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A v e r a g e ( A R I M A ) M o d e l f o r f o r
FinancialEngineering
Term Paper
Submitted to:
Dr. Nalini P.
Group – 6:Shradha Saraogi – 2012PP0!2
Dee"ak P – 2012PP0!#
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Contents
Introduction2
%iterature Revie2
*+,ectives of the Stud-.
/i'e Series Modeling.
ARIMA (" d ) Model
Data and Methodolog-!
3'"irical Anal-sis4
MA3 to assess the 5orecasting Accurac-1.
MAP3 to assess the 5orecasting Poer1.
%,ung67o8 /est or 9hite :oise /est1
AR;< /est 1
;oncluding *+servations 1!
%i'itations of the Stud-1!
References 1=
Appendices 1#
Dee"ak > Prasanna > Ra' Prasad > Shradha1 > P a g e
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Introduction /he use of intelligent s-ste's and advanced techniues for 'arket "rediction has
+een idel- esta+lished /he develo"'ent of accurate techniues is critical to
econo'ists investors and anal-sts /he traditional statistical 'odels used in the
recent -ears for "redicting ?nancial 'arkets fail to ca"ture the inter relationshi"s
+eteen 'arket varia+les
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Percentage 3rror (MAP3) ere used as factors for evaluating the "erfor'ance of the
'odels Dunis et al (2012) in his "a"er co'"ared the "erfor'ance of A::
'odel and the traditional ARMA 'odel in forecasting 3HRHSD e8change rate
during the ?nancial crisis of 2004 and found that A:: 'odel as far su"eriorto the traditional ARMA 'odel
$ariations of ARMA 'odel such as the vector ARMA for forecasting of /reasur- +ill
rates and changes in 'one- su""l- have +een discussed +- Aksu et all in 1JJ1 and
seasonal fractionall- dierenced ARMA 'odel for long range forecasting of revenue
of I7M +- Ra- in 1JJ. Siss :ational 7ank (S:7) uses ARIMA 'odel for forecasting
the inKation over the short ter' "eriod and literature regarding the 'odel
e'"lo-ed and factors considered regarding this has also +een studied A"art fro'
this ARIMA has +een used in forecasting a ide variet- of ite's 5or instance %isa
7ianchi (1JJ#) used ARIMA to "redict arrivals in a call center in his "a"er
FI'"roving forecasting for tele'arketing centers +- ARIMA 'odeling ithinterventionG /here have +een atte'"ts to co'+ine the dierent 'odels to for' a
h-+rid 'odel Lhang Peter (200.) F/i'e Series 5orecasting Hsing a Shradha. > P a g e
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• Stationary – /hose ti'e series those hose statistical "ro"erties re'ain
constant over ti'e /his consistenc- 'a- range even u"6to the fourth 'o'ents
(e8"ectations variance ske6ness and kurtosis)
MC !po" In#e$ %MCCOM&E'
M;C 5uture Inde8 (M;C;*MD3C) is a signi?cant +aro'eter for the "erfor'ance
of co''odities 'arket and ould +e an ideal invest'ent tool in
co''odities 'arket over a "eriod of ti'e M;C also co'"utes the dail- S"ot
Inde8 value (M;C;*MD3C) for its M;C ;*MD3C M;C ARI M;C M3/A%
M;C 3:3RE +- using the current s"ot "rices of the res"ective co''odities
vis a vis their s"ot "rices in the sa'e +ase "eriod of average of 2001 /he
M;C ;*MD3C is the si'"le eighted average of the three grou" indices 6
M;C ARI M;C M3/A% M;C 3:3RE /he grou" indices are co'"uted
+ased on eo'etric Mean
Gol# ( !il)er !po"
In India old and silver "rices generall- rise hen senti'ents on the econo'- and
the ?nancial 'arkets are +earish or there is uncertaint- over future trends Riding
the rall- gold e8change6traded funds (3/5s) in India gave their highest ever
'onthl- return of 1!N in August 2011 All this ca'e ith increased volatilit-O there
ere 'an- 'onths hen +oth gold and silver gave negative returns old and silver
follo an al'ost si'ilar "attern and historicall- the- have 'aintained a ratio that
has Kuctuated idel- +eteen 1! and 100 since the 1J40s
CN NIFT* /he ;:C :ift- also called the :ift- !0 or si'"l- the :ift- is :ational Stock
38change of Indias +ench'ark inde8 for Indian euit- 'arket ;:C in its na'e
stands for ;RISI% :S3 Inde8 /he ;:C :ift- covers 22 sectors of the Indian
econo'- and oers invest'ent 'anagers e8"osure to the Indian 'arket in one
"ortfolio /he to" to contri+utors (in ter's of eight) to ;:C :ift- !0 Inde8 include
?nancial services (2!2=N) and I/ sector (1=2N) *ther sectors like industrial
'anufacturing contri+ute ,ust 04.N eightage hile there is no eightage for
agricultural sector in the inde8 /he inde8 as initiall- calculated on full 'arket
ca"italiQation 'ethodolog- 5ro' une 2= 200J the co'"utation as changed to
free Koat 'ethodolog- /he +ase "eriod for the ;:C :ift- inde8 is :ove'+er .
1JJ!
ARIMA !" d" #$ Model /he data series that e are orking on are non6stationar- /herefore to +etter
understand the data or to "redict future "oints in the series e need a uni6variate
'odel that converts the non6stationar- data into a stationar- data *ne such 'odel
Dee"ak > Prasanna > Ra' Prasad > Shradha > P a g e
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is ARIMA Autoregressive Integrated Moving Average hich is one of the 'ost
co''onl- used linear 'odels /he other 'odels include :on6linear 'odels like
dierent versions of Arti?cial :eural :etorks (A::) Model etc
7oth Autoregressive (AR) and Moving Average (MA) 'odels e8"ress dierent kindsof stochastic de"endence AR "rocesses enca"sulate a Markov6like ualit- here
the future de"ends on the "ast hereas MA "rocesses co'+ine ele'ents of
rando'ness fro' the "ast using a 'oving indo An o+vious ste" is to co'+ine
+oth t-"es of +ehavior into an ARMA(" ) 'odel hich is o+tained +- a si'"le
concatenation
Ct T1CtU1 V W W W V T"CtU" V Xt V Y1XtU1 V W W W V YXtU
Auto6regressive ele'ent " lingering eects of "receding scores
Integrated ele'ent d trends in the data
Moving Average ele'ent lingering eects of "receding rando'
shocks
/hese are the in"ut "ara'eters for ARIMA /herefore so'e of the uestions to +e
ansered +efore running the 'odel are 6 Shradha! > P a g e
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o+served si'"le line "lot of the data a 'ore a""ro"riate 'ethod ould +e to "lot
the autocorrelation function to o+serve if the lags are inKuencing the current value
of data or not If e ?nd that there is signi?cant autocorrelation "resent in the data
then it 'eans that data is not stationar- Data can +e transfor'ed into stationar-
data +- si'"le dierencing /he dierenced data is then checked for stationar-
nature if the ?rst dierence does give us the stationar- data then e 'ove on to
second dierenced data /his "rocess ill continue until e get transfor' the data
to +e stationar- In general e attain stationar- data ithin ?rst to dierenced
data "oints onl- *nce the stationar- data is o+tained note the degree of dierence
value /his ill serve as the value of FdG in ARIMA ("d)
/he second ste" in ARIMA i'"le'entation is "o i#en"i7 "3e au"ocorrela"ion
or#er 8p9 an# "3e or#er o7 mo)ing a)erage. 89 /hese values can +e
o+tained fro' the autocorrelation function (A;5) and "artial autocorrelation function
(PA;5) of the dierenced data 7- looking at the autocorrelation function of thedierenced data the order of 'oving average 'odel can +e "redicted /his is done
+- o+served hich of the lags is signi?cantl- correlated to the current value if the
second lag in A;5 is signi?cantl- correlated to the current value then e sa- that
the value is 2 Si'ilarl- +ased on the lag that is signi?cantl- correlated to the
current value in PA;5 e "redict the order of auto regressive 'odel
A;ai;e Shradha= > P a g e
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(Autoregressive Moving Average) ARIMA (Autoregressive Integrated Moving
Average) or SARIMA (Seasonal Autoregressive Integrated Moving Average)
A;ai;e in7orma"ion cri"erion %AIC'
It is a 'easure of the relative ualit- of a statistical 'odel for a given set of dataAs such AI; "rovides a 'eans for 'odel selection
AI; deals ith the trade6o +eteen the goodness of ?t of the 'odel and the
co'"le8it- of the 'odel It is founded on infor'ation entro"- it oers a relative
esti'ate of the infor'ation lost hen a given 'odel is used to re"resent the
"rocess that generates the data
In the general case the AI; is
here k is the nu'+er of "ara'eters in the statistical 'odel and % is the
'a8i'iQed value of the likelihood function for the esti'ated 'odel
iven a set of candidate 'odels for the data the "referred 'odel is the one ith
the 'ini'u' AI; value
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&m!irical AnalysisMCCOM&E
5irst e have considered M;C;*MD3C hich is considered to +e acting as a
signi?cant +aro'eter for the "erfor'ance of co''odities 'arket in India and
ould +e an ideal invest'ent tool in co''odities 'arket over a "eriod of ti'e
000!0000
1000001!0000200000
2!0000.00000.!000000000!0000!00000
6#0000
6=0000
60000
620000
000
20000
0000
=0000
#0000
M;C;*MD3C Inde8 "rices (Rs)
;lose 5irst Dierence
/he a+ove line "lot for dail- closing "rices of M;C;*MD3C shos that the closing
"rices of this inde8 do not re"resent stationar- data /he ?rst dierence values"lotted are nearer to rando' alk values can +e considered stationar- Also the
A;5 for actual closing "rices of M;C;*MD3C have shon signi?cant autocorrelation
+eteen the lag values and the current values
1 2 . ! = 4 # J 10
-4,B
-0,B
,B
0,B
4,B
ACF
A;5 H% %%
Autocorrelation 5unction (A;5) for ?rst dierenced M;C;*MD3C closing "rices
Dee"ak > Prasanna > Ra' Prasad > Shradha# > P a g e
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Partiall- Autocorrelation 5unction (PA;5) for ?rst dierenced M;C;*MD3C closing
"rices
1 2 . ! = 4 # J 10
-4+B
-4,B
-0+B
-0,B
-+B
,B
+B
0,B
0+B
PACF
PA;5 H% %%
*n o+serving the A;5 and PA;5 gra"hs of the ?rst dierenced M;C;*MD3C closing
"rices e can inter"ret that the order of auto regression F"G is 1 hich is o+tained
fro' "artiall- auto correlated function and the order of 'oving averages FG is also
1 hich is o+tained fro' auto correlated function Prasanna > Ra' Prasad > ShradhaJ > P a g e
ARIMA %p/#/'AICalue @e." Mo#el
ARIMA (110) =.!1 7est Model
ARIMA (011) =.!1ARIMA (012) =.41=
ARIMA (111) =.41=ARIMA (210) =.41=
ARIMA (112) =.J1JARIMA (211) =.J1J
ARIMA (212) =.!12.
ARIMA (010) :A
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3cono'ists consider gold "rices as a good indicator of the health of the econo'- In
the "ast it has +een o+served that investors Kock to gold hen the- are "rotecting
their invest'ents fro' either a crisis or inKation 9hen gold "rices dro" that usuall-
'eans the econo'- is health- /hats +ecause investors have left gold for other
'ore lucrative invest'ents like stocks +onds or real estate
0!000
10000
1!000
20000
2!000
.0000
.!000
6.0000062!0000
620000061!000061000006!0000000!00001000001!0000
old S"ot "rices (Rs)
S"ot Price(Rs ) 5irs t Dierence
/he line "lot for s"ot 'arket "rices of *%D in the co''odit- 'arket shos that
the s"ot "rices of the co''odit- do not re"resent stationar- data /he ?rst
dierence values "lotted are nearer to rando' alk values can +e considered
stationar- Also the A;5 for actual s"ot "rices of *%D have shon signi?cant
autocorrelation +eteen the lag values and the current values
Auto ;orrelation 5unction (A;5) for ?rst dierenced *%D s"ot "rices
1 2 . ! = 4 # J 10
-0,B
-+B
,B
+B
0,B
0+B
ACF
A;5 H% %%
Partiall- Auto ;orrelation 5unction (PA;5) for ?rst dierenced *%D s"ot "rices
Dee"ak > Prasanna > Ra' Prasad > Shradha10 > P a g e
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1 2 . ! = 4 # J 10
-0,B
-+B
,B
+B
0,B
0+B
PACF
PA;5 H% %%
*n o+serving the A;5 and PA;5 gra"hs of the ?rst dierenced M;C;*MD3C closing
"rices e can inter"ret that the
order of auto regression F"G is 2
hich is o+tained fro' "artiall- autocorrelated function and the order of
'oving averages FG is also 2 hich
is o+tained fro' auto correlated
function Prasanna > Ra' Prasad > Shradha11 > P a g e
ARIMA
%p/#/'
AIC
alue @e." Mo#elARIMA (210) 40!J2 7est Model
ARIMA (012) 40!J2
ARIMA (111) 40!J2
ARIMA (110) 40!=J!
ARIMA (011) 40!=J!
ARIMA (112) 40!#J#
ARIMA (211) 40!#J#
ARIMA (212) 40=102
ARIMA (010) :A
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0
10000
20000
.0000
0000
!0000
=0000
40000
6#00000
6=00000
600000
6200000
000
200000
00000
=00000
Silver S"ot Prices (Rs)
1st Di
old and silver follo an al'ost si'ilar "attern and historicall- the- have
'aintained a ratio that has Kuctuated idel- +eteen 1! and 100 since the 1J40s
Si'ilar to old "rices Silver "rices also rise hen senti'ents on the econo'- and
the ?nancial 'arkets are +earish or there is uncertaint- over future trends
/he a+ove line "lot for s"ot 'arket "rices of SI%$3R in the co''odit- 'arket shos
that the s"ot "rices of the co''odit- do not re"resent stationar- data /he ?rst
dierence values "lotted are nearer to rando' alk values can +e considered
stationar- Also the A;5 for actual s"ot "rices of SI%$3R have shon signi?cantautocorrelation +eteen the lag values and the current values
Auto ;orrelation 5unction (A;5) for ?rst dierenced SI%$3R s"ot "rices
1 2 . ! = 4 # J 10
-0+B
-0,B
-+B
,B
+B
0,B
0+B
ACF
A;5 H% %%
Dee"ak > Prasanna > Ra' Prasad > Shradha12 > P a g e
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Partiall- Auto ;orrelation 5unction (PA;5) for ?rst dierenced SI%$3R s"ot "rices
1 2 . ! = 4 # J 10
-0+B
-0,B
-+B
,B
+B
0,B
0+B
PACF
PA;5 H% %%
/hough fro' the a+ove A;5and PA;5 gra"hs for the ?rst
dierenced values see' to
i'"l- that the value of " is #
and is # /his is +ecause of
the o+served signi?cant
correlation of current values
ith #th lag in A;5 and PA;5
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000
100000
200000
.00000
00000
!00000
=00000
400000
6.00
6200
6100
0
100
200
.00
;:C :I5/E Prices (Rs)
;lose 1st Di
/he a+ove line "lot for dail- closing "rices of ;:C :ift- shos that the closing "rices
of this inde8 do not re"resent stationar- data /he ?rst dierence values "lotted are
nearer to rando' alk values can +e considered stationar- Also the A;5 for actual
closing "rices of ;:C :ift- have shon signi?cant autocorrelation +eteen the lag
values and the current values
Autocorrelation 5unction (A;5) for ?rst dierenced ;:C :ift- closing "rices
1 2 . ! = 4 # J 10
-0+B
-0,B
-+B
,B
+B
0,B
0+B
ACF
A;5 H% %%
Partiall- Autocorrelation 5unction (PA;5) for ?rst dierenced ;:C :ift- closing
"rices
Dee"ak > Prasanna > Ra' Prasad > Shradha1 > P a g e
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1 2 . ! = 4 # J 10
-0+B
-0,B
-+B
,B
+B
0,B
0+B
PACF
PA;5 H% %%
As fro' the a+ove A;5 and PA;5
gra"hs for the ?rst dierenced
values do not directl- tell an-thinga+out the "ossi+le values for " and
the actual values of ARIMA 'odel
"ara'eters are deter'ined +ased
on the AI; values +elo
AI; /est 6 9e kno that the 'odel
ith loest value AI; is the +est
'odel In this case e o+serve that
ARIMA(110) is the +est 'odel ith loest AI; value
MA& to assess the 'orecasting Accuracy /he a+ove ta+le shos the forecasting accurac- of
ARIMA 'odels that e have a""lied on M;C;*MD3C
*%D s"ot "rices SI%$3R s"ot "rices and ;:C :ift-
using error 'easure Mean Average 3rror (MA3) It is
o+served fro' the ta+le that MA3 does e8ist in each
of the forecasts and thus there is ala-s an error
ele'ent hen ARIMA 'odel is used to "redict future
values
MA(& to assess the 'orecasting (ower /he a+ove ta+le shos the forecasting "oer of
ARIMA 'odels that e have a""lied on M;C;*MD3C
*%D s"ot "rices SI%$3R s"ot "rices and ;:C :ift-
using error 'easure Mean Average Percentage 3rror
(MAP3) It is o+served fro' the ta+le that MAP3 is
least in ARIMA (1 1 0) 'odel for the M;C;*MD3C
Dee"ak > Prasanna > Ra' Prasad > Shradha1! > P a g e
ARIMA%p/#/'
AICalue @e." Mo#el
ARIMA (110) ###= 7est ModelARIMA (011) ###=
ARIMA (012) #!0#JARIMA (111) #!0#J
ARIMA (210) #!0#JARIMA (112) #!2J.
ARIMA (211) #!2J.ARIMA (212) #!J4
ARIMA (010) :A
IN&ICE!DCommo#i"ie.
MAE
M;C;*MD3C 2J2#
*%D 2J24
SI%$3R ##2=1
;:C :I5/E 1...
IN&ICE!DCommo#i"ie.
MAPE
M;C;*MD3C 04244N
*%D 0#1#1N
SI%$3R 1J#.1N
;:C :I5/E 22044N
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"rices So it is e8"eriential that this 'odel has "erfor'ed +etter than all the other
ARIMA 'odels Also it can +e o+served that the MAP3 is highest in the case ;:C
:ift- hich is ver- 'uch e8"ected as
the volatilit- of euit- stocks is higher
than that of the co''odit- 'arket
Since ARIMA is a linear 'odel it can
+e used to "redict co''odit- "rices
than to "redict the euit- 'arket
/his is "roved ith the MAP3 anal-sis
hich shos highest MAP3 for ;:C
:ift-
Prasanna > Ra' Prasad > Shradha1= > P a g e
IN&ICE!DCommo#i"ie.
&Fp-)alue
M;C;*MD3C =`
00001
12 0000
*%D = 0J1#
12 0!4.
SI%$3R = 0=1.
12 00==;:C :I5/E = 0#14
12 0!20
IN&ICE!DCommo#i"ie.
Lag !core C P-alue Pre.en"
M;C;*MD3C 1 2#44! .#1= =#36= /RH3
2 !1401 !JJ1= #36JJ /RH3
*%D 1 #=#J .#1= 43610# /RH3
2 J!4#=# !JJ1= 13620# /RH3
SI%$3R 1 !02=2 .#1= 136111 /RH3
2 JJJ00. !JJ1= 136214 /RH3
;:C :I5/E 1 244=0 .#1= !36J! /RH3 2 #014= !JJ1= 361#. /RH3
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this e have a""lied the AR;< test on all the data values that e used in this stud-
"ro,ect /he results ere "resented in the a+ove ta+le 5ro' the a+ove ta+le it can
+e o+served all the ti'e6series data do have conditional heteroscedasticit- and
hence and AR;
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References
OURNAL PAPER!
P :ason ;ha"ter 11 FStationar- and non6stationar- ti'e seriesG Dr /ri"ath- : (2011) FA ;o'"arison of Arti?cial :eural :etork (A::) Model
Auto Regressive Integrated Moving Average (ARIMA) Model for 5orecasting Indian
Stock MarketG International ournal of ;onte'"orar- 7usiness Studies /ina akaa et al 2011 F3lectricit- "rice forecasting – ARIMA 'odel a""roachG LsuQsanna
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HE@!ITE!
C%S/A/ Statistical and Data Anal-sis Softare for 3C;3% 8lstatco' S"ider ?nancials – :u'C% su""ort e+site s"ider?nancialco' *nline coursed on ?nancial econo'etrics htt"sonlinecoursesscience"suedu
!TAN&AR& TET @OO!
ohn ; Prasanna > Ra' Prasad > Shradha1J > P a g e
https://onlinecourses.science.psu.edu/https://onlinecourses.science.psu.edu/
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A!!endicesMAE an# MAPE calcula"ion.
MCCOM&E
&a"ePre#ic"e#
alue.Ac"ualalue. Error
Percen"ageError
1122201. 0214! 0=!! .40 104!N
112.201. 021=# 0=!! .44 1044N112!201. 021=J 0124. #J= 022.N
112=201. 021=J 0.!21 1.!2 0..!N1124201. 021=J 002#. 1##= 041N
112#201. 021=J .J4!4 !J! 11!=N
112J201. 021=J .JJ1# .021 04!4N
MEAN AERAGE ERROR %MAE' 4J4K
MEAN AERAGE PERCENTAGE ERROR %MAPE' ,4KB
GOL&
&a"e Pre#ic"e# alue.Ac"ualalue. Error Percen"age Error
1121201. .0J00!= .0#!#00 2!= 01.#N
1122201. .0#J#!. .0J#400 ##4 02#=N
112!201. .0#J4.2 .0.#00 !J.2 1#10N
112=201. .0#J42J .0#J#00 041 0002N
1124201. .0#J42J .04!000 142J 04JN
112#201. .0#J42# .0.4J00 !1#2# 140=N
112J201. .0#J42# .0JJ00 .J#2# 1.0=N
MEAN AERAGE ERROR %MAE' 42J4
MEAN AERAGE PERCENTAGE ERROR %MAPE' ,K0KB
!ILER
&a"ePre#ic"e#
alue.Ac"ualalue. Error
Percen"ageError
1121201. !!241J J400 !#01J 12J1N
1122201. !!24.! J0=00 =21.! 1.#N
112!201. !!24. 2#=00 121. 2#0.N112=201. !!24. !0!000 44. 10=0N1124201. !!24. #.00 =J.. 1!=N
112#201. !!24. 11100 11=. .211N
112J201. !!24. .4J00 11#. 2!##N
MEAN AERAGE ERROR %MAE' KK460
MEAN AERAGE PERCENTAGE ERROR %MAPE' 0JK1B
Dee"ak > Prasanna > Ra' Prasad > Shradha20 > P a g e
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8/9/2019 Term Paper_Group 6
22/28
FINANCIAL ENGINEERING – TERMPAPER
GROUP - 6
CN NIFT*
&a"e Pre#ic"e# alue.Ac"ualalue. Error Percen"age Error
1121201. =2000 !JJJ0! 20J! .1=N
1122201. =2000 !JJ!! 20#!! .4#N
112!201. =2000 =11!.! ##=! 1!0N
112=201. =2000 =0!J10 1J0 2.J1N
1124201. =2000 =0!410 1=J0 22!N
112#201. =2000 =0J1#! 1121! 1#1N
112J201. =2000 =14=10 24J0 0!2N
MEAN AERAGE ERROR %MAE' 01121 MEAN AERAGE PERCENTAGE ERROR %MAPE' 44,KB
Pre#ic"ion. an# Re.i#ual.
Dec11 A"r12 ul12 *ct12 an1. Ma-1. Aug1. :ov1. Mar1
.200
.00
.=00
.#00
000
200
00
=00
#00
ARIMA %MCCOM&E'
;lose ARIMA (;lose) $alidation
Prediction %oer +ound (J!N) H""er +ound (J!N)
&a"e
Clo.e
MCCOM&E
Dee"ak > Prasanna > Ra' Prasad > Shradha21 > P a g e
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8/9/2019 Term Paper_Group 6
23/28
FINANCIAL ENGINEERING – TERMPAPER
GROUP - 6
6#00
6=00
600
6200
0
200
00
=00
#00
Re.i#ual. %MCCOM&E'
&a"e
Re.i#ual
GOL& .po" price.
Dec11 A"r12 ul12 *ct12 an1. Ma-1. Aug1. :ov1. Mar1
2!000
2=000
24000
2#000
2J000
.0000
.1000
.2000
..000
.000
ARIMA %GOL& !po" Price%R.''
S "ot Price(Rs ) ARIMA (S "ot Price(Rs )) $alidation
Prediction %oer +ound (J!N) H""er +ound (J!N)
&a"e
!po" Price%R.'
Dee"ak > Prasanna > Ra' Prasad > Shradha22 > P a g e
-
8/9/2019 Term Paper_Group 6
24/28
-
8/9/2019 Term Paper_Group 6
25/28
FINANCIAL ENGINEERING – TERMPAPER
GROUP - 6
6#000
6=000
6000
62000
0
2000
000
=000
Re.i#ual. %!ILER'
&a"e
Re.i#ual
CN Ni7"
Dec11 A"r12 ul12 *ct12 an1. Ma-1. Aug1. :ov1. Mar1
!00
!000
!!00
=000
=!00
4000
ARIMA %CN Ni7"'
;lose ARIMA (;lose) $alidation
Prediction %oer +ound (J!N) H""er +ound (J!N)
&a"e
Clo.e
Dee"ak > Prasanna > Ra' Prasad > Shradha2 > P a g e
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8/9/2019 Term Paper_Group 6
26/28
FINANCIAL ENGINEERING – TERMPAPER
GROUP - 6
6.00
6200
6100
0
100
200
.00
Re.i#ual. %CN Ni7"'
&a"e
Re.i#ual
Normali" "e." an# H3i"e noi.e "e." re.ul".
MCCOM&E
:or'alit- test and hite noise tests(Residuals)
Statistic D5 $alue"6
value
arue67era 21.1J
#4
`0000
1
7o86Pierce = .!=#4
`0000
1
%,ung67o8 = .=044
`0000
1
Mc%eod6%i = =J2J
`0000
1
7o86Pierce 12 .=121 0000
Dee"ak > Prasanna > Ra' Prasad > Shradha2! > P a g e
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8/9/2019 Term Paper_Group 6
27/28
FINANCIAL ENGINEERING – TERMPAPER
GROUP - 6
%,ung67o8 12 .=!2. 0000
Mc%eod6%i 12 #1##=
`0000
1
GOL&:or'alit- test and hite noise tests(Residuals)
Statistic D5 $alue"6
value
arue67era 2.2.24
2=`
00001
7o86Pierce = 1JJ= 0J20%,ung67o8 = 2020 0J1#
Mc%eod6%i = =#1 0.417o86Pierce 12 10240 0!J2
%,ung67o8 12 10J2 0!4.
Mc%eod6%i 12 1.!1 024J
!ILER:or'alit- test and hite noise tests(Residuals)
Statistic D5 $alue"6
value
arue67era 24.0J
##`
00001
7o86Pierce = 1 0=21%,ung67o8 = 4= 0=1.
Mc%eod6%i = 2=110 00007o86Pierce 12 1J=#2 004.
%,ung67o8 12 20040 00==
Mc%eod6%i 12 .0!1 0002
CN NIFT* :or'alit- test and hite noise tests
Dee"ak > Prasanna > Ra' Prasad > Shradha2= > P a g e
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8/9/2019 Term Paper_Group 6
28/28
FINANCIAL ENGINEERING – TERMPAPER
GROUP - 6
(Residuals)
Statistic D5 $alue"6
value
arue67era 2 41202`
00001
7o86Pierce = 2J00 0#21%,ung67o8 = 2J.4 0#14
Mc%eod6%i = 1#14= 000=7o86Pierce 12 10#! 0!2
%,ung67o8 12 1110# 0!20
Mc%eod6%i 12 4J.!2`
00001
Dee"ak > Prasanna > Ra' Prasad > Shradha