting each one of
136
00:19:50,970 --> 00:19:52,730
them, by talking to each one of them.
137
00:19:52,730 --> 00:20:00,380
Either through telephonic interview, or by
sending questionnaire survey, or making face-to-face
138
00:20:00,380 --> 00:20:02,010
contacts.
139
00:20:02,010 --> 00:20:11,190
Then if there are n numbers of such customers
with whom contacts could be made and their
140
00:20:11,190 --> 00:20:21,890
individual requirements could be obtained,
then the average requirement is x1 plus x2
141
00:20:21,890 --> 00:20:25,690
etc plus xn/n.
142
00:20:25,690 --> 00:20:33,000
This is the average individual requirement
that multiplied by the total number of estimated
143
00:20:33,000 --> 00:20:40,570
potential customers N is taken as the market
demand.
144
00:20:40,570 --> 00:20:46,870
This is a very simple method, but this is
a very powerful method, because it directly
145
00:20:46,870 --> 00:21:03,180
asks the potential customers to talk about
their individual requirements.
146
00:21:03,180 --> 00:21:09,020
Now we go to the End-use method.
147
00:21:09,020 --> 00:21:17,510
Here, we include particularly the celebrated
input-output model of Leontief.
148
00:21:17,510 --> 00:21:24,660
It is useful in making consumption demand
projection of various industries at a national
149
00:21:24,660 --> 00:21:30,120
level and this is very useful for planning
at the national level.
150
00:21:30,120 --> 00:21:38,820
So, at the enterprise level, it is not so
much used, but at the national level, the
151
00:21:38,820 --> 00:21:43,640
input-output model is quite useful.
152
00:21:43,640 --> 00:21:49,950
We will just have 2 or 3 slides on what this
input-output model is.
153
00:21:49,950 --> 00:22:01,220
Let us first of all define Xi as the output
of industry i, Xic as the consumption demand
154
00:22:01,220 --> 00:22:14,800
of industry i. Xim as the amount of goods
imported by industry i, Xie as the amount
155
00:22:14,800 --> 00:22:27,750
of exports made by industry i, Xif as the
final consumption demand of industry I and
156
00:22:27,750 --> 00:22:38,140
aij is the fraction of output of industry
j consumed by industry i.
157
00:22:38,140 --> 00:22:46,810
Now from the above particularly these 4 things
Xif the final consumption demand of industry
158
00:22:46,810 --> 00:22:59,340
I equal to its own consumption plus imports
minus exports.
159
00:22:59,340 --> 00:23:01,210
This is the relationship therefore.
160
00:23:01,210 --> 00:23:05,310
Xif equal to Xic plus Xim minus Xie.
161
00:23:05,310 --> 00:23:20,400
Let us understand here we are trying to say
the consumption demand of industry 1 is its
162
00:23:20,400 --> 00:23:30,370
own consumption, final consumption plus the
amount of goods produced in different industries,
163
00:23:30,370 --> 00:23:39,180
a fraction of consumes for example steel industry
consumes some coal, some iron ore, and things
164
00:23:39,180 --> 00:23:40,850
of that type.
165
00:23:40,850 --> 00:23:48,620
So each one of them is an industry exclude
probably the coal industry iron ore X this
166
00:23:48,620 --> 00:23:57,980
industry, so a fraction of different industries
is consumed by steel industry and similarly
167
00:23:57,980 --> 00:24:04,900
coal industry consume something from other
industries so these are input output coefficients.
168
00:24:04,900 --> 00:24:08,690
a's are input output coefficients.
169
00:24:08,690 --> 00:24:18,160
So we have if there are n number of industries
we have n number of this equations and x1
170
00:24:18,160 --> 00:24:28,540
contains a11X1 and therefore it we take it
this side, it becomes 1 minus a11 into X1
171
00:24:28,540 --> 00:24:29,670
equal to this.
172
00:24:29,670 --> 00:24:41,310
So, therefore it can be shown that the final
consumption demand vector, Xf is I minus a
173
00:24:41,310 --> 00:24:43,930
inverse into x.
174
00:24:43,930 --> 00:24:49,560
X is this vector.
175
00:24:49,560 --> 00:24:56,980
Xf is the vector of final consumption demand
plus exports net of imports of various goods.
176
00:24:56,980 --> 00:25:04,610
I is the identity matrix containing once it
is diagonal 0 elsewhere.
177
00:25:04,610 --> 00:25:17,310
A is the matrix of input-output coefficients
a11, a12, an1, an2, ann.
178
00:25:17,310 --> 00:25:26,390
Now this model was used in many countries
including there for a very large number of
179
00:25:26,390 --> 00:25:27,910
years.
180
00:25:27,910 --> 00:25:33,840
Now we talk about time-series analysis.
181
00:25:33,840 --> 00:25:44,420
Time-series analysis we can broadly group
them under 3 headings: Trend analysis, regression
182
00:25:44,420 --> 00:25:49,010
method, and leading indicator method.
183
00:25:49,010 --> 00:25:55,800
Let us look at them one by one.
184
00:25:55,800 --> 00:26:01,500
What we mean by a time series basically.
185
00:26:01,500 --> 00:26:11,060
When we consider a time series basically,
we talk about only 1 variable, let us x.
186
00:26:11,060 --> 00:26:21,760
X1 at time 1, X2 at time 2, X3 at time 3,
etc.
187
00:26:21,760 --> 00:26:31,510
So this is called a discrete time series,
where our time T equal to 1 value of x is
188
00:26:31,510 --> 00:26:38,280
x1, at time T equal to 2 the value of x is
x2 and so on so forth.
189
00:26:38,280 --> 00:26:46,020
This is called a discrete time series.
190
00:26:46,020 --> 00:26:58,230
Normally, it is written as Xt t equals 1,
2.
191
00:26:58,230 --> 00:27:08,610
Now it is time series can have different components.
192
00:27:08,610 --> 00:27:23,370
It will have a component analysis, a trend,
a seasonality, a cyclicity, and random fluctuations.
193
00:27:23,370 --> 00:27:25,000
We can write it in this manner.
194
00:27:25,000 --> 00:27:30,600
We can show it in this manner in a graphical
form.
195
00:27:30,600 --> 00:27:34,171
So that this is time t and this is Xt.
196
00:27:34,171 --> 00:27:46,750
X versus t
can take different steps.
197
00:27:46,750 --> 00:27:57,030
Suppose, it is exactly constant it is same
at all times t, then we will say that this
198
00:27:57,030 --> 00:28:06,610
is the average value or a constant value,
but this hardly happens.
199
00:28:06,610 --> 00:28:18,740
X is something like the demand variable whose
forecast we will like to make
200
00:28:18,740 --> 00:28:26,440
and it is unlikely that it is constant at
least we shall expect that there will be certain
201
00:28:26,440 --> 00:28:30,760
random fluctuations around this constant value.
202
00:28:30,760 --> 00:28:45,100
So we might expect values such as this.
203
00:28:45,100 --> 00:28:51,840
So which means that there is an average value
and there is a random fluctuation or an error
204
00:28:51,840 --> 00:28:54,950
term.
205
00:28:54,950 --> 00:29:00,400
So this is what I am trying to say that this
is a case where there is an average, but this
206
00:29:00,400 --> 00:29:08,070
is a case where there is an average plus a
noise.
207
00:29:08,070 --> 00:29:31,790
Let us take another case.
208
00:29:31,790 --> 00:29:43,400
Now here is a case of Xt varying with t and
we can say that it has an average.
209
00:29:43,400 --> 00:29:51,990
The average at the trend and there is a random
fluctuation around it.
210
00:29:51,990 --> 00:30:05,520
So this is average plus there is a linear
trend in this case, plus error, random fluctuation
211
00:30:05,520 --> 00:30:10,050
or an error around it.
212
00:30:10,050 --> 00:30:16,770
So there are 3 components of a time series
present in Xt.
213
00:30:16,770 --> 00:30:48,950
Take up another case, where t, Xt shows now
if you look at this, it has an average as
214
00:30:48,950 --> 00:31:05,290
a trend and it is associated with a seasonality,
a perfect seasonality.
215
00:31:05,290 --> 00:31:18,130
So this has an average plus trend plus seasonality.
216
00:31:18,130 --> 00:31:25,210
Seasonal products like fans, air conditioners.
217
00:31:25,210 --> 00:31:37,280
We will so average trend and seasonality,
but it is unlikely that there is no random
218
00:31:37,280 --> 00:31:38,910
error present.
219
00:31:38,910 --> 00:32:05,600
So we might in fact come across cases where
it is something like this.
220
00:32:05,600 --> 00:32:13,970
Now this blue colour variation says that it
has all the components of average, trend,
221
00:32:13,970 --> 00:32:21,960
seasonality, and also it has an error term.
222
00:32:21,960 --> 00:32:30,660
So this is the fourth component of a time
series that we have shown here.
223
00:32:30,660 --> 00:32:36,380
Another component of the time series is cyclicity.
224
00:32:36,380 --> 00:32:47,160
We have had business cycles where the demand
shows not regular fluctuations, irregular
225
00:32:47,160 --> 00:32:49,170
fluctuations of different periodicity.
226
00:32:49,170 --> 00:33:03,250
So where we say that there is a rise in the
value and there is a fall here and a fall
227
00:33:03,250 --> 00:33:06,450
here and fall here and a rise here.
228
00:33:06,450 --> 00:33:17,310
Now this periodicity may not be same unlike
the case of seasonality where the periodicity
229
00:33:17,310 --> 00:33:22,250
exactly equal in this case it may not be equal.
230
00:33:22,250 --> 00:33:28,610
Another cycle could be of this nature.
231
00:33:28,610 --> 00:33:32,490
So here you will see that differs.
232
00:33:32,490 --> 00:33:35,930
The values are different.
233
00:33:35,930 --> 00:33:42,560
The troughs are also different.
234
00:33:42,560 --> 00:33:47,149
So this is the case of cycles.
235
00:33:47,149 --> 00:34:02,020
We call business cycle 2 to 5 year and there
are different other cycles such as Kuznet
236
00:34:02,020 --> 00:34:05,190
cycle, Kondratieff f cycle.
237
00:34:05,190 --> 00:34:22,300
Kuznet cycle periodicity is between 5 to 10
years, Kondratieff cycles are called long
238
00:34:22,300 --> 00:34:28,030
waves between 50 to 100 years.
239
00:34:28,030 --> 00:34:36,149
Basically, we are trying to say that if we
are concentrating on a particular variable
240
00:34:36,149 --> 00:34:38,960
whose value in the future.
241
00:34:38,960 --> 00:34:47,520
We would like to estimate then we can make
an analysis of the past values of that particular
242
00:34:47,520 --> 00:34:57,130
variable x, that x in our case is demand and
we can make an analysis of the time series
243
00:34:57,130 --> 00:35:00,260
data of the value of x.
244
00:35:00,260 --> 00:35:07,630
It has got 5 components average, trend, seasonality,
cyclicity, and random fluctuation as I have
245
00:35:07,630 --> 00:35:19,710
just told you and autocorrelation since we
are dealing with only 1 variable Xt.
246
00:35:19,710 --> 00:35:28,790
We can find how Xt is related to its lagged
variable Xt minus 1 or Xt minus 1 is related
247
00:35:28,790 --> 00:35:32,530
with Xt minus 2 etc.
248
00:35:32,530 --> 00:35:38,890
This is called autocorrelation and with the
help of autocorrelation studies we can find
249
00:35:38,890 --> 00:35:46,440
out whether trend is present, seasonality
is present, therefore autocorrelation holds
250
00:35:46,440 --> 00:35:53,750
a very important place in the time series
analysis, but unfortunately we do not have
251
00:35:53,750 --> 00:36:00,860
time to discuss and go into the details, but
I will give you some idea about what I am
252
00:36:00,860 --> 00:36:03,460
trying to say here.
253
00:36:03,460 --> 00:36:11,300
Trend analysis is a first thing that I am
showing.
254
00:36:11,300 --> 00:36:19,130
Here I am trying to say that this diagram,
this is the average value and that has a trend,
255
00:36:19,130 --> 00:36:25,410
but the actual data and has had no fluctuations.
256
00:36:25,410 --> 00:36:32,480
So suppose we are assuming a linear trend,
then the equation of Xt is nothing by a plus
257
00:36:32,480 --> 00:36:40,480
bT plus there is a random fluctuation, but
at least we are able to find out an estimate
258
00:36:40,480 --> 00:36:47,560
of the average value at any time T so given
the pass data, we can basically make a projection
259
00:36:47,560 --> 00:36:53,170
of the pass data, but assuming a linear fit
to the pass data.
260
00:36:53,170 --> 00:36:59,800
The linear fit is given by the equation Xt
equal to a plus bt.
261
00:36:59,800 --> 00:37:07,250
So given a time T, we can find out the value
of Xt and normally we use the least square
262
00:37:07,250 --> 00:37:11,060
estimates meaning that we actually take the
data.
263
00:37:11,060 --> 00:37:19,820
This error at different time points we find
out and we find out the intercept value of
264
00:37:19,820 --> 00:37:25,330
this a and b, trend.
265
00:37:25,330 --> 00:37:37,950
We estimate on the basis of a criterion of
minimizing the square of the error.
266
00:37:37,950 --> 00:37:40,770
Now there can be different types of trend
analysis.
267
00:37:40,770 --> 00:37:47,920
Suppose we assume exponential trend that means
we take Xt equal to a into e to the power
268
00:37:47,920 --> 00:37:52,550
bT we can make a log transformation.
269
00:37:52,550 --> 00:37:56,430
We can say ln Xt equals ln a plus bT.
270
00:37:56,430 --> 00:38:07,140
Now this then becomes linear in the parameter
just as it is in the case of liner trend.
271
00:38:07,140 --> 00:38:16,030
We can even assume a double-log or a log-log
relationship between x and T in this manner,
272
00:38:16,030 --> 00:38:26,980
suppose that x equal to a into T to the power
b taking ln, we get ln X equal to ln a plus
273
00:38:26,980 --> 00:38:33,520
b of ln T. This once again is linear in parameter.
274
00:38:33,520 --> 00:38:41,710
So by making suitable transformations we can
convert a nonlinear relationship as this or
275
00:38:41,710 --> 00:38:53,330
this into a linear relationship in parameter
and thereby we can use the simple regression
276
00:38:53,330 --> 00:39:02,080
techniques to find out the values of a and
b and therefore to find a relationship between
277
00:39:02,080 --> 00:39:09,710
x T and T which is what can be done.
278
00:39:09,710 --> 00:39:21,290
Now we not only use time, not just use time
as the independent variable, but we take different
279
00:39:21,290 --> 00:39:31,230
other variables as the independent or explanatory
such as X1, X2, and Xn.
280
00:39:31,230 --> 00:39:35,930
Suppose that we are assuming that there are
different other variables such as X1, X2,
281
00:39:35,930 --> 00:39:45,710
and Xn that determine the value of y and then
we call this a multiple regression equation.
282
00:39:45,710 --> 00:39:50,240
This is that error term about which I was
talking.
283
00:39:50,240 --> 00:39:59,260
And we will like to find out the estimates
of the values of the parameters b0, b1, b2,
284
00:39:59,260 --> 00:40:08,560
and bn to
be able to find out y.
285
00:40:08,560 --> 00:40:14,580
Once again we tried to minimize the least
square error, minimize the square error and
286
00:40:14,580 --> 00:40:21,740
xi is the ith independent variable.
287
00:40:21,740 --> 00:40:30,770
We are not discussing here the methods of
regression analysis, but we just trying to
288
00:40:30,770 --> 00:40:38,950
tell you the methods that are normally used.
289
00:40:38,950 --> 00:40:50,200
Next, we just expose to you certain advance
topics in time series analysis we call them
290
00:40:50,200 --> 00:40:58,930
autoregressive moving average methods, autoregressive,
AR standing for autoregressive, MA standing
291
00:40:58,930 --> 00:41:03,430
moving average method.
292
00:41:03,430 --> 00:41:06,980
We are talking about time series analysis.
293
00:41:06,980 --> 00:41:17,640
So let us say that y is the time series data
Y and this is 1 period lagged value Y t minus
294
00:41:17,640 --> 00:41:28,620
1, e period lagged value Y t minus 2, k period
lag value is Y t minus k and this is the error
295
00:41:28,620 --> 00:41:30,110
term.
296
00:41:30,110 --> 00:41:43,310
Now if Yt is related to its past value in
this manner then it is called AR of the order
297
00:41:43,310 --> 00:41:46,250
k, autoregressive model of k.
298
00:41:46,250 --> 00:41:58,730
Moving average model of order l on the other
hand is related to et in this manner a plus
299
00:41:58,730 --> 00:42:11,060
b1 et minus 1 plus b2 et minus 2, bk et minus
l plus et is called the moving average model
300
00:42:11,060 --> 00:42:23,830
of order l sometimes both are joined to give
ARMA model of order k and l. k for autoregressive
301
00:42:23,830 --> 00:42:30,530
part of ARMA model, l for the moving average
part of the ARMA model.
302
00:42:30,530 --> 00:42:43,210
So Yt equal to taking from here b1 Y t minus
1 plus b2 Yt minus 2 etc bk Yt minus k plus
303
00:42:43,210 --> 00:42:51,550
a plus et+ extra fit which is b1 et minus
1 etc.
304
00:42:51,550 --> 00:42:59,681
Now this looks quite complicated in actual
practice one can just have k equal to 1 and
305
00:42:59,681 --> 00:43:09,680
l equal to 1 in which case if this becomes
much simpler.
306
00:43:09,680 --> 00:43:19,490
Now sometimes say for example here what we
have done, we are showing here that the difference
307
00:43:19,490 --> 00:43:28,540
of 2 individual adjacent time series data
is stationary.
308
00:43:28,540 --> 00:43:33,210
So Yt minus Yt minus 1 is et.
309
00:43:33,210 --> 00:43:40,620
So we take a difference the value and work
with the difference value.
310
00:43:40,620 --> 00:43:42,350
This is called ARIMA.
311
00:43:42,350 --> 00:43:45,360
I standing for integrated.
312
00:43:45,360 --> 00:43:49,310
Autoregressive integrated moving average methods.
313
00:43:49,310 --> 00:43:51,740
So when we difference.
314
00:43:51,740 --> 00:43:59,180
We difference to make nonstationary data stationary.
315
00:43:59,180 --> 00:44:09,910
Now here let us say this is same as an AR
model.
316
00:44:09,910 --> 00:44:18,530
An average value error term and this is a
Y related with Y t minus 1.
317
00:44:18,530 --> 00:44:24,980
This is a case of a MA1, You can see this
is a constant.
318
00:44:24,980 --> 00:44:30,870
This error term and this is the moving average
term.
319
00:44:30,870 --> 00:44:35,700
Here both AR and MA are present without differencing.
320
00:44:35,700 --> 00:44:43,380
so this is a case of ARIMA 1, 1 which is this
part is autoregressive this part is moving
321
00:44:43,380 --> 00:44:48,790
average and this is constant and this is error
term.
322
00:44:48,790 --> 00:44:54,780
Next we talk about the leading indicator method.
323
00:44:54,780 --> 00:45:10,900
Basically leading indicator method is like
saying that find out if Y is the
324
00:45:10,900 --> 00:45:18,570
demand which we would like to estimate for
a product find out some other indicator for
325
00:45:18,570 --> 00:45:32,790
Y, for example if cars sale more in the market
then wheels with change more therefore if
326
00:45:32,790 --> 00:45:40,550
you are interested to project the demand of
wheels you see how Y is changing.
327
00:45:40,550 --> 00:45:48,430
If Y is rising, it is expected that X will
rise, but not exactly in the same phase with
328
00:45:48,430 --> 00:46:00,250
a phase difference that is why we say the
demand of Y is a plus b Xt minus k.
329
00:46:00,250 --> 00:46:12,240
So this is also called a barometer because
x is acting like a barometer for Y.
330
00:46:12,240 --> 00:46:15,950
We now come to econometrics method.
331
00:46:15,950 --> 00:46:22,060
basically econometrics methods can be single
regression equation such as the one that we
332
00:46:22,060 --> 00:46:29,970
have already discussed or it can be simultaneous
equations such as the 2 equations that I have
333
00:46:29,970 --> 00:46:42,510
written you will see here that Ct the consumption
expenditure at period t is a function of Yt,
334
00:46:42,510 --> 00:46:53,990
the income, but Yt in term is also related
to Ct therefore it contains 2 equations and
335
00:46:53,990 --> 00:47:03,000
there is a circular polarity between Y and
C as you will see here.
336
00:47:03,000 --> 00:47:15,490
Now econometrics itself is a very important
and difficult topic to discuss.
337
00:47:15,490 --> 00:47:24,580
This is just to expose to you the fact that
forecast models can be quite complex.
338
00:47:24,580 --> 00:47:41,190
Now here we are trying to say that there are
different forecasting methods and that normally
339
00:47:41,190 --> 00:47:49,740
we use to find out which forecasting method
is the best we use different criteria.
340
00:47:49,740 --> 00:47:57,200
To use a different criteria, we first of all
find out the forecast error ei this is called
341
00:47:57,200 --> 00:48:00,220
forecast error.
342
00:48:00,220 --> 00:48:13,740
Suppose that the value available with us for
the variable x at time I is Xi and using the
343
00:48:13,740 --> 00:48:22,770
method we can find out we can estimate or
we can see that the forecast value of x at
344
00:48:22,770 --> 00:48:25,040
time I is Fi.
345
00:48:25,040 --> 00:48:31,710
Then the difference between the 2 is taken
as the forecast error and the criteria that
346
00:48:31,710 --> 00:48:37,570
we can use can be many, I have just listed
3 of them.
347
00:48:37,570 --> 00:48:46,110
This is mean square error which is all the
squares over n terms average value dividing
348
00:48:46,110 --> 00:48:49,520
by n mean square error.
349
00:48:49,520 --> 00:48:56,310
It can be mean absolute error, absolute values
at this and the average is this.
350
00:48:56,310 --> 00:48:59,320
It can also be mean absolute percentage error.
351
00:48:59,320 --> 00:49:05,820
Percentage error is basically Xi minus Fi
by Xi into 100.
352
00:49:05,820 --> 00:49:11,900
Absolute value is taken here and average so
one can use any one of these 3.
353
00:49:11,900 --> 00:49:21,350
There are many other methods also and one
can use them to find out which forecasting
354
00:49:21,350 --> 00:49:25,260
method should be use.
355
00:49:25,260 --> 00:49:35,790
Finally we come to the case of some many forecasting
methods are available, which forecasting method
356
00:49:35,790 --> 00:49:37,560
to use?
357
00:49:37,560 --> 00:49:39,500
Now this is a difficult task.
358
00:49:39,500 --> 00:49:52,130
There are once again many ways by which the
different forecasts can be used to have the
359
00:49:52,130 --> 00:49:54,070
best possible forecast.
360
00:49:54,070 --> 00:50:02,930
What is suggested here is that one can make
forecasts using different forecasting methods.
361
00:50:02,930 --> 00:50:10,110
Let us say that there are cases forecasting
methods and each one of them yields different
362
00:50:10,110 --> 00:50:12,420
forecasts for the same time period.
363
00:50:12,420 --> 00:50:19,440
Let us say that the forecasts are F1, F2,
F2, etc up to Fk.
364
00:50:19,440 --> 00:50:28,850
What is suggested is there you give certain
weightages, weightages W1, W2 etc Wk indicating
365
00:50:28,850 --> 00:50:36,020
the importance and the confidence you are
associating or attaching to each individual
366
00:50:36,020 --> 00:50:37,190
forecast.
367
00:50:37,190 --> 00:50:48,750
Then sum the average that is W1 into F1 plus
W2 into F2 there is a mistake here it should
368
00:50:48,750 --> 00:50:56,600
be F2 and plus Wk Fk all that should be added.
369
00:50:56,600 --> 00:51:06,530
These words should sum up to 1 if that happens,
this forecast is taken as the best forecast.
370
00:51:06,530 --> 00:51:16,850
Now friends, as you must have seen I have
over the topic of forecasting is quite involving.
371
00:51:16,850 --> 00:51:24,190
it can be highly mathematical, but the fact
remains that one never knows unless the actual
372
00:51:24,190 --> 00:51:32,720
time in the future happens one does not know
whether your demand is accurate or correct.
373
00:51:32,720 --> 00:51:39,650
In the absence of such future information,
the only way there are 2 ways I would say
374
00:51:39,650 --> 00:51:48,530
1 to use the expert analyze or to use the
pass data.
375
00:51:48,530 --> 00:51:58,910
If you use expert analyze one should use a
panel of experts, find out what they have
376
00:51:58,910 --> 00:52:06,040
to say about the future demand and other consensus.
377
00:52:06,040 --> 00:52:12,950
If on another hand you are using pass data,
there is a large number of mathematical methods,
378
00:52:12,950 --> 00:52:23,290
regression methods, econometric methods, time-series
methods, they can always give some estimates,
379
00:52:23,290 --> 00:52:33,471
but finally you can always give them certain
weights and take a average value of the forecast
380
00:52:33,471 --> 00:52:34,471
of the demand.
381
00:52:34,471 --> 00:52:36,470
Thank you very much.