Munich Personal RePEc Archive
Forecasting model of small scale
industrial sector of West Bengal
Bera, Soumitra Kumar
Calcutta University, Banaras Hindu University, North Eastern Hill
University
20 November 2010
Online at
https://mpra.ub.uni-muenchen.de/28144/
Forecasting model of small
scale industrial sector of West
Bengal.
Soumitra Kumar Bera
BSc Economics (CU), MFT (BHU), PhD (NEHU) [email protected]
Ec o no mic fo r e c a s t ing ha s lo ng e nga ge d t he a t t e nt io n o f a c a d e mic ia n, p r o fe s s io na ls , p la nne r s a nd p o lic y ma k e r s . I n t he fa c e o f unc e r t a int ie s , a lmo s t e ve r y e c o no mic d e c is io n d e p e nd s up o n fo r e c a s t s . I f t he fo r e c a s t s s ugge s t a d is ma l p ic t ur e a he a d , t he n e c o no mic s ys t e m ma y d o it s b e s t t o c ha nge t he s c e na r io s o t ha t glo o my fo r e c a s t s ma y no t c o me t r ue . F o r e c a s t ing invo lve s p r e d ic t ing fut ur e va lue s o f e c o no mic va r ia b le s wit h a s lit t le e r r o r a s p o s s ib le ( Gup t a , 2 0 0 3 ) . F o r t his p ur p o s e , fo r e c a s t e r s ha ve e mp lo ye d va r io us t ime s e r ie s t e c hniq ue s in s ho r t r un e c o no mic fo r e c a s t ing. Amo ng t he va r io us me t ho d s o f fo r e c a s t ing, t he Aut o - Re gr e s s ive I nt e gr a t e d M o ving Ave r a ge ( ARI M A) mo d e l, t ho ugh c o mp lic a t e d o ne , is a p o we r ful me t ho d t o ge ne r a t e a c c ur a t e fo r e c a s t s in t he s ho r t - r un wit ho ut invo lving e c o no mic t he o r y ( M a k r id a k is , 1 9 9 8 ) .
The r e a r e q uit e a fe w a nd no t e wo r t hy e mp ir ic a l a t t e mp t s ma d e b y r e s e a r c he r s t o ge ne r a t e e c o no mic fo r e c a s t s . N o t a b le a mo ngs t t he m a r e : Sabia
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(1977) , Bawa (1980), Nachane (1981) , Bowersox (1981), Bowersox (1981), Ibrahim and Otsuki (1982), Armstrong (1983), Mentzer (1984), Fildes (1984), Sarkar (1989), Poonam and Gupta (1990), Diebold and Rudebusch (1991), Fildes (1992), Gupta (1993), Fildes (1995), Mentzer (1995), Fildes (1998Sethi (1999) Razzaque and Ruhul Amin (2000), Naresh (2003), Gupta (2002), Afzal (2002), Gupta (2003), Taylor (2003), Gupta (2004), Armstrong (2005), Armstrong (2006), Taylor (2006) and Gupta (2006) have generated the forecasts of economic variables for India as well as abroad. F o r e c a s t ing a t ma c r o a nd mic r o le ve l is q uit e p o p ula r in t he we s t b ut it s a p p lic a t io n t o I nd ia n d a t a , e s p e c ia lly in ind us t r ia l s e c t o r is r a r e a nd t he r e s e e ms t o b e n o t a s ingle c o mp r e he ns ive s t ud y d e a ling wit h ge ne r a t io n fo r e c a s t s o f s ma ll s c a le ind us t r ia l s e c t o r a t a ggr e ga t e a nd d is a ggr e ga t e le ve l. K e e p ing t his fa c t int o c o ns id e r a t io n p r e s e nt s t ud y is a n e nd e a vo r in t his d ir e c t io n.
W e s t Be nga l o c c up ie s a p la c e o f p r id e in t he ind us t r ia l ma p o f I nd ia whic h is a t t r ib ut a b le t o it s s ma ll- s c a le ind us t r ia l s e c t o r ( La l, 1 9 6 6 ) . The s t a t e inhe r it e d a ve r y we a k ind us t r ia l b a s e whe n p a r t it io ne d in 1 9 4 7 a nd s uffe r e d a fur t he r e r o s io n whe n go t r e o r ga nize d in 1 9 6 6 ( S ingh 1 9 9 5 ) . M o r e r e c e nt ly it ha s b e e n t hr o ugh a p e r io d o f t ur b ule nc e whic h no t o nly a ffe c t e d t he ind us t r ia l gr o wt h a d ve r s e ly b ut t e nd e d t o c a us e s o me o ut - migr a t io n o f ind us t r y t o o . W it h t he r e s t o r a t io n o f p e a c e , t h e s t a t e go ve r nme nt t r ie d t o a c t iva t e t he p r o c e s s o f ind us t r ia l d e ve lo p me nt wit h t he ho p e t o e nt e r int o a ne w e r a o f p r o gr e s s ( Bha t ia , 1 9 9 9 ) .
O bje c t i v e s o f t he s t ud y
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P r e s e nt s t ud y ha s b e e n c o nd uc t e d k e e p ing in mind t he fo llo wing o b j e c t ive s : 1 . To ge ne r a t e fo r e c a s t s o f p r o d uc t io n, d ir e c t e mp lo yme nt , fixe d c a p it a l a nd numb e r o f unit s o f s ma ll s c a le ind us t r ia l s e c t o r o f W e s t Be nga l.
2 . To r e c o mme nd a p p r o p r ia t e fo r e c a s t ing mo d e l t o p r e p a r e fo r e c a s t s o f s ma ll s c a le ind us t r ia l s e c t o r o f W e s t Be nga l.
D a t a ba s e a nd Ana l y t i c a l Fra me wo rk :
P r e s e nt s t ud y is b a s e d o n s e c o nd a r y d a t a fo r t he p e r io d 1 9 7 0 - 7 1 t o 2 0 0 6 - 0 7 . The a ggr e ga t e d a t a r e la t ing t o t he va r ia b le s : numb e r o f unit s , d ir e c t e mp lo yme nt , fixe d c a p it a l a nd p r o d uc t io n o f s ma ll - s c a le ma nufa c t ur ing ind us t r y gr o up s o f W e s t Be nga l we r e c ulle d fr o m Dir e c t o r a t e o f I nd us t r ie s , W e s t Be nga l. The fo r e c a s t s o f t he a b o ve me nt io ne d va r ia b le s fo r a le a d t ime o f 1 3 ye a r s we r e ge ne r a t e d a p p lying o f ‘Bo x-Jenkins’ ARIMA method.
The p r e s e nt p a p e r is a n e nd e a vo r t o ge ne r a t e fo r e c a s t s b y a p p lying s o p his t ic a t e d univa r ia t e Bo x J e nk ins ARI M A mo d e ling. Univa r ia t e Bo x -J e nk ins ( UB-J ) a p p r o a c h is b a s e d o n id e nt ifying t he p a t t e r n fo llo we d b y p a s t va lue s o f a s ingle va r ia b le a nd t he n e xt r a p o la t ing t he p a t t e r n in t he p a s t fo r ne a r fut ur e a s we ll ( P a nk r a t z, 1 9 8 3 ; M a k r id a k is 1 9 8 7 ) . O ne o f t he a d va nt a ge s o f Bo x- J e nk ins o ve r o t he r fo r e c a s t ing mo d e ls is t ha t t his mo d e ling is no t b a s e d o n e c o no mic t he o r y a nd c a p a b le o f c a p t ur ing s light e s t va r ia t io n in t he d a t a ( M a k r id a k is , 1 9 7 8 ) . Bo x - J e nk ins me t ho d o lo gy r e s t s o n t he s imp lifying a s s ump t io n t ha t t he p r o c e s s whic h ha s ge ne r a t e d a s ingle t ime s e r ie s , is t he s t a t io na r y p r o c e s s b ut unfo r t una t e ly mo s t t ime s e r ie s e nc o unt e r e d a r e r a r e ly
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s t a t io na r y, s t ill it is p o s s ib le t o t r a ns fo r m t he m t o s t a t io na r y b y t he a p p r o p r ia t e le ve l o f d iffe r e nc ing ( ma ximum up t o s e c o nd le ve l) ( Bo x & J e nk ins , 1 9 6 8 ; S P S S , 1 9 9 9 ) . The d e gr e e o f d iffe r e nc ing t r a ns fo r ms a no n -s t a t io na r y -s e r ie -s int o a -s t a t io na r y o ne . I f no n - -s t a t io na r y i-s a d d e d t o a mixe d ARI M A mo d e l, t he n t he ge ne r a l ARI M A ( p , d , q ) is o b t a ine d , it ha s t he fo r m a s und e r :
ΦP( B ) ( 1 - B )d Yt = C + θq ( B ) et
o r
ΦP( B ) Wt = C + θq ( B ) et … ( 1 )
whic h will b e no n- s t a t io na r y unle s s d = 0 .
The mo d e l is s a id t o b e o f t he o r d e r ( p , d , q ) , whe r e p , d a nd q a r e us ua lly 0 , 1 o r 2 ( M a k r id a k is , 1 9 9 8 ; Ha nk e , 2 0 0 1 ) . Ha ving t e nt a t ive ly id e nt ifie d o ne o r mo r e mo d e ls t ha t s e e m lik e ly t o p r o vid e p a r s imo nio us a nd s t a t is t ic a lly a d e q ua t e r e p r e s e nt a t io n o f a va ila b le d a t a , t he ne xt s t e p is t o e s t ima t e t he va lue s o f t he p a r a me t e r s . S um o f s q ua r e s o f t he r e s id ua ls we r e c o mp ut e d b y us ing ma ximum lik e liho o d e s t ima t io n me t ho d give n t he r e s p e c t ive init ia l e s t ima t e s o f t he p a r a me t e r s , o p t imum va lue s o f t he p a r a me t e r s we r e s e a r c he d b y imp r o ving t he init ia l e s t ima t e s it e r a t ive ly b y s up p le me nt ing t he m wi t h t he info r ma t io n c o nt a ine d in t he t ime s e r ie s . F o r a give n mo d e l invo lving k p a r a me t e r s , t he it e r a t ive p r o c e d ur e wa s c o nt inue d t ill t he d iffe r e nc e b e t we e n s uc c e s s ive va lue s o f s um o f s q ua r e d r e s id ua l b e c a me s o s ma ll t ha t c o uld b e igno r e d fo r p r a c t ic a l c o ns id e r a t io ns ( Bo x, J e nk ins a nd Re ins e ll, 1 9 9 4 , p . 2 2 5 ) .
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I n o r d e r t o ma k e a n a s s e s s me nt o f t he va lid it y o f t he e s t ima t e d mo d e ls fo r t he give n t ime s e r ie s , fo llo wing d ia gno s t ic me a s ur e s we r e wo r k e d o ut :
( a ) Aut o c o rre l a t i o ns o f re s i dua l s: The a ut o c o r r e la t io n c o e ffic ie nt wa s wo r k e d o ut b y a p p lying fo r mula give n in t he e q ua t io n ( 2 ) .
n- k ∑ et . et + k
t = 1
rk ( e )= - - - -; k = 1,2,…ℓ …(2)
n ∑ et 2
t = 1
The ma j o r c o nc e r n o f AC F o f r e s id ua ls wa s t ha t whe t he r t he r e s id ua ls we r e s ys t e ma t ic a lly d is t r ib ut e d a c r o s s t he s e r ie s o r t he y c o nt a in s o me s e r ia l d e p e nd e nc y ( Box & Pierce, 1970). Ac c e p t a nc e o f t he hyp o t he s e s o f s e r ia l d e p e nd e nc y c o nc lud e s t ha t t he e s t ima t e d ARI M A mo d e l is ina d e q ua t e .
( b) Po rt ma nt e a u Te s t : Lj ung- Bo x Q s t a t is t ic s wa s c o mp ut e d fr o m t he
model’s residuals by us ing
ℓ
Q = n (n+2) ∑ rk ( e )2 ( n- k ) - 1 …( 3 )
N o n- s ignific a nc e o f p o r t ma nt e a u t e s t wa s t a k e n t o imp ly t he ge ne r a t e d r e s id ua ls c o uld b e c o ns id e r e d a whit e no is e , t he r e b y ind ic a t ing t he a d e q ua c y o f e s t ima t e d mo d e l ( DeLurgio. 1998).
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( c ) S um o f S qua re s o f Erro r ( S S E) : S um o f s q ua r e s o f t he e r r o r s o f fit t e d mo d e ls wa s c o mp ut e d . W e s e le c t e d t ha t mo d e l a d e q ua t e , in c a s e o f whic h S S E wa s minimu m.
( d) Ak a i k e I nf o rma t i o n Cri t e ri a ( AI C) : AI C wa s c o mp ut e d t o d e t e r mine b o t h ho w we ll t he mo d e l fit s t he o b s e r ve d s e r ie s , a nd t he numb e r o f p a r a me t e r us e d in t he fit . W e c o mp a r e d t he va lue AI C wit h o t he r fit t e d mo d e l t o t he s a me d a t a s e t a nd we s e le c t e d t ha t fit t e d mo d e l a d e q ua t e in c a s e o f whic h AI C wa s minimum. The AI C is c o mp ut e d a s und e r :
AI C = n l o g ( S S E) + 2 k … (4) whe r e
k = N umb e r o f p a r a me t e r s t ha t a r e fit t e d in t he mo d e l lo g = N a t ur a l lo ga r it hm
n = numb e r o f o b s e r va t io ns in t he s e r ie s S S E = S um o f S q ua r e d Er r o r s
W hile s e le c t ing a d e q ua t e mo d e l a d iffe r e nc e in AI C va lue o f 2 o r le s s wa s no t r e ga r d e d a s s ub s t a nt ia l a nd we s e le c t e d t he s imp le mo d e l wit h le s s e r p a r a me t e r s .
( e ) S c hwa rz B a y e s i a n I nf o rma t i o n Cri t e ri a ( S B C) : S BC is a mo d ific a t io n t o AI C ; it is b a s e d o n Ba ye s ia n c o ns id e r a t io n. Lik e AI C it wa s c o mp ut e d t o d e t e r mine ho w we ll t he mo d e l fit s a mo ngs t t he c o mp e t ing mo d e ls , a nd we s e le c t e d t ha t mo d e l a d e q ua t e in c a s e o f S BC wa s minimum. The S BC is a s und e r :
S B C = n l o g ( S S E) + k l o g ( n) … (5)
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O n t he b a s is o f a b o ve me nt io ne d ya r d s t ic k , fina lly s e le c t e d mo d e l fo r e a c h
va r ia b le wa s us e d fo r fo r e c a s t ing a s d is c us s e d a s fo llo ws . F o r ma k ing fo r e c a s t s e q ua t io n ( 2 ) wa s uns c r a mb le d t o e xp r e s s Yt a nd et b y
us ing t he r e la t io n Wt = ( 1 - B)d Yt. Give n t he d a t a up t o t ime t t he o p t ima l
Λ
fo r e c a s t s o f Yt + ℓ [ d e s igna t e d b y Yt (ℓ )] made a time t was taken as
c o nd it io na l e xp e c t a t io n o f Yt + ℓ , where t, is the forecast origin and ℓ is the fo r e c a s t le a d - t ime . Er r o r t e r m et c o mp le t e ly d is a p p e a r e d o nc e we ma d e
fo r e c a s t s mo r e t ha n q p e r io d a head. Thus for ℓ > q, then ℓ period ahead fo r e c a s t wa s ma d e a s und e r :
^ ^ ^ ^ ^ ^
Yt + ℓ = C + Φ1 Yt +ℓ-1+ … + Φp Yt +ℓ-p …(7)
Table 1: Initial estimate of the Parameters
Variable
ARIMA (1,d,o)
ARIMA
(0,d,1) ARIMA (1,d,1) ARIMA (2,d,2)
C AR1 C
MA
1 C AR1 MA
1 C
AR
Variable
ARIMA
(0,d,2) ARIMA (1,d,2) ARIMA (2,d,o) ARIMA (2,d,1)
C
MA 1
M A2 C
A R 1 MA 1 M A2 C
AR
1 AR2 C AR 1 AR 2 M A1 No. of units -24. 62 -0.05 5 -0.0 42 -24. 44 0. 25 6 0.19 89 -0.0 316 -24.6 6 0.0 59 0.03 487 -24. 59 0.24 78 0.0 246 3 0.1 88 8 Direct employm ent -11 5.5 0.24 2 -0.0 45 -14 0.2 -0. 82 -0.63 7 0.2 352 -129. 1 -0.2 34 -0.07 44 -13 2.2 -1.07 4 -0.2 724 -0.8 65 Fixed Investme nt 10. 86 7 0.38 87 0.3 37 10. 87 0. 72 1 1.12 09 -0.1 21 9.01 58 -0.2
19 -0.2 11. 31 2 0.61 33 -0.0 405 0.9 97 2 Producti on 61. 66 0.06 45 0.0 65 62. 02 -0. 81 -0.39 6 0.5 269 59.3 13 -0.4 46 -0.32 87 60. 42 5 -0.21 -0.2 522 0.2 71 9
Note: In all Cases d=2
Table 2: Comparative Results from Various Models Variable Estima te ARIM A (1,d,o) ARIM A (0,d,1) ARIM A (1,d,1) ARIM A (2,d,2) ARIM A (0,d,2) ARIM A (1,d,2) ARIM A (2,d,0) ARIM A (2,d,1) No. of units
Sum of Square s 1.66E+ 08 1.66E+ 08 1.65E+ 08 159315 396 165401 646 1.65E+ 08 1.65E+ 08 165364 076.8 Standa rd error 2274.7 63 -310.05 7 2309.9 49 2317.4 78 2309.6 644 2347.2 68 2309.5 86 2347.5 677 AIC 624.10 63 624.11 5 626.15 12 629.03 157 626.14 387 628.24 3 626.14 15 628.25 078 SBC 627.15 9 627.16 77 630.73 03 636.66 337 630.72 293 634.34 85 630.72 05 634.35 622 Q 9.398 9.465 9.275 8.693 9.196 9.197 9.2 9.234
Direct employ ment
error AIC 700.67 83 700.62 24 702.67 4 704.77 747 702.63 687 704.33 82 702.57 63 704.00 241 SBC 703.73 1 703.67 51 707.25 31 712.40 927 707.21 595 710.44 37 707.15 53 710.10 785 Q 8.781 8.709 8.745 5.826 8.785 7.646 8.708 7.573
Fixed Investm ent
Sum of Square s
14326.
48 139926
122744 .8 122214 .5 130387 .34 125146
.8 138538
122374 .63 Standa rd error 66.892 99 66.012 39 61.052 2 62.611 696 64.224 265 62.756 14 66.736 94 61.780 526 AIC 384.32 88 383.50 76 381.01 61 384.97 594 383.14 065 383.73 38 385.24 48 382.95 364 SBC 387.38 16 386.56 04 385.59 52 392.60 775 387.71 973 389.83 93 389.82 39 389.05 908 Q 6.828 6.382 3.954 4.083 3.816 4.721 4.636 3.78
Producti on
Sum of Square s 28207 09 256031 5 272929 1 244828 6 255221 5.4 245385 4 249916 0 247551 3.7 Standa rd error 296.39 17 281.57 4 288.52 02 286.96 581 285.68 924 283.00 97 282.48 36 285.64 443 AIC 485.63 12 482.32 77 486.47 85 487.05 498 484.29 146 485.01 75 483.57 3 485.35 054 SBC 488.68 39 485.38 04 491.05 76 494.68 678 488.87 054 491.12 3 488.15 21 491.45 599 Q 7.458 5.583 7.246 5.069 5.466 5.018 4.532 4.701 Note: In all Cases d=2
Table 3: Optimum Model for Forecasting
Variable
Optimum
Model C AR1 AR2 MA1 MA2 AIC SBC Q
Iterat ions
No. of units
ARIMA(1, d,0) -25.39 0.061 244 624.1 063 627.1 59 9.3
98 1
Direct employmen t ARIMA(2, d,2) -54.14 42 0.867 29 -0.694 68 1.132 019 -0.995 17 704.7 775 712.4 093 5.8
26 12
Fixed Investment ARIMA(1, d,1) 11.21 315 0.596 046 0.993 615 381.0 161 385.5 952 3.5
94 10 ARIMA(0, 61.06 0.516 482.3 485.3 5.5
Note: In all Cases d=2
Table 4: Forecasts on the basis of Optimum Model
Year No. of units
Direct employment
Fixed
Investment Production
2007-08 206499.3423 961401.2809 6387.31395 32816.15406 2008-09 207261.0613 971969.6597 6761.29781 35065.83157 2009-10 207997.3964 982991.4036 7150.873 37376.57606 2010-11 208708.3467 993409.3768 7554.27094 39748.38755 2011-12 209393.9123 1002943.965 7970.43748 42181.26602 2012-13 210054.0931 1012087.03 8398.74427 44675.21148 2013-14 210688.8891 1021459.398 8838.81681 47230.22393 2014-15 211298.3004 1031257.823 9290.43188 49846.30336 2015-16 211882.3268 1041221.673 9753.45642 52523.44979 2016-17 212440.9686 1050988.224 10227.81112 55261.6632 2017-18 212974.2255 1060423.946 10713.44872 58060.9436 2018-19 213482.0977 1069665.002 11210.34103 60921.29098 2019-20 213964.585 1078922.248 11718.47127 63842.70536
CAGRs 0.3 0.96 5.18 5.68
R ES ULTS AN D D I S CUS S I O N
The r e s ult s ha ve b e e n d is c us s e d in b r ie f und e r t he fo llo wing s ub - he a d s :
S t a t i o na ri t y o f Ti me - S e ri e s :
I n o r d e r t o c o nfir m t he me a n s t a t io na r it y a nd t o c a lc ula t e a p p r o p r ia t e le ve l o f d iffe r e nc ing, c o r r e lo gr a m a nd Lj ung Bo x Q - s t a t is t ic s we r e c o mp ut e d fo r o r igina l a nd a ft e r d iffe r e nc ing o f d a t a up t o s e c o nd le ve l ( figur e s a nd r e s ult s fo r t he o r igina l s e r ie s a r e no t s ho wn he r e fo r t he c a us e o f s imp lic it y a nd b r ie fne s s ) . All t he e mp ir ic a l r e s ult s c o nfir me d t ha t a ft e r t he s e c o nd d iffe r e nc ing a ll t he fo ur va r ia b le s a c hie ve d s t a t io na r it y ( d e t a ils a r e no t d is c us s e d he r e ) .
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I n t his s t e p a ft e r c o mp a r ing S a mp le Aut o c o r r e la t io n F unc t io ns a nd P a r t ia l Aut o c o r r e la t io n func t io ns wit h t he ir t he o r e t ic a l c o unt e r p a r t s , it wa s fo und t ha t t he va lue o f AR a nd M A p r o c e s s d id no t e xc e e d e d t he o r d e r 2 . I n o r d e r t o o ve r c o me t he s ub j e c t ivit y in s e le c t io n o f t he a p p r o p r ia t e o r d e r o f ARI M A mo d e l in t he p r e s e nt s t ud y we ha ve c o ns id e r e d a l t he p o s s ib le e ight c o mb ina t io ns o f ARI M A mo d e ls d e p e nd ing o n t he va lue s o f p , d , q a s p a nd q c a n t a k e a ny va lue o ut o f 0 , 1 , 2 . The p o s s ib le c o mb ina t io ns a r e : {( 1 , d , 0 ) ; ( 2 . d , 0 ) ; ( 0 , d , 1 ) ; ( 1 , d , 1 ) ; ( 2 , d , 2 ) ; ( 0 , d , 2 ) ; ( 1 , d , 2 ) & ( 2 , d , 1 . ) } . He r e , fo r a ll t he e ight mo d e ls t he va lue o f‘d’ a s a lr e a d y id e nt ifie d 1 s 2 .
Es t i ma t i o n o f di f f e re nt O rde re d AR I M A mo de l s :
As d is c us s e d e a r lie r , in o r d e r t o ma k e c ho ic e fo r s uit a b le fo r e c a s t ing mo d e ls , ARI M A p r o c e s s o f t he o r d e r ( 1 , 2 , 0 ) , ( 2 . 2 , 0 ) , ( 0 , 2 , 1) , ( 1 , 2 , 1) , ( 2 , 2 , 2 ) , ( 0 , 2 , 2 ) , ( 1 , 2 , 2 ) , ( 2 , 2 , 1 ) we r e e s t ima t e d o n a ll t he d a t a o f fo ur va r ia b le s . F o r e s t ima t ing p a r a me t e r s o f s e le c t e d mo d e ls , we ha ve s t a r t e d wit h s o me init ia l va lue s o f Ci Φ1 , Φ2 , 1 θ2 fo r d iffe r e nt o r d e r e d mo d e ls a s e xhib it e d in Ta b le 1 .
I ns e r t Ta b le 1
The n we mo d ifie d init ia l va lue s b y s ma ll s t e p s , while o b s e r ving s um o f s q ua r e d r e s id ua l. W e ha ve s e le c t e d t ho s e va lue s o f p a r a me t e r s a s t he fina l e s t ima t e s in c a s e o f whic h s um o f s q ua r e d r e s id ua ls w e r e le a s t . The e s t ima t e s o f p a r a me t e r s he r e us e d in t he la s t s t a ge t o c a lc u la t e ne w va lue s ( fo r e c a s t s ) o f t he s e r ie s . I n t he p r e s e nt e xe r c is e e s t ima t io n wa s p e r fo r me d o n t r a ns fo r me d ( d iffe r e nc e d ) d a t a a nd b e fo r e ge ne r a t ing fo r e c a s t s we ha ve
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int e gr a t e d ( inve r s e o f d iffe r e nc ing) t he s e r ie s t o ma k e fo r e c a s t s c o mp a t ib le wit h t he input data. Estimation of the Models’ parameters was carried out t hr o ugh ma ximum lik e liho o d me t ho d ( Bo x, J e nk ins a nd Re ins e ll, 1 9 9 4 , p . 2 2 5 ) .
D i a g no s t i c t e s t i ng o f di f f e re nt AR I M A mo de l s :
I n t his s t a ge s e le c t io n o f b e s t fit t e d mo d e ls a nd it s a d e q ua c y wa s c he c k e d o n t he b a s is o f va r io us c r it e r ia a s me nt io ne d e a r lie r in e q ua t io ns 2 t o 5 . As p e r t he a b o ve me nt io ne d me a s ur e s , a mo d e l is c o ns id e r e d b e s t fo r ne xt s t a ge i. e . fo r e c a s t ing if it p o s s e s s e s minimum s um o f s q ua r e s o f r e s id ua ls , minimum va lue o f s t a nd a r d e r r o r , minimum AI C va lue , minimum va lue o f S BC , a nd minimum va lue o f no n- s ignific a nt Bo x- Lj ung Q s t a t is t ic s . Alt e r na t ive mo d e ls fo r e a c h va r ia b le we r e e xa mine d c o mp a r ing t he va lue s o f t he s e p a r a me t e r s . O nly t ha t mo d e l in c a s e o f e a c h va r ia b le ha s b e e n s e l e c t e d whic h s a t is fie d ma ximum numb e r o f a b o ve me nt io ne d c r it e r io n.
Va lue s o f t he a b o ve me nt io ne d c r it e r io n ( e xc e p t c o r r e lo gr a m o f r e s id ua ls ) c o mp ut e d fr o m t he d iffe r e nt o r d e r e d ARI M A mo d e ls fo r e a c h va r ia b le ha ve b e e n p r e s e nt e d in Ta b le 2 . Almo s t in a ll t h e c a s e s fo r d iffe r e nt o r d e r ARI M A mo d e ls , c o r r e lo gr a m o f r e s id ua ls s ho we d no s e r ia l d e p e nd e nc y ( C o r r e lo gr a m fo r r e s id ua ls a r e no t s ho wn he r e a s t he numb e r o f figur e s w e r e la r ge ) .
I ns e rt Ta bl e 2
Ta b le 2 d e p ic t s t he va lue s o f a ll t he p a r a me t e r s in c a s e o f a l l t he fo ur va r ia b le s . Exa mina t io n o f Ta b le 2 ha s r e ve a le d t ha t in c a s e o f numb e r o f unit s , AI C a nd S BC we r e minimum i. e . 6 2 4 . 1 0 6 2 8 a nd 6 2 7 . 1 5 9 r e s p e c t ive ly
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fo r t he mo d e l ( 1 , 2 , 0 ) . S um o f s q ua r e o f e r r o r s wa s o b s e r ve d lo we s t fo r t he mo d e l ( 1 , 2 , 2 ) t o t he t une o f 1 6 5 3 2 6 8 9 7 . 2 , while lo we s t va lue ( 8 . 6 9 3 ) o f Q -s t a t i-s t ic -s wa -s fo und fo r t he mo d e l o f t he o r d e r ( 2 , 2 , 2 ) . W hile lo we -s t -s t a nd a r d e r r o r wa s o b s e r ve d a s 2 2 7 5 . 0 6 8 in c a s e o f t he mo d e l ( 0 , 2 , 1 ) . F ur t he r p e r us a l o f Ta b le 2 s ho ws t ha t AI C ( 7 0 0 . 6 2 2 3 5 ) a nd S B C ( 7 0 3 . 6 7 5 0 7 we r e le a s t in c a s e o f t he mo d e l ( 0 , 2 , 1 ) while s um o f s q ua r e o f e r r o r s ( 1 9 8 7 2 6 0 1 7 7 . 9 ) , s t a nd a r d e r r o r ( 6 8 7 4 . 5 3 3 5 ) a s we ll a s Q - s t a t is t ic s ( 5 . 8 2 6 ) o b s e r ve d minimum fo r t he mo d e l ( 2 , 2 , 2 ) . F ur t he r gla nc e a t Ta b le 2 e xhib it e d t ha t s um o f s q ua r e o f e r r o r s ( 1 2 2 2 1 4 . 5 0 ) a nd Q - s t a t is t ic s ( 3 . 8 7 0 ) we r e minimum fo r t he mo d e ls ( 2 , 2 , 2 ) a nd ( 2 , 2 , 1 ) r e s p e c t ive ly in c a s e o f t he va r ia b le fixe d c a p it a l inve s t me nt . W he r e a s , s t a nd a r d e r r o r ( 6 1 . 0 5 2 1 9 5 ) , AI C ( 3 8 1 . 0 1 6 0 8 ) a nd S BC ( 3 8 5 . 5 9 5 1 6 ) we r e o b s e r ve d minimum fo r t he mo d e l ( 1 , 2 , 1 ) . A c lo s e e xa mina t io n o f Ta b le 2 ha s r e ve a le d t ha t in c a s e o f t he p r o d uc t io n, t he s t a nd a r d e r r o r ( 2 8 1 . 5 7 3 9 7 ) , AI C ( 4 8 2 . 3 2 7 6 9 ) a nd S BC ( 4 8 5 . 3 8 0 4 1 ) we r e minimum fo r t he mo d e l ( 0 , 2 , 1 ) , while in c a s e o f Q - s t a t is t ic s minimum va lue o f 4 . 5 3 2 wa s o b s e r ve d in c a s e o f mo d e l o f t he o r d e r ( 2 , 2 , 0 ) a s c o mp a r e d t o o t he r c o mp e t ing mo d e ls , whe r e a s le a s t s um o f s q ua r e o f e r r o r s wa s d e t e c t e d minimu m i. e . 2 4 4 8 2 8 6 . 0 fo r t he mo d e l ( 2 , 2 , 2 ) .
The o p t imum mo d e ls ( b a s e d o n s a t is fa c t io n o f ma ximum n umb e r o f c r it e r io n b y a p a r t ic ula r mo d e l) ha ve b e e n e xp r e s s e d in Ta b le 3 . P e r us a l o f Ta b le 3 r e ve a le d t ha t t he mo d e ls ( 1 , 2 , 0 ) , ( 2 , 2 , 2 ) , ( 1 , 2 , 1) , a nd ( 0 , 2 , 1 ) we r e o p t imum in c a s e o f t he va r ia b le s : numb e r o f unit s , d ir e c t e mp lo yme nt , fixe d c a p it a l inve s t me nt a nd p r o d uc t io n r e s p e c t ive ly.
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I ns e rt Ta bl e 3
Fo re c a s t s :
Aft e r e xt r a c t ing t he o p t imum mo d e ls fo r ge ne r a t io n o f fo r e c a s t s , t he ne xt s t e p is t o p r e p a r e fo r e c a s t s o f numb e r o f unit s , e mp lo yme nt , c a p it a l inve s t me nt a nd p r o d uc t io n o f s ma ll s c a le ind us t r ia l s e c t o r o f W e s t Be nga l. Ta b le 4 highlight s fo r e c a s t s o f numb e r o f unit s , e mp lo yme nt , fixe d c a p it a l, inve s t me nt a nd p r o d uc t io n fo r le a d t ime o f 1 3 ye a r s b a s e d o n o p t ima l mo d e ls .
I ns e rt Ta bl e 4
P e r us a l o f Ta b le 4 r e ve a le d t ha t in t he ye a r 2 0 0 7 - 0 8 , t he p r e d ic t e d numb e r s o f unit s a r e 2 0 5 7 1 2 , e xp e c t e d t o r is e t o 2 0 7 2 6 1 in 2 0 0 9 - 1 0 a nd t o 2 1 1 8 8 2 in 2 0 1 5 - 1 6 a nd fina lly e xp e c t e d t o b e 2 1 3 9 6 4 b y t he ye a r 2 0 1 9 - 2 0 . Exa mina t io n o f Ta b le 4 d e p ic t s t ha t t he fo r e c a s t s fo r t he d ir e c t e mp lo yme nt in s ma ll s c a le ind us t r ia l s e c t o r o f W e s t Be nga l a r e 9 6 1 4 0 1 in 2 0 0 7 0 8 a nd 9 8 2 9 9 1 in 2 0 0 9 -1 0 a nd fur t he r e xp e c t e d t o inc r e a s e t o -1 0 -1 2 0 8 7 in 2 0 -1 2 - -1 3 a nd wo uld p r o b a b ly gr o w t o 1 0 7 8 9 2 2 in 2 0 1 9 - 2 0 . F ur t he r e xa mina t io n o f Ta b le 4 s ho ws t ha t fixe d c a p it a l inve s t me nt wa s e xp e c t e d t o b e 6 7 3 8 7 . 3 2 Rs . C r o r e in t he ye a r 2 0 0 7 - 0 8 , wo uld p r o b a b ly r is e t o 7 9 7 0 . 4 3 Rs . C r o r e in 2 0 1 1 - 1 2 a nd t he n t o 1 0 7 1 3 . 4 4 Rs . C r o r e in 2 0 1 7 - 1 8 a nd fina lly e xp e c t e d t o e xp a nd t o 1 1 7 1 8 . 4 7 Rs . C r o r e in 2 0 1 9 - 2 0 . Ta b le 4 a ls o r e ve a le d t ha t p r o d uc t io n is a nt ic ip a t e d t o e xp a nd fr o m 3 2 8 1 6 . 1 5 Rs . C r o r e in 2 0 0 7 0 8 t o 3 5 0 6 5 . 8 3 Rs . C r o r e in 2 0 0 8 -0 9 . I t is fur t he r a nt ic ip a t e d t ha t t he p r o d uc t io n figur e wo uld gr o w t o 5 2 5 2 3 . 4 4 Rs . C r o r e in 2 0 1 5 - 1 6 a nd t he n t o 6 3 8 4 2 . 7 0 Rs . C r o r e t ill 2 0 1 9 - 2 0 . As fa r gr o wt h o f numb e r o f unit s is c o nc e r ne d , t he y a r e e xp e c t e d t o gr o w a t
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c o mp o und a nnua l r a t e o f 0 . 3 0 while e mp lo yme nt , inve s t me nt a nd p r o d uc t io n wo uld p r o b a b ly gr o w a t t he r a t e o f 0 . 9 6 , 5 . 1 8 a nd 5 . 6 8 p e r c e nt r e s p e c t ive ly. This c le a r ly ind ic a t e s t ha t in t he c o ming d a ys no t o nly p r o d uc t ivit y o f c a p it a l b ut c a p it a l int e ns it y will a ls o inc r e a s e . But t he me a ge r r a t e o f gr o wt h o f e mp lo yme nt c o nfir ms t ha t in s ub s e q ue nt ye a r s t he r e is le s s s c o p e o f la b o ur a b s o r p t io n in t he S ma ll S c a le I nd us t r ia l o f W e s t Be nga l.
Co nc l udi ng R e ma rk s :
N o d o ub t , W e s t Be nga l is b a s ic a lly a n a gr ic ult ur a l s t a t e b ut it ha s ma d e ho ne s t e ffo r t s t o p r o vid e imp e t us t o t he ind us t r ia l s e c t o r e s p e c ia lly s ma ll s c a le ind us t r ia l s e c t o r ( Gup t a , 2 0 0 6 ) . The Aut o Re gr e s s ive I nt e gr a t e d M o ving Ave r a ge ( ARI M A) mo d e l t hr o ugh Bo x - J e nk ins a p p r o a c h ha s b e e n us e d t o ge ne r a t e fo r e c a s t s r e ga r d ing va r ia b le s o f s ma ll s c a le ind us t r ia l s e c t o r o f W e s t Be nga l. I t is e xp e c t e d t ha t numb e r o f unit s a nd e mp lo yme nt wo uld p r o b a b ly gr o w a t a s lo we r p a c e a s c o mp a r e d t o inve s t me nt a nd p r o d uc t io n. The fo r e c a s t s ha ve d e p ic t e d a b r ight p ic t ur e a he a d b ut wit h lo w s c o p e o f e mp lo yme nt o p p o r t unit ie s fo r la b o ur e r s . The s e fo r e c a s t s c a n p r o vid e Go ve r nme nt a nd p o lic y ma k e r s a d ir e c t io n t o d e s ign p o lic ie s a c c o r d ingly t o p us hup gr o wt h in t his s e c t o r .
I n t he light o f t he fo r e c a s t s it is r e q uir e d o n t h e p a r t o f t he s t a t e go ve r nme nt t o t a k e a ll s o r t c o nc e r t e d e ffo r t s init ia t ive s t o s t r e ngt he n t he ind us t r ia l b a s e in W e s t Be nga l. I n t his r e ga r d c a t a s t r o p hic c ha nge s a r e r e q uir e d s o fa r a s
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ind us t r ia l p o lic y o f W e s t Be nga l is c o nc e r ne d . W e s t Be nga l go ve r nme nt s ho uld a nno unc e p a c k a ge o f inc e nt ive s no t o nly fo r e xis t ing ind us t r ia lis t s b ut a ls o fo r ne w ve nt ur is t s . M o r e o ve r t a x b e ne fit s , lo a n o n s o ft - t e r ms a nd infr a s t r uc t ur a l fa c ilit ie s s ho uld b e in t he p r io r it y lis t o f ind us t r ia l b lue p r int o f W e s t Be nga l. La s t b ut no t t he le a s t wo ma n e nt r e p r e ne ur s hip s ho uld b e p r o mo t e d in t he s t a t e a t p a r wit h le a d ing ind us t r ia l e c o no mie s o f t he wo r ld , t o p r o vid e s t r o ng fo o t ing t o s ma ll S c a le ind us t r y o f W e s t Be ng
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