Forecasting model of small scale industrial sector of West Bengal

Volltext

(1)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/ MPRA Paper No. 28144, posted 18 Jan 2011 20:07 UTC.

(2) Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. Forecasting model of small scale industrial sector of West Bengal. Soumitra Kumar Bera BSc Economics (CU), MFT (BHU), PhD (NEHU) soumitramac@gmail.com. Ec o no mic. fo r e c a s ting. ha s. lo ng. e nga ge d. the. a tte ntio 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 the fa c e o f unc e r ta intie 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 ts . I f the fo r e c a s ts s ugge s t a. d is ma l p ic tur e a he a d , the n e c o no mic s ys te m ma y d o its b e s t to c ha nge the. s c e na r io s o tha t glo o my fo r e c a s ts ma y no t c o me tr ue . F o r e c a s ting invo lve s p r e d ic ting futur e va lue s o f e c o no mic va r ia b le s with a s little e r r o r a s p o s s ib le. ( Gup ta , 2 0 0 3 ) . F o r this p ur p o s e , fo r e c a s te r s ha ve e mp lo ye d va r io us time s e r ie s te c hniq ue s in s ho r t r un e c o no mic fo r e c a s ting. Amo ng the va r io us. me tho d s o f fo r e c a s ting, the Auto - Re gr e s s ive I nte gr a te d M o ving Ave r a ge ( ARI M A) mo d e l, tho ugh c o mp lic a te d o ne , is a p o we r ful me tho d to ge ne r a te a c c ur a te. fo r e c a s ts. in. the. s ho r t - r un. witho ut. invo lving. e c o no mic. the o r y. ( M a k r id a k is , 1 9 9 8 ) .. The r e a r e q uite a fe w a nd no te wo r thy e mp ir ic a l a tte mp ts ma d e b y. r e s e a r c he r s to ge ne r a te e c o no mic fo r e c a s ts . N o ta b le a mo ngs t the m a r e : Sabia. 1.

(3) (1977) , Bawa (1980), Nachane (1981) , Bowersox (1981), Bowersox (1981), Ibrahim and Otsuki (1982), Armstrong (1983), Mentzer (1984), Fildes (1984), Sarkar (1989), Poonam and Gupta. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. (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 ting a t ma c r o a nd mic r o le ve l is q uite p o p ula r in. the we s t b ut its a p p lic a tio n to I nd ia n d a ta , e s p e c ia lly in ind us tr ia l s e c to r is. r a r e a nd the r e s e e ms to b e n o t a s ingle c o mp r e he ns ive s tud y d e a ling with ge ne r a tio n. fo r e c a s ts. o f s ma ll s c a le. ind us tr ia l s e c to r. a t a ggr e ga te a nd. d is a ggr e ga te le ve l. K e e p ing this fa c t into c o ns id e r a tio n p r e s e nt s tud y is a n e nd e a vo r in this d ir e c tio 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 the ind us tr ia l ma p o f I nd ia. whic h is a ttr ib uta b le to its s ma ll- s c a le ind us tr ia l s e c to r ( La l, 1 9 6 6 ) . The s ta te inhe r ite d a ve r y we a k ind us tr ia l b a s e whe n p a r titio 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 ntly it ha s b e e n thr o ugh a p e r io d o f tur b ule nc e whic h no t o nly a ffe c te d the ind us tr ia l. gr o wth a d ve r s e ly b ut te nd e d to c a us e s o me o ut - migr a tio n o f ind us tr y to o . W ith the r e s to r a tio n o f p e a c e , th e s ta te go ve r nme nt tr ie d to a c tiva te the. p r o c e s s o f ind us tr ia l d e ve lo p me nt with the ho p e to e nte r into a ne w e r a o f p r o gr e s s ( Bha tia , 1 9 9 9 ) .. Obje c t iv e s o f t he s t ud y. 2.

(4) P r e s e nt s tud y ha s b e e n c o nd uc te d k e e p ing in mind the fo llo wing o b je c tive s : 1 . To ge ne r a te fo r e c a s ts o f p r o d uc tio n, d ir e c t e mp lo yme nt, fixe d c a p ita l a nd. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. numb e r o f units o f s ma ll s c a le ind us tr ia l s e c to 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 te fo r e c a s ting mo d e l to p r e p a r e fo r e c a s ts o f s ma ll s c a le ind us tr ia l s e c to r o f W e s t Be nga l.. D a t a ba s e a nd Ana ly t ic a l Fra me wo rk :. P r e s e nt s tud y is b a s e d o n s e c o nd a r y d a ta fo r the p e r io d 1 9 7 0 - 7 1 to 2 0 0 6 - 0 7 . The. a ggr e ga te. e mp lo yme nt,. d a ta. fixe d. r e la ting. to. c a p ita l a nd. the. va r ia b le s : numb e r. p r o d uc tio n. o f units ,. o f s ma ll- s c a le. d ir e c t. ma nufa c tur ing. ind us tr 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 to r a te o f I nd us tr ie s , W e s t Be nga l. The fo r e c a s ts o f the a b o ve me ntio ne d va r ia b le s fo r a le a d time o f 1 3 ye a r s we r e ge ne r a te d a p p lying o f ‘ Bo x- J e nk ins ’ ARI M A me tho d .. The. p r e s e nt. s o p his tic a te d. paper. is. univa r ia te. an. e nd e a vo r. to. Bo x - J e nk ins. ge ne r a te. ARI M A. fo r e c a s ts. mo d e ling.. b y a p p lying. Univa r ia te Bo x -. J e nk ins ( UBJ ) a p p r o a c h is b a s e d o n id e ntifying the p a tte 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 the n e xtr a p o la ting the p a tte r n in the p a s t fo r. ne a r futur e a s we ll ( P a nk r a tz, 1 9 8 3 ; M a k r id a k is 1 9 8 7 ) . O ne o f the a d va nta ge s. o f Bo x- J e nk ins o ve r o the r fo r e c a s ting mo d e ls is tha t this mo d e ling is no t b a s e d o n e c o no mic the o r y a nd c a p a b le o f c a p tur ing s lighte s t va r ia tio n in the. d a ta ( M a k r id a k is , 1 9 7 8 ) . Bo x - J e nk ins me tho d o lo gy r e s ts o n the s imp lifying a s s ump tio n tha t the p r o c e s s whic h ha s ge ne r a te d a s ingle time s e r ie s , is the. s ta tio na r y p r o c e s s b ut unfo r tuna te ly mo s t time s e r ie s e nc o unte r e d a r e r a r e ly. 3.

(5) s ta tio na r y,. s till it. a p p r o p r ia te. is p o s s ib le to. le ve l o f d iffe r e nc ing. tr a ns fo r m the m to ( ma ximum up. to. s ta tio na r y b y the. s e c o nd. le ve l). ( Bo x. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. &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 tr a ns fo r ms a no n s ta tio na r y s e r ie s into a s ta tio na r y o ne . I f no n - s ta tio na r y is a d d e d to a mixe d. ARI M A mo d e l, the n the ge ne r a l ARI M A ( p , d , q ) is o b ta ine d , it ha s the fo r m a s und e r :. Φ P ( B ) ( 1 - B ) d Yt = C + θ q ( B ) e t or. Φ P ( B ) Wt = C + θ q ( B ) e t. … (1). whic h will b e no n- s ta tio na r y unle s s d = 0 .. The mo d e l is s a id to b e o f the 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 te nta tive ly id e ntifie d o ne o r mo r e mo d e ls tha t s e e m lik e ly to p r o vid e p a r s imo nio us a nd s ta tis tic a lly a d e q ua te r e p r e s e nta tio n o f a va ila b le d a ta , the ne xt s te p is to e s tima te the. va lue s o f the p a r a me te r s . S um o f s q ua r e s o f the r e s id ua ls we r e c o mp ute d b y us ing ma ximum lik e liho o d. e s tima tio n me tho d give n the r e s p e c tive initia l. e s tima te s o f the p a r a me te r s , o p timum va lue s o f the p a r a me te r s we r e s e a r c he d. b y imp r o ving the initia l e s tima te s ite r a tive ly b y s up p le me nting the m wi th the info r ma tio n c o nta ine d in the time s e r ie s .. F o r a give n mo d e l invo lving k. p a r a me te r s , the ite r a tive p r o c e d ur e wa s c o ntinue d till the d iffe r e nc e b e twe 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 tha t c o uld b e. igno r e d fo r p r a c tic a l c o ns id e r a tio ns ( Bo x, J e nk ins a nd Re ins e ll, 1 9 9 4 , p . 2 2 5 ) .. 4.

(6) I n o r d e r to ma k e a n a s s e s s me nt o f the va lid ity o f the e s tima te d mo d e ls fo r the give n time s e r ie s , fo llo wing d ia gno s tic me a s ur e s we r e wo r k e d o ut: o f re s idua ls : The a uto c o r r e la tio n c o e ffic ie nt wa s. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. ( a ) Aut o c o rre la t io ns. wo r k e d o ut b y a p p lying fo r mula give n in the e q ua tio n ( 2 ) .. rk ( e ) =. n- k ∑ e t . e t +k t=1 -----------------; k = 1,2,…ℓ n ∑ et 2 t=1. …(2). The ma jo r c o nc e r n o f AC F o f r e s id ua ls wa s tha t whe the r the r e s id ua ls we r e. s ys te ma tic a lly d is tr ib ute d a c r o s s the s e r ie s o r the y c o nta in s o me s e r ia l d e p e nd e nc y ( Box & Pierce, 1970). Ac c e p ta nc e o f the hyp o the s e s o f s e r ia l d e p e nd e nc y c o nc lud e s tha t the e s tima te d ARI M A mo d e l is ina d e q ua te .. ( b) Po rt ma nt e a u Te s t : Ljung- Bo x Q s ta tis tic s wa s c o mp ute d fr o m the mo d e l’ s r e s id ua ls b y us ing. ℓ Q = n ( n+ 2 ) ∑ r k ( e ) 2 ( n- k ). -1. …( 3 ). N o n- s ignific a nc e o f p o r tma nte a u te s t wa s ta k e n to imp ly the ge ne r a te d r e s id ua ls c o uld b e c o ns id e r e d a white no is e , the r e b y ind ic a ting the a d e q ua c y o f e s tima te d mo d e l ( DeLurgio. 1998).. 5.

(7) ( 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 the e r r o r s o f fitte d mo d e ls wa s c o mp ute d . W e s e le c te d tha t mo d e l a d e q ua te , in c a s e o f whic h S S E. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. wa s minimu m.. ( d) Ak a ik e I nf o rma t io n Crit e ria ( AI C) : AI C wa s c o mp ute d to d e te r mine. b o th ho w we ll the mo d e l fits the o b s e r ve d s e r ie s , a nd the numb e r o f p a r a me te r us e d in the fit.. W e c o mp a r e d the va lue AI C with o the r fitte d. mo d e l to the s a me d a ta s e t a nd we s e le c te d tha t fitte d mo d e l a d e q ua te in c a s e o f whic h AI C wa s minimum. The AI C is c o mp ute d a s und e r :. … (4). AI C = n lo g ( S S E) + 2 k. whe r e. k. = N umb e r o f p a r a me te r s tha t a r e fitte d in the mo d e l. lo g. = N a tur a l lo ga r ithm. n. = numb e r o f o b s e r va tio ns in the s e r ie s. SSE. = S um o f S q ua r e d Er r o r s. W hile s e le c ting a d e q ua te 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 ta ntia l a nd we s e le c te d the s imp le mo d e l with le s s e r p a r a me te r s . (e ). S c hwa rz B a y e s ia n I nf o rma t io n Crit e ria ( S B C) : S BC is a mo d ific a tio n. to AI C ; it is b a s e d o n Ba ye s ia n c o ns id e r a tio n. Lik e AI C it wa s c o mp ute d to. d e te r mine ho w we ll the mo d e l fits a mo ngs t the c o mp e ting mo d e ls , a nd we s e le c te d tha t mo d e l a d e q ua te 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 lo g ( S S E) + k lo g ( n). 6. … (5).

(8) O n the b a s is o f a b o ve me ntio ne d ya r d s tic k , fina lly s e le c te 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 ting a s d is c us s e d a s fo llo ws .. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. F o r ma k ing fo r e c a s ts e q ua tio n ( 2 ) wa s uns c r a mb le d to e xp r e s s Yt a nd e t b y us ing the r e la tio n W t = ( 1 - B) d Y t . Give n the d a ta up to time t the o p tima l Λ. fo r e c a s ts o f Y t. +. ℓ. [ d e s igna te d b y Y t ( ℓ ) ] ma d e a time t wa s ta k e n a s. c o nd itio na l e xp e c ta tio n o f Y t + ℓ , whe r e t, is the fo r e c a s t o r igin a nd ℓ is the. fo r e c a s t le a d - time . Er r o r te r m e t c o mp le te ly d is a p p e a r e d o nc e we ma d e fo r e c a s ts mo r e tha n q p e r io d a h e a d .. Thus fo r ℓ > q , the n ℓ p e r io d a he a d. fo r e c a s t wa s ma d e a s und e r :. ^ ^ ^ ^ ^ ^ Yt + ℓ = C + Φ 1 Yt +ℓ-1 + … + Φ p Yt +ℓ-p. …(7). Table 1: Initial estimate of the Parameters. Variable. ARIMA (1,d,o). C. No. of units Direct employm ent Fixed Investme nt. Productio n. 25.3 9 114. 502. 8.52 264 58.1 952 7. AR1 0.06 124 4 0.22 072 0.17 886 0.33 037. ARIMA (0,d,1) MA 1 C 25.4 0.05 4 749 124. 0.22 478 027 8.88 0.33 019 259 2 8 61.0 0.51 669 621 8 2. ARIMA (1,d,1) MA 1 C AR1 - 0.35 0.29 24.9 500 087 64 6 5 120. 0.07 0.15 728 906 054 11.2 0.59 0.99 131 604 361 5 6 5 68.0 826. 0.63 614. 7. 0.99 27. C. 22.6 176 54.1 442 11.2 804 61.7 058 4. ARIMA (2,d,2) AR MA 1 1 AR2 - 0.36 0.41 162 0.56 74 5 961 - 1.13 0.86 0.69 201 729 468 9 - 0.56 0.43 913 0.00 044 1 247 0.88 0.65 0.44 456 238 587. MA 2 0.40 080 8 0.99 517 0.99 208 8 0.49 198.

(9) ARIMA (0,d,2) MA M 1 A2 0.05 0.0 5 42 0.24 0.0 2 45. ARIMA (1,d,2) A R MA M C 1 1 A2 - 0. 24. 25 0.19 0.0 44 6 89 316 14 0. 0.63 0.2 0.2 82 7 352 0. 10. 72 1.12 0.1 87 1 09 21 62. 0. 0.39 0.5 02 81 6 269. ARIMA (2,d,o) AR 1. ARIMA (2,d,1) AR 1. AR 2 0.0 246 3 0.2 724 0.0 405 0.2 522. M A1 0.1 88 8 0.8 65 0.9 97 2 0.2 71 9. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. Variable. No. of units Direct employm ent Fixed Investme nt. C 24. 62 11 5.5 10. 86 7. Producti on. 61. 66. 0.38 87. 0.3 37. 0.06 45. 0.0 65. C. 24.6 6 129. 1. 9.01 58 59.3 13. AR2. 0.0 59 0.2 34 0.2 19 0.4 46. 0.03 487 0.07 44. -0.2 0.32 87. C 24. 59 13 2.2 11. 31 2 60. 42 5. 0.24 78 1.07 4 0.61 33. 0.21. Note: In all Cases d=2. Table 2: Comparative Results from Various Models. Variable No. of units. Estima te Sum of Square s Standa rd error AIC. Direct employ ment. SBC Q Sum of Square s Standa rd. ARIM A (1,d,o). ARIM A (0,d,1). ARIM A (1,d,1). 1.66E+ 08. 1.65E+ 159315 165401 1.65E+ 08 396 646 08. 1.65E+ 165364 08 076.8. 2274.7 63 624.10 63 627.15 9 9.398. 1.66E+ 08 310.05 7 624.11 5 627.16 77 9.465. 2309.9 49 626.15 12 630.73 03 9.275. 2317.4 78 629.03 157 636.66 337 8.693. 2309.6 644 626.14 387 630.72 293 9.196. 2347.2 68 628.24 3 634.34 85 9.197. 2309.5 86 626.14 15 630.72 05 9.2. 1.57E+ 09 7009.6 98. 1.57E+ 09 7003.9 58. 1.57E+ 148726 09 0178 7112.9 6874.5 73 335. 1.569E +09 7108.4 871. 1.55E+ 09 7175.3 3. 1.57E+ 153576 09 1371 7102.0 7134.2 94 047. 8. 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). 2347.5 677 628.25 078 634.35 622 9.234.

(10) error AIC. 700.62 24 703.67 51 8.709. 702.67 4 707.25 31 8.745. 704.77 747 712.40 927 5.826. 702.63 687 707.21 595 8.785. 704.33 82 710.44 37 7.646. 702.57 63 707.15 53 8.708. 704.00 241 710.10 785 7.573. 14326. 48. 139926. 122744 122214 130387 125146 122374 .8 .5 .34 .8 .63 138538. 66.892 99 384.32 88 387.38 16 6.828. 66.012 39 383.50 76 386.56 04 6.382. 61.052 2 381.01 61 385.59 52 3.954. 28207 09. 256031 272929 244828 255221 245385 249916 247551 5 1 6 5.4 4 0 3.7. 296.39 17 485.63 12 488.68 39 7.458. 281.57 4 482.32 77 485.38 04 5.583. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. SBC Q Sum of Square s Standa rd error. 700.67 83 703.73 1 8.781. Fixed Investm ent. AIC. Producti on. SBC Q Sum of Square s Standa rd error AIC. SBC Q. 288.52 02 486.47 85 491.05 76 7.246. 62.611 696 384.97 594 392.60 775 4.083. 286.96 581 487.05 498 494.68 678 5.069. 64.224 265 383.14 065 387.71 973 3.816. 285.68 924 484.29 146 488.87 054 5.466. 62.756 14 383.73 38 389.83 93 4.721. 283.00 97 485.01 75 491.12 3 5.018. 66.736 94 385.24 48 389.82 39 4.636. 282.48 36 483.57 3 488.15 21 4.532. 61.780 526 382.95 364 389.05 908 3.78. 285.64 443 485.35 054 491.45 599 4.701. Note: In all Cases d=2. Table 3: Optimum Model for Forecasting. Variable. No. of units Direct employmen t Fixed Investment Production. Optimum Model ARIMA(1, d,0) ARIMA(2, d,2) ARIMA(1, d,1) ARIMA(0, d,1). C 25.39 54.14 42 11.21 315 61.06 698. AR1 0.061 244. AR2. MA1. MA2. 0.867 0.694 1.132 0.995 68 17 29 019 0.596 0.993 046 615 0.516 212. 9. AIC 624.1 063. SBC 627.1 59. Q 9.3 98. 704.7 775 381.0 161 482.3 277. 712.4 093 385.5 952 485.3 804. 5.8 26 3.5 94 5.5 83. Iterat ions 1. 12 10 3.

(11) Note: In all Cases d=2. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. Table 4: Forecasts on the basis of Optimum Model Direct Fixed Year No. of units employment Investment 2007-08 206499.3423 961401.2809 6387.31395 2008-09 207261.0613 971969.6597 6761.29781 2009-10 207997.3964 982991.4036 7150.873 2010-11 208708.3467 993409.3768 7554.27094 2011-12 209393.9123 1002943.965 7970.43748 2012-13 210054.0931 1012087.03 8398.74427 2013-14 210688.8891 1021459.398 8838.81681 2014-15 211298.3004 1031257.823 9290.43188 2015-16 211882.3268 1041221.673 9753.45642 2016-17 212440.9686 1050988.224 10227.81112 2017-18 212974.2255 1060423.946 10713.44872 2018-19 213482.0977 1069665.002 11210.34103 2019-20 213964.585 1078922.248 11718.47127 CAGRs 0.3 0.96 5.18. Production 32816.15406 35065.83157 37376.57606 39748.38755 42181.26602 44675.21148 47230.22393 49846.30336 52523.44979 55261.6632 58060.9436 60921.29098 63842.70536 5.68. R ES ULTS AN D D I S CUS S I ON. The r e s ults ha ve b e e n d is c us s e d in b r ie f und e r the fo llo wing s ub - he a d s : S t a t io na rit y o f Time - S e rie s :. I n o r d e r to c o nfir m the me a n s ta tio na r ity a nd to c a lc ula te a p p r o p r ia te le ve l o f. d iffe r e nc ing, c o r r e lo gr a m a nd Ljung Bo x Q - s ta tis tic s we r e c o mp ute d fo r o r igina l a nd a fte r d iffe r e nc ing o f d a ta up to s e c o nd le ve l ( figur e s a nd r e s ults fo r the o r igina l s e r ie s a r e no t s ho wn he r e fo r the c a us e o f s imp lic ity a nd b r ie fne s s ) .. All. the. e mp ir ic a l. r e s ults. c o nfir me d. tha t. a fte r. the. s e c o nd. d iffe r e nc ing a ll the fo ur va r ia b le s a c hie ve d s ta tio na r ity ( d e ta ils a r e no t d is c us s e d he r e ) .. M o de l I de nt if ic a t io n:. 10.

(12) I n this s te p a fte r c o mp a r ing S a mp le Auto c o r r e la tio n F unc tio ns a nd P a r tia l Auto c o r r e la tio n func tio ns with t he ir the o r e tic a l c o unte r p a r ts , it wa s fo und. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. tha t the 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 the o r d e r 2 . I n o r d e r to. o ve r c o me the s ub je c tivity in s e le c tio n o f the a p p r o p r ia te o r d e r o f ARI M A mo d e l in the p r e s e nt s tud y we ha ve c o ns id e r e d. a l the. p o s s ib le. e ight. c o mb ina tio ns o f ARI M A mo d e ls d e p e nd ing o n the va lue s o f p , d , q a s p a nd q. c a n ta k e a ny va lue o ut o f 0 , 1 , 2 . The p o s s ib le c o mb ina tio 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. the e ight mo d e ls t he va lue o f‘ d ’ a s a lr e a d y id e ntifie d 1 s 2 .. Es t ima t io n o f dif f e re nt Orde re d AR I M A mo de ls :. As d is c us s e d e a r lie r , in o r d e r to ma k e c ho ic e fo r s uita b le fo r e c a s ting mo d e ls , ARI M A p r o c e s s o f the 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 tima te d o n a ll the d a ta o f. fo ur va r ia b le s . F o r. e s tima ting p a r a me te r s o f s e le c te d mo d e ls , we ha ve s ta r te d with s o me initia l va lue s o f C i Φ 1 , Φ 2 ,  1 θ 2 fo r d iffe r e nt o r d e r e d mo d e ls a s e xhib ite d in Ta b le 1 . I ns e r t Ta b le 1. The n we mo d ifie d initia l va lue s b y s ma ll s te 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 te d tho s e va lue s o f p a r a me te r s a s the fina l. e s tima te 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 tima te s o f p a r a me te r s he r e us e d in the la s t s ta ge to c a lc u la te ne w va lue s ( fo r e c a s ts ) o f the. s e r ie s .. In. the p r e s e nt e xe r c is e e s tima tio n wa s p e r fo r me d. on. tr a ns fo r me d ( d iffe r e nc e d ) d a ta a nd b e fo r e ge ne r a ting fo r e c a s ts we ha ve. 11.

(13) inte gr a te d ( inve r s e o f d iffe r e nc ing) the s e r ie s to ma k e fo r e c a s ts c o mp a tib le with the inp ut d a ta .. Es tima tio n o f the M o d e ls ’ p a r a me te r s wa s c a r r ie d o ut. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. thr o ugh ma ximum lik e liho o d me tho d ( Bo x, J e nk ins a nd Re ins e ll, 1 9 9 4 , p . 225).. D ia g no s t ic t e s t ing o f dif f e re nt AR I M A mo de ls :. I n this s ta ge s e le c tio n o f b e s t fitte d mo d e ls a nd its a d e q ua c y wa s c he c k e d o n the b a s is o f va r io us c r ite r ia a s me ntio ne d e a r lie r in e q ua tio ns 2 to 5 . As p e r. the a b o ve me ntio 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 ta ge i. e . fo r e c a s ting 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 ta 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- Ljung Q s ta tis tic s . Alte r na tive 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 the va lue s o f the s e p a r a me te r s .. O nly tha 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 te d whic h s a tis fie d ma ximum numb e r o f a b o ve me ntio ne d c r ite r io n.. Va lue s o f the a b o ve me ntio ne d c r ite 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 ute d fr o m the 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 nte d in Ta b le 2 . Almo s t in a ll th 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 the numb e r o f figur e s w e r e la r ge ) . I ns e rt Ta ble 2. Ta b le 2 d e p ic ts the va lue s o f a ll the p a r a me te r s in c a s e o f a l l the fo ur va r ia b le s . Exa mina tio n o f Ta b le 2 ha s r e ve a le d tha t in c a s e o f numb e r o f units , 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 tive ly. 12.

(14) fo r the 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 the mo d e l ( 1 , 2 , 2 ) to the tune 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 -. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. s ta tis tic s wa s fo und fo r the mo d e l o f the o r d e r ( 2 , 2 , 2 ) . W hile lo we s t s ta 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 the mo d e l ( 0 , 2 , 1 ) . F ur the r p e r us a l. o f Ta b le 2 s ho ws tha 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 the 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 ta 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 ta tis tic s ( 5 . 8 2 6 ) o b s e r ve d minimum fo r the mo d e l ( 2 , 2 , 2 ) . F ur the r gla nc e a t Ta b le 2 e xhib ite d tha 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 ta tis tic s ( 3 . 8 7 0 ) we r e minimum fo r the mo d e ls. ( 2 , 2 , 2 ) a nd ( 2 , 2 , 1 ) r e s p e c tive ly in c a s e o f the va r ia b le fixe d c a p ita l inve s tme nt. W he r e a s , s ta 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 the mo d e l ( 1 , 2 , 1 ) . A c lo s e e xa mina tio n o f Ta b le 2 ha s r e ve a le d tha t in c a s e o f the p r o d uc tio n, the. s ta 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 the mo d e l ( 0 , 2 , 1 ) , while in c a s e o f Q - s ta tis tic 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 the o r d e r ( 2 , 2 , 0 ) a s c o mp a r e d to o the r c o mp e ting 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 te c te d minimu m i. e . 2 4 4 8 2 8 6 . 0 fo r the mo d e l ( 2 , 2 , 2 ) .. The o p timum mo d e ls ( b a s e d o n s a tis fa c tio n o f ma ximum n umb e r o f c r it e r io n b y a p a r tic 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 tha t the mo d e ls ( 1 , 2 , 0 ) , ( 2 , 2 , 2 ) , ( 1 , 2 , 1) , a nd ( 0 , 2 , 1 ) we r e o p timum in c a s e o f the va r ia b le s : numb e r o f units , d ir e c t e mp lo yme nt, fixe d c a p ita l inve s tme nt a nd p r o d uc tio n r e s p e c tive ly.. 13.

(15) I ns e rt Ta ble 3 Fo re c a s t s :. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. Afte r e xtr a c ting the o p timum mo d e ls fo r ge ne r a tio n o f fo r e c a s ts , the ne xt s te p. is to p r e p a r e fo r e c a s ts o f numb e r o f units , e mp lo yme nt, c a p ita l inve s tme nt. a nd p r o d uc tio n o f s ma ll s c a le ind us tr ia l s e c to r o f W e s t Be nga l. Ta b le 4 highlights. fo r e c a s ts. of. numb e r. of. units ,. e mp lo yme nt,. fixe d. c a p ita l,. inve s tme nt a nd p r o d uc tio n fo r le a d time o f 1 3 ye a r s b a s e d o n o p tima l mo d e ls . I ns e rt Ta ble 4. P e r us a l o f Ta b le 4 r e ve a le d tha t in the ye a r 2 0 0 7 - 0 8 , the p r e d ic t e d numb e r s. o f units a r e 2 0 5 7 1 2 , e xp e c te d to r is e to 2 0 7 2 6 1 in 2 0 0 9 - 1 0 a nd to 2 1 1 8 8 2 in. 2 0 1 5 - 1 6 a nd fina lly e xp e c te d to b e 2 1 3 9 6 4 b y the ye a r 2 0 1 9 - 2 0 . Exa mina tio n. o f Ta b le 4 d e p ic ts tha t the fo r e c a s ts fo r the d ir e c t e mp lo yme nt in s ma ll s c a le ind us tr ia l s e c to 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 the r e xp e c te d to inc r e a s e to 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 to 1 0 7 8 9 2 2 in 2 0 1 9 - 2 0 . F ur the r e xa mina tio n o f Ta b le 4 s ho ws. tha t fixe d c a p ita l inve s tme nt wa s e xp e c te d to 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 to 7 9 7 0 . 4 3 Rs . C r o r e in 2 0 1 1 - 1 2 a nd the n to 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 te d to e xp a nd to 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 tha t p r o d uc tio n is a ntic ip a te d to. 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 to 3 5 0 6 5 . 8 3 Rs . C r o r e in 2 0 0 8 09.. I t is fur the r a ntic ip a te d tha t the p r o d uc tio n figur e wo uld gr o w to. 5 2 5 2 3 . 4 4 Rs . C r o r e in 2 0 1 5 - 1 6 a nd the n to 6 3 8 4 2 . 7 0 Rs . C r o r e till 2 0 1 9 - 2 0 .. As fa r gr o wth o f numb e r o f units is c o nc e r ne d , the y a r e e xp e c te d to gr o w a t. 14.

(16) c o mp o und a nnua l r a te o f 0 . 3 0 while e mp lo yme nt, inve s tme nt a nd p r o d uc tio n wo uld p r o b a b ly gr o w a t the r a te 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 tive ly.. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. This c le a r ly ind ic a te s tha t in the c o ming d a ys no t o nly p r o d uc tivity o f c a p ita l. b ut c a p ita l inte ns ity will a ls o inc r e a s e . But the me a ge r r a te o f gr o wth o f e mp lo yme nt c o nfir ms tha t in s ub s e q ue nt ye a r s the r e is le s s s c o p e o f la b o ur a b s o r p tio n in the S ma ll S c a le I nd us tr ia l o f W e s t Be nga l.. Co nc luding 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 ultur a l s ta te b ut it ha s ma d e. ho ne s t e ffo r ts to p r o vid e imp e tus to the ind us tr ia l s e c to r e s p e c ia lly s ma ll s c a le ind us tr ia l s e c to r ( Gup ta , 2 0 0 6 ) . The Auto Re gr e s s ive I nte gr a te d. M o ving Ave r a ge ( ARI M A) mo d e l thr 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 to ge ne r a te fo r e c a s ts r e ga r d ing va r ia b le s o f s ma ll s c a le ind us tr ia l s e c to r o f W e s t Be nga l. I t is e xp e c te d tha t numb e r o f units 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 to inve s tme nt a nd. p r o d uc tio n. The fo r e c a s ts ha ve d e p ic te d a b r ight p ic t ur e a he a d b ut with lo w s c o p e o f e mp lo yme nt o p p o r tunitie s fo r la b o ur e r s . The s e fo r e c a s ts 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 tio n to d e s ign p o lic ie s a c c o r d ingly to p us hup gr o wth in this s e c to r .. I n the light o f the fo r e c a s ts it is r e q uir e d o n th e p a r t o f the s ta te go ve r nme nt to ta k e a ll s o r t c o nc e r te d e ffo r ts initia tive s to s tr e ngthe n the ind us tr ia l b a s e. in W e s t Be nga l. I n this r e ga r d c a ta s tr o p hic c ha nge s a r e r e q uir e d s o fa r a s. 15.

(17) ind us tr 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 ntive s no t o nly fo r e xis ting ind us tr ia lis ts b ut. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. a ls o fo r ne w ve ntur is ts . M o r e o ve r ta x b e ne fits , lo a n o n s o ft - te r ms a nd infr a s tr uc tur a l fa c ilitie s s ho uld b e in the p r io r ity lis t o f ind us tr ia l b lue p r int. o f W e s t Be nga l. La s t b ut no t the le a s t wo ma n e ntr e p r e ne ur s hip s ho uld b e p r o mo te d in the s ta te a t p a r with le a d ing ind us tr ia l e c o no mie s o f the wo r ld , to p r o vid e s tr o ng fo o ting to s ma ll S c a le ind us tr y o f W e s t Be ng R e f e re nc e s :. Afzal Mohammad (et al.). 2002. Forecasting: A dilemma of modules. Pakistan Economic and Social Review 40(1): 1-18.. Armstong, J. S. 1983. Relative accuracy of judgmental and extrapolative methods in forecasting annual earnings. Journal of Forecasting. 15(2): 437–447.. Armstrong J. S. 2005. The forecasting canon: nine generalizations to improve forecast accuracy. Foresight 1(1): 49- 65.. Armstrong J. S. 2006. Findings from evidence-based forecasting: methods for reducing forecast error. Forthcoming (after revisions) in the International Journal of Forecasting.. Bartlett, M. S. 1946. On the theoretical specification of sampling properties of autocorrelated time series. Journal of Royal Statistical Society 8(27).. Bawa, R. S. and G. S. Kainth .1980. A time series analysis of net national product of India, Margin 12(3):51 – 80.. Bhatia G. S. 1999. The impact of new economic policy on output and employment in manufacturing sector: a case study of West Bengal in V. S. Mahajan (ed.), Economic Reforms and Liberalization, New Delhi: Deep & Deep.. 16.

(18) Bowersox J. Donald, (et al.). 1981. Simulated product sales forecasting: A model for short-range forecasting operational decision making. Research in Marketing 4(2): 39-68.. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. Bowersox J. Donald, (et al.). 1981. Simulated product sales forecasting: A model for short-range forecasting operational decision making. Research in Marketing 4(2): 39-68.. Box, G. E. P. and D. A. Pierce .1970. Distribution of Residual Autocorrelations in ARIMA Time Series Models. Journal of American Statistical Association, 65(4): 1509 – 1526.. Box, G. E. P., G. M. Jenkins, and G. C. Reinsell.1994 .Time series analysis: Forecasting and control, Englewood Cliffs, N. J.: Prentice – Hall.. Box, G. E. P., G. M. Jenkins.1968. Some Recent Advance in Forecasting and Control. Applied Statistics: 91 – 109.. DeLurgio. 1998. Forecasting Principles and Application. New York: McGraw-Hill International Edition.. Fildes Robert, M. Makridakis (et al.). 1998. Generalizing about univariate forecasting methods: Further empirical evidence. International Journal of Forecasting 14: 339–358.. Fildes, R. 1992. The evaluation of extrapolative forecasting method. International Journal of Forecasting 8(1): 81 – 98.. Fildes, R. and E. J. Lusk. 1984. The Choice of a Forecasting Model. Omega 12(5): 427–435.. Fildes, R. and S. Makridakis. 1998. Forecasting and loss function. International Journal of Forecasting 4(3): 545–550.. Fildes, R. Makridakis, S. 1995. The impact of empirical accuracy studies on time series analysis and forecasting. International Statistical Review 63: 289–308.. 17.

(19) Francis X. Diebold and Glenn P. Rudebusch.1991. Forecasting output with the composite leading index: a real time analysis. Journal of American Statistical Association. 86(4):. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. 603-610.. Gupta, Sanjeev and R. S. Bawa. 2002. An analysis of long -term trends and forecasts of oilseeds output in India. Indian Journal of Quantitative Economics 17(1-2): 111-131.. Gupta, Sanjeev and R. S. Bawa. 2004. Growth performance and sales forecasts of two-wheeler industry in India. Indian Journal of Applied Economics 1(1): 158-165.. Gupta, Sanjeev and R. S. Bawa. 2006. Growth performance and sales forecasts of automobile industry in India. Forthcoming in the Indian Journal of Quantitative Economics 21(1-2).. Gupta, Sanjeev. 2003. Forecasting of Agricultural Output in India. New Delhi: Saloni Publishing House.. Gupta, Sanjeev and R. S. Bawa. 2006. Growth performance of small scale industry in West Bengal: A comparative study of pre–liberalization & liberalization periods Apeejay Journal of Management & Technology. 1(1): 50-55. Hanke, J. E. (et al.). 2001. Business Forecasting. New Delhi: Pearson Education.. Ibrahim, I. B, and T, Otsuki.1982. Forecasting GNP components using the method of Box and Jenkins. Southern Economic Journal: 461 – 470.. Kumar Naresh and Balraj Singh .2003. Forecasts of Indian Automobile Industry Using Mathematical Models, Paradigm 3(2):105-116.. Ljung G. M. and G. E. P. Box. 1978. On measurement of lack of fit in time series models. Biometrika. 65: 67–72.. Makridakis, S. (et al.). 1984. The Forecasting Accuracy of Major Time Series Methods. Chichester: John Wiley.. 18.

(20) Makridakis, S. and S. C. Wheelwright. 1987. The Handbook of Forecasting: a Manager’s Guide New York: John Wiley.. Be in w or vol are ht igin ve ! T tp a s p he :// l s la R w o g e w ur ia P w c ry E .ib e: . c im at Pl Pl ea a ap se gia ub do rism lis hi n' ng t c Co ite m .c om th mi is tte /jo pa e ur na pe is co ls r /C bu nv IB t l in oo ce IM k d A/ fo th vo r t at lu he th m is e7 pa /v 7n pe 11 r .h tm l.. Makridakis, S., and S. C. Wheelwright, and R. J. Hyndman. 1998. Forecasting: Methods and Applications New York: John Wiley & Sons.. Makridakis, S., and Wheelwright, S. C. 1978. Interactive Forecasting: Univariate and Multivariate Methods San Francisco CA: Holden-Day.. Mentzer John T. and James E. Cox. 1984. Familiarity, application, and performance of sales forecasting techniques. Journal of Forecasting 3(1): 276-278.. Mentzer John T. and Keneneth B Kah. 1995. Forecasting in consumer and industrial markets. Journal of Business Forecasting: 21-28.. Nachane, D. M. (et. al). 1981. Forecasting freight and passenger traffic on Indian railways: generalized adaptive filtering approach. The Indian Economic Journal 29(2): 99-116.. Newbold, P. and C. W. J. Granger. 1974. Experience with forecasting principles abstract of. handbook article forecasting univariate time series and the combination of forecasts. Journal of Royal Statistics Society 137(3): 131–165.. Pankratz, A. 1983. Forecasting with Univariate Box-Jenkins Models: Concepts and Cases New. Ramaswamy, K. V. 1994. Small-scale manufacturing industries-some aspects of size, growth and structure. Economic and Political Weekly 29(9): 13 -22.. Sabia, J. L. M. 1977. Autoregressive integrated moving average (ARIMA) model for birth forecasting. Journal of the American Statistical Association 72(354):264 – 270.. Sethi, A. S. 1999. Forecasting savings in India in post - liberalization scenario: a note. Indian Journal of Quantitative Economics, 14(2): 159 – 166.. 19.

(21)