NEW FORECASTING MODELS 1

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1 NEW FORECASTING MODELS Gang L School of Managemen Unversy of Surrey Guldford GU2 7XH Uned Kngdom Tel: Fax: Emal: g.l@surrey.ac.uk Hayan Song School of Hoel and Toursm Managemen The Hong Kong Polyechnc Unversy Hung Hom, Kowloon Hong Kong Tel: Fax: Emal: hmsong@polyu.edu.hk ABSTRACT Toursm forecasng plays an mporan role n oursm plannng and managemen. Varous forecasng echnques have been developed and appled o he oursm conex, amongs whch economerc forecasng has been wnnng an ncreasng populary n oursm research. Ths paper herefore ams o nroduce he laes developmens of economerc forecasng approaches and her applcaons o oursm demand analyss. Parcular emphases are placed on he me varyng parameer (TVP) forecasng echnque and s applcaon o he almos deal demand sysem (AIDS). The dscussons n hs paper fall no wo man pars, n lne wh he wo broad caegores of economerc forecasng approaches: he frs par refers o he sngle-equaon forecasng echnques, focusng parcularly on boh long-run and shor-erm TVP models. The second par nroduces he sysem-of-equaons forecasng models, represened by he AIDS and s dynamc versons ncludng he combnaon wh he TVP echnque, wll be dscussed one by one followng he order of mehodologcal developmens. KEYWORDS: Forecasng Models, Tme Varyng Parameer (TVP), Almos Ideal Demand Sysem (AIDS) The auhors acknowledge he fnancal suppor of he Hong Kong Unversy Gran Councl's Compeve Earmarked Research Gran - B-Q976. INTRODUCTION Consderng he daa avalably, oursm forecasng echnques fall no wo major caegores: quanave and qualave forecasng. If lle or no quanave nformaon s avalable, bu suffcen qualave knowledge exss, qualave forecasng approaches are approprae. When suffcen quanfable nformaon abou he pas s avalable and he objecve numercal measuremens are conssen over he hsorcal perod, quanave forecasng should be adoped. Consderng he number of publshed sudes, quanave forecasng domnaes he oursm leraure.

2 Quanave forecasng mehods can be furher dvded no wo subcaegores: causal and non-causal mehods, dependng on f here are any explanaory varables ncluded or no n he models. Causal mehods, prncpally he economerc models, can no only predc he rends of fuure oursm demand, bu also nerpre he causes of varaons n oursm demand. Hence, causal forecasng mehods can provde useful nformaon for boh polcy evaluaon n he publc secor and sraegy formulaon n varous oursm busnesses. Ths paper focuses on he laes developmens of economerc forecasng mehods and her applcaons n he oursm conex. A parcular emphass wll be gven o he TVP esmaon approach appled o boh sngle-equaon and sysem-of-equaon models. TVP SINGLE-EQUATION MODELS One of he assumpons behnd convenonal fxed-parameer economerc echnques s ha he coeffcens of he models are consan over he whole sample perod. Ths mples ha he economc srucure generang he daa does no change over me (Judge e al, 985). However, he changng economc envronmen may nduce people o reac dfferenly a varous pons n me, boh quanavely and qualavely o gven smulaons. To overcome he lmaons of he radonal fxed-parameer models, a more advanced and flexble economerc mehod: he TVP model, has been developed, whch allows one o undersand and forecas consumer behavour more accuraely. The TVP model relaxes he resrcon on he parameer consancy and akes accoun of he possbly of parameer changes over me. The TVP echnque was nally developed n he engneerng scence and was recenly appled o socoeconomc sudes, mosly adoped n he sngle-equaon modellng framework. TVP Long-Run Model (TVP-LRM) TVP models are normally specfed n a sae space (SS) form. SS modellng assumes ha he dynamc feaures of he sysem under sudy are deermned by he unobserved varables assocaed wh a seres of observaons (Durbn and Koopman, 200). The SS presenaon allows unobserved varables o be ncluded no, and esmaed along wh, he observable varables. By nferrng he relevan properes of he unobserved seres from he knowledge of he observaons, he evoluon of he sysem can be more precsely descrbed and predced. A lnear SS model can be wren as: y = α + ε, ε N(0, H ), =,..., T () Z ~ + = Tα η, ~ N( a, P ) α + α, η N(0, Q ), (2) ~ where y s he dependen varable; Z s a vecor of ndependen varables; α s an unobserved vecor called sae vecor; ε refers o he emporary dsurbance and η he permanen dsurbance, ε and η are Gaussan dsurbances, whch are serally ndependen and ndependen of each oher a all me pons; The marces T, H and Q are nally assumed o be known. Equaon () s called he observaon equaon, and Equaon (2) called he sae equaon. In mos of he economc applcaons, he evoluon of α s assumed o follow a mulvarae random walk..e., α = α + η +. Ths assumpon s also appled n he curren sudy. The nal value of can be esmaed by maxmum lkelhood from he frs few observaons of y and α,.e., α, Z. P s he 2

3 varance of α (Durbn and Koopman, 200; Harvey, 989). The raonale behnd hs model s ha he evoluon of he concernng sysem over me s deermned by α accordng o he sae equaon. Meanwhle, snce s unobservable, he analyss mus be based on he observaons of y, ha s, Z and T are dependen on y,, y. The defnon of he sae vecor α for a parcular model depends on s consrucon. Is elemens have a subsanve nerpreaon, e.g., as a rend or seasonaly. From a echncal pon of vew, he purpose of specfyng a SS form s o se up α n such a way ha conans all he relevan nformaon on he sysem a me and ha does so by havng as small a number of elemens as possble (Harvey, 989, p02). Once a TVP model has been specfed n a SS form, he Kalman fler procedure (Kalman, 960) can be employed o calculae he opmal (mnmum mean square error, MMSE) esmaor of he sae vecor a me, gven he nformaon avalable up o me -. Snce he Kalman fler yelds a T + = T α T T + T and he MMSE esmaor of α gven all he observaons, he one-sep-ahead T+ forecas can be drecly produced by: ~ ~ yt + T = Z T + a (3) T+ T ~ where Z T+ s he vecor of one-sep-ahead forecass of explanaory varables such as he dsposable ncome or he consumer prce ndex. The forecass of hese macroeconomc ndcaors are normally avalable from he naonal sascs offce, or projeced usng he approprae non-causal me-seres forecasng approach. Correspondngly, he mul-sep forecass can also be recursvely generaed. Full llusraon of he Kalman fler echnque s avalable from Harvey (989). Snce he observaon equaon () s based on he classcal economerc model he sac or long-run conegraon (CI) model, he TVP specfcaon of Equaon () s known as TVP-LRM. TVP Error Correcon Model (TVP-ECM) Equaon () suggess ha he TVP-LRM emphases he evoluon of explanaory varables and s effec on he dependen varable. Alhough s useful o examne he annual demand for oursm over a long perod, he dynamc changes of oursm demand n he shor erm are also concerned by oursm busnesses. To serve hs purpose, an error correcon model (ECM) could be consdered. Engle and Granger (987) showed ha n a sysem of wo varables, f a long-run equlbrum relaonshp exss, he shor-erm dsequlbrum relaonshp beween he wo varables can be represened by an ECM. The ECM reflecs he mechansm of he shor-run adjusmen owards he long-run equlbrum n he sysem. If here are more han wo varables n he sysem, s possble ha here wll be more han one CI relaonshps, and correspondngly he ECM becomes a vecor ECM. The convenonal fxed-parameer ECM assumes ha he speed of shor-run adjusmen s consan over me. In he changng envronmen such an assumpon seems o be oo src and arbrary. In fac, even assumng he exsence of a sable long-run combnaon, one may fnd sgns of nsably n he 3

4 shor-run adjusmen mechansm (Ramajo, 200). Therefore, s more realsc o specfy he TVP shor-run dynamcs whn he long-run equlbrum framework. Such a specfcaon s ermed TVP-ECM. Compared o he classcal long-run TVP model, he TVP-ECM adds one more resrcon exsence of he CI relaonshp, and focuses on he shor-erm adjusmen, he speeds of whch vary over me. Afer confrmng he accepance of a CI relaonshp, a TVP-ECM can be esmaed. Smlar o he TVP-LRM, he TVP-ECM can also be specfed n a SS form. In he case where he lag lengh of he dfferenced varables s zero, whch has been proved o be approprae n mos oursm sudes usng annual daa, he observaon equaon of he TVP-ECM can be wren as: y = Z β + λ eˆ + v (4) where e y Z αˆ are he OLS resduals from he CI funcon y = Z α + e, where ˆ = α (whou a subscrp) s a fxed parameer vecor. e represens he error correcon mechansm. β and λ are he TVP vecors, and v s he emporary dsurbance erm. The sae equaon sll akes he same form as Equaon (2), and α ( β, λ ). The esmaon mehod s he same as ha of he TVP-LRM. = I should be noed ha dummy varables can be readly ncorporaed no boh he TVP-LRM and he TVP-ECM, n order o capure he effecs of one-off evens such as he Iraq War and 9. errors aack. Snce hese one-off evens are regarded as exogenous facors for oursm demand, s no necessary o esmae he parameers usng he TVP echnque and he fxed parameers are approprae for dummy varables n a TVP model. Applcaons of TVP Models n Toursm ˆ TVP models n boh long-run and dynamc forms have been successfully appled n economc sudes such as modellng and forecasng raonal expecaon formaons, nflaon, and demand for money and oher producs (e.g., Bohara and Sauer, 992; Swamy e al, 990; and Hackl and Weslund, 996). However, applcaons of TVP models o oursm forecasng are sll rare, wh he followng noable excepons. Rddngon (999) ulsed he TVP-LRM o analyse and forecas sk demand n Scoland. Song and W (2000) used he TVP-LRM o examne he demand elascy changes over me regardng he demand for Korean oursm by UK and USA resdens. L e al (2005a) and Song e al (2003b) showed he superory of he TVP-LRM o s fxed-parameer counerpars n erms of forecasng accuracy n her sudes on oursm demand n Denmark and Thaland, respecvely. L e al (2006) examned he forecasng performance of boh TVP-LRM and TVP-ECM relave o a number of fxed-parameer economerc and me seres models n an emprcal sudy of UK oursm demand n some key Wesern European desnaons. Table shows ha he overall performance of he TVP-LRM n erms of demand level forecasng s he bes amongs all he models n he comparson. The TVP-ECM always performs above average. As far as demand growh s concerned, he TVP-LRM and TVP-ECM ouperform all of her compeors. In parcular, he TVP-ECM generaes he mos accurae one-year-ahead and wo-years-ahead forecass. The conssenly superor performance of he TVP-LRM and TVP-ECM suggess ha he TVP echnque s an effecve ool for oursm demand 4

5 forecasng. 5

6 Table Forecasng Accuracy over Dfferen Forecasng Horzons Horzon Measure Nave ARIMA Sac ADLM VAR WB-ECM JML-ECM EG-ECM TVP-LRM TVP-ECM -year-ahead MAPE (8) (9).405 (0) () 0.59 (5) 0.69 (6) (4) (7) 0.50 (3) (2) 2-years-ahead MAPE.0 (9).089 (8).778 (0) (2) (6).066 (7) (4) (5) () (3) 3-years-ahead MAPE.69 (0).29 (9).06 (8) (2) (7) (6) (3) (4) 0.28 () (5) 4-years-ahead MAPE.293 (9).374 (0).269 (8) 0.46 (2).208 (7) (6) (3) (5) () (4) Overall MAPE.082 (8).097 (9).367 (0) (2) (7) (6) (3) (5) () (4) -year-ahead MAE 0.76 (7) 0.77 (8) (0) 0.08 (2) 0.2 (5) 0.45 (6) 0.2 (4) 0.8 (9) 0. (3) () 2-years-ahead MAE 0.62 (0) 0.53 (9) 0.28 (8) 0.02 (3) 0.7 (6) 0.22 (7) 0.07 (5) 0.05 (4) (2) () 3-years-ahead MAE 0.7 (9) 0.72 (0) 0.40 (7) 0.05 (4) 0.5 (8) 0.26 (6) (2) (3) () 0.07 (5) 4-years-ahead MAE 0.44 (6) 0.45 (7) (0) 0.02 (2) 0.33 (5) 0.74 (9) 0.07 (3) 0.64 (8) 0.08 () 0.22 (4) Overall MAE 0.64 (9) 0.62 (8) 0.94 (0) 0.04 (4) 0.3 (5) 0.42 (7) 0.03 (3) 0.37 (6) () 0.00 (2) Noe: The upper half of he able refers o he forecass of level varables, and he lower dfferenced varables. Fgures n parenheses are rankngs. Nave refers o he nave no-change model; ARIMA he auoregressve negraed movng average model; Sac he sac regresson; ADLM auoregressve dsrbued lagged model; VAR he vecor auoregressve model; WB-ECM he Wckens and Breusch ECM; JML he Johansen maxmum lkelhood ECM; EG-ECM he Engle Granger ECM. MAPE sands for mean absolue percenage errors; MAE sands for mean absolue errors. Source: L e al (2006b). 6

7 AIDS MODELS As addressed earler, causal forecasng mehods have advanages over he non-causal approach n erms of her ables o nerpre he reasons of oursm demand varaons. Eadngon and Redman (99) noed ha he sngle-equaon economerc forecasng approach s ncapable of analysng he nerdependence of budge allocaons o dfferen consumer goods/servces. For example, he oursm decson-makng nvolves a choce among a group of alernave desnaons. A change of prce n one desnaon may affec ourss decsons on ravellng o a number of alernave desnaons, and also nfluence her expendures n hose desnaons. Clearly, he sngle-equaon mehodology canno adequaely model he nfluence of a change n oursm prce n a parcular desnaon on he demand for ravellng o all oher desnaons. Meanwhle, he sngle-equaon approach canno be used o es he symmery and addng-up hypoheses, whch are assocaed wh he exsng demand heores. The sysem-of-equaons approach naed by Sone (954) overcomes he above lmaons. By ncludng a group of equaons (one for each consumer good) n he sysem and esmang hem smulaneously, hs approach perms he examnaon of how consumers choose bundles of goods n order o maxmse her uly wh budge consrans. Alhough here are a number of sysem approaches avalable, he almos deal demand sysem (AIDS), nroduced by Deaon and Muellbauer (980), has been he mos commonly used mehod for analysng consumer behavour. As he auhors descrbed, he AIDS model possesses he followng aracve feaures: I gves an arbrary frs-order approxmaon o any demand sysem; I sasfes he axoms of consumers whou nvokng parallel lnear Engel curves; I has a funconal form whch comples wh known household-budge daa; I s easy o esmae and largely avod he need for non-lnear esmaon; The resrcons of homogeney and symmery can be esed hough lnear resrcons on fxed parameers n he model; I has a flexble funconal form and does no mpose any a pror resrcons on he elasces, whch means any good n he sysem can be eher nferor or normal, and eher a subsue or a complemen o he ohers (Fuj e al, 985). Alhough he Roerdam and ranslog models also hold some of hese feaures, neher of hem conans all hese feaures smulaneously. Havng explc heorecal underpnnngs, AIDS s more approprae for oursm demand analyss. Sac LAIDS The orgnal AIDS nalsed by Deaon and Muellbauer (980) akes a sac funconal form and s specfed as: w = α + γ log p + β log( x / P) + ν (5) j where w s he budge share of he h good, p s he prce of he h good, x s oal expendure on all goods n he sysem, P s he aggregae prce ndex for he sysem, v s he dsurbance erm, 2 v ~ N(0, σ ), n s he number of he producs n he sysem, α, β and γ j are he parameers o j j 7

8 be esmaed. The aggregae prce ndex P s defned as: log P= a0 + α log p + γ j log p log p j (6) 2 j where a0 s a parameer o be esmaed. Replacng P wh he Sone s (954) prce ndex (P) defned by Equaon (7), he lnearly approxmaed AIDS s derved and ermed LAIDS. = The LAIDS wh dummy varables can hen be wren as: log P w log p (7) x w = α + γ j log p j + β log + ϕk dumk + v (k=, 2,, m) (8) j P k where dum k s a dummy varable, whch handles he nervenon of he exogenous shock; m s he number of dummy varables ncluded n he sysem; ϕ k s a parameer o be esmaed. Equaon (8) can be re-wren more compacly n he vecor-marx noaon: w = Πz + ϕ dum + v (9) where z s a q-vecor of nercep, log prces and log real oal expendure varables ( q = n+ 2 ); Π and ϕ are ( n q) and n mparameer marces, respecvely; Π= ( π, π 2,... π ) n, where π s a q-vecor. The LAIDS model s normally esmaed by he eraed seemngly unrelaed regresson (SUR) logarhm (see Zellner, 962 for deals). To comply wh he properes of demand heory, some resrcons are mposed on he parameers n Equaon (8), such as Addng-up ( α =, γ =, β = 0 and ϕ = 0 ), Homogeney ( j = 0 j j 0 γ ) and Symmery ( γ j = γ j ). Subjec o he sasfacon of he above resrcons, he unresrced LAIDS n Equaon (8) can be furher wren as wo resrced versons: he homogeneous LAIDS and he homogeneous and symmerc LAIDS. The laer s he mos heorecally sound, and he furher analyss and forecasng should be based on hs verson. However, he hypoheses of he above resrcons mgh be rejeced by sascal ess n emprcal sudes. In hs case, he unresrced LAIDS or homogeneous LAIDS has o be consdered. Whn he LAIDS framework, he demand elasces can be calculaed as: he expendure elascyε = + β / w, he uncompensaed prce elascy ε j = δ j + γ j / w β w j / w and he x compensaed prce elascy ε j = δ j + γ j / w + w j ( δ j= for =j; δ j =0 for j). The elasces calculaed from he LAIDS model have a sronger heorecal bass han he sngle-equaon models. Therefore, he LAIDS model can provde more relable nformaon for oursm demand analyss. k 8

9 Dynamc LAIDS In he sac LAIDS, whch s also known as he long-run LAIDS model, s mplcly assumed ha here s no dfference beween consumers shor-run and long-run behavour,.e. he consumers behavour s always n equlbrum. However, n realy, hab perssence, adjusmen coss, mperfec nformaon, ncorrec expecaons and msnerpreed real prce changes ofen preven consumers from adjusng her expendure nsanly o prce and ncome changes (Anderson and Blundell, 983). Therefore, unl full adjusmen akes place consumers are ou of equlbrum. Ths s one of he reasons why mos sac LAIDS models canno sasfy he heorecal resrcons (Duffy, 2002). Moreover, he sac LAIDS pays no aenon o he sascal properes of he daa and he dynamc specfcaon arsng from me seres analyss. I s well known ha mos economc daa are non-saonary, and he presence of un roos may nvaldae he asympoc dsrbuon of esmaors. Therefore, radonal sascs such as, F and R 2 are unrelable, and he leas squares esmaon of he sac LAIDS ends be spurous (Chambers, 993; Granger and Newbold, 974). Furhermore, he sac LAIDS s unlkely o generae accurae shor-run forecass (Chambers and Nowman, 997). However, he nroducon of he CI/ECM no he LAIDS models can solve he above problems, as he error correcon LAIDS EC-LAIDS augmens he long-run equlbrum relaonshp wh a shor-run adjusmen mechansm. Before examnng he CI relaonshp, all varables concerned need o be esed for un roos (orders of negraon). The Augmened Dckey-Fuller (ADF) and Phllps-Perron (PP) sascs can be employed for hs purpose. Once he orders of negraon of he varables have been denfed, eher he Engle and Granger (987) wo-sage approach or he Johansen (988) maxmum lkelhood approach can be used o es for he CI relaonshp among he varables n he models (Song and W, 2000). Followng Engle and Granger s wo-sage approach, he EC-LAIDS can be wren n he followng form (Edgeron e al, 996; Chambers and Nowman, 997; Duffy, 2002): A φ + v (0) ( L) w = B( L) z + ( L) dum +Γ( w Πz ϕdum ) l h where A ( L) = I + = A L, B ( L) = B = L and φ ( L) = φ 0 L are marx polynomals n he = 0 lag operaor L. l and h can be deermned by usng order selecon echnques. ( w ) Πz ϕ dum s he error correcon erm. Gven ha annual daa are used, mos oursm demand sudes employng ECMs have shown ha seng he lag lengh of dfferenced varables equal o zero s approprae. Thus, Equaon (0) can be reduced o he followng form (see Durbarry and Snclar, 2003): w = B z + φ dum +Γ + v () ( w Πz ϕdum ) s where B s an ( n q) marx, and φ s an ( n m) marx; Γ s an ( n n) marx. Consderng he degrees of freedom and sascal sgnfcance of he esmaes of he error correcon erms, some emprcal sudes, such as Ray (985), used a more resrcve formulaon, nvolvng only he dsequlbrum n he own budge share n each equaon. In oher words, Γ becomes dagonal, and he off-dagonal erms, he esmaes of whch are normally nsgnfcan, are resrced o zero. The dagonal form of Γ also mples ha Γ are equal,.e., Γ s a negave scalar. 9

10 Equaon () reflecs boh long-run and shor-run effecs n he same model. In he shor run, changes n expendure shares depend on changes n prces, real expendure, dummes, and he dsequlbrum error n he prevous perod. In he long run, when all dfferenced erms become zero, Equaon () s reduced o Equaon (9),.e., he sysem acheves s seady sae. TVP-LAIDS As has been addressed above, TVP models have advanages over her fxed-parameer counerpars. In addon, varous emprcal sudes have shown he superor forecasng performance of TVP models n comparson o oher convenonal economerc models. Meanwhle, he superory of he AIDS model over he sngle-equaon approach has also been evaluaed. Hence, combnaon of he TVP echnque and he AIDS/LAIDS model s lkely o creae boh heorecally sound and more accurae forecasng mehods. Conssen wh he developmen of LAIDS specfcaons, he TVP-LAIDS famly comprses boh he long-run verson TVP-LR-LAIDS, and he shor-run dynamc TVP-EC-LAIDS, dependng on wheher he error correcon mechansm s ncorporaed no he LAIDS specfcaon. TVP-LR-LAIDS Relaxng he fxed-parameer resrcon, he unresrced long-run LAIDS of Equaon (8) can be re-wren as a TVP sysem. I should be noed ha once he esmaes of he fxed-parameer LAIDS have shown he sascal sgnfcance of dummy varables, hey should also be ncluded no TVP formulaons, bu as exogenous varables hey have fxed parameers (Ramajo, 200). Therefore each equaon of he TVP-LR-LAIDS can be wren n he followng one-dmenson SS form: w = z π + ϑ dum + u u N(0, H ), + π = π + ξ ~ π ~ N( c, P ) ξ, =,..., T ~ N(0, Q ) (2) (3) where w and u are he h elemens of vecors w and u respecvely; ϑ s he h row of ϑ ; ξ s a q-vecor of dsurbance erms. π s an unobserved sae vecor, and follows a mulvarae random walk. The marces H and Q are nally assumed o be known. Correspondngly, he whole sysem can be specfed as: w = z Π + ϑdum + u (4) Π + = Π + ξ (5) where z = I z, Π = π π,..., π ) and ξ ξ, ξ,..., ξ ). n (, 2 n = ( 2 n In homogeney or symmery resrced LAIDS, he resrcons (M), whch are lnear, can be wren as: M = GΠ (6) where G s he coeffcen marx of he resrcon. Combnng he lnear resrcon of Equaon (6) wh Equaon (4) gves a new augmened measuremen equaon n he form: 0

11 W = Z + D + U Π w z ϑdum u where W = ; Z = ; D = M ; U = G 0. 0 (7) TVP-EC-LAIDS In he pervous secons, he TVP-ECM and EC-LAIDS have been nroduced. Boh of hese models have a parcular emphass on he shor-erm dynamcs of he sysem concerned. A furher combnaon beween hem generaes he TVP-EC-LAIDS, whch s so far he mos advanced developmen of he LAIDS famly. Specfcally, he TVP-EC-LAIDS feaures he varyng shor-erm adjusmen owards he long-run seady sae of demand. As wh Equaons (2) and (3), each equaon of he unresrced TVP-EC-LAIDS can be descrbed as he followng SS form: w = ( z ) π + θ dum + u (8) π + = π + ξ (9) where z z, w Πz ) ; π s he correspondng parameer vecor; θ s he h row of θ ; u s he h em of u, he dsurbance vecor of he measuremen equaon; andξ s he = ( dsurbance vecor of he sae equaon. Correspondngly, he sae space form of he whole unresrced TVP-EC-LAIDS s specfed as: w = ( z ) Π + θ dum + u (20) = Π + Π + ξ (2) where z = I q+ ( z ) ; Π = ( π, π 2,..., π n ) ; ξ = ( ξ, ξ 2,..., ξ n ). Once he unresrced LAIDS passes he resrcon ess, he homogeney-resrced or boh homogeney and symmery-resrced verson of TVP-LR-LAIDS and TVP-EC-LAIDS can be esmaed usng he Kalman fler algorhm, and forecass can be generaed correspondngly. Esmaons of he sngle-equaon TVP models, he sac and dynamc (fxed-parameer) LAIDS, as well as he sngle-equaon esmaon of TVP-LAIDS models (.e., each equaon of he sysem s esmaed separaely), can all be carred ou usng he compung program Evews 5.0.The sysem esmaon of he TVP-LR-LAIDS and TVP-EC-LAIDS can be performed by he SAS 8.02 marx programmng language IML. Applcaons of LAIDS o Toursm Forecasng Alhough he LAIDS models have been employed wdely n food demand modellng, applcaons n he feld of oursm demand are sll lmed. A dealed revew of he LAIDS relaed o oursm can be

12 found n L e al (2005b). All of hese LAIDS applcaons analysed allocaons of ourss expendure n a group of desnaons, wh only one excepon, Fuj e al (985), who nvesgaed ourss expendure on dfferen consumer goods n a parcular desnaon. Mos of he LAIDS sudes n he oursm conex adoped he orgnal sac verson, whle Durbarry and Snclar (2003) and L e al (2005a) specfed he EC-LAIDS models o examne he dynamcs of ourss consumpon behavour. The emprcal sudy of L e al (2005a) examned UK oubound oursm demand n Wesern Europe. The fve major desnaons n hs area, Span, France, Greece, Ialy and Porugal, are he focuses of hs sudy, wh he oher seveneen counres aggregaed no a sngle group. Each of he sx desnaon counres/group s regarded as an aggregaed oursm produc, purchased by UK vsors. The emprcal resuls show ha oursm demand by UK resdens s mos sensve o prce changes n Greece and leas sensve o prce changes n Ialy. The cross-prce elasces ndcae ha France and Span, Ialy and Porugal, and France and Greece are lkely o be subsues n he mnds of UK ourss. Wh regard o forecasng performance, he EC-LAIDS always ouperforms he sac LAIDS, and n general he EC-LAIDS s over 40% more accurae han he sac LAIDS. L e al (2006a) furher developed he TVP-LR-LAIDS and TVP-EC-LAIDS o analyse he evoluons of demand elasces over me and o examne her forecasng performance. Fgure shows he esmaes of compensaed own-prce elasces n he unresrced TVP-LR-LAIDS models. These graphs exhb dfferen evoluon paerns of he prce elascy. Relavely large flucuaons whch occurred n he early 980s are assocaed wh he global economc recesson durng hs perod. Snce he md 980s, he sensvy of oursm demand for France, Greece and Ialy o her prce changes has become relavely sable, whle he oppose phenomena can be observed n he cases of demand for Porugal and Span oursm, wh he nfluence of he Gulf War n he early 990s beng evden. As far as he forecasng performance s concerned, he unresrced TVP-LR-LAIDS and TVP-EC-LAIDS ouperform all of he oher fxed-parameer counerpars n he overall evaluaon of demand level forecass. I suggess ha he more advanced forecasng echnques conrbue o he mprovemens of forecasng accuracy, and herefore should be appled more broadly n fuure oursm sudes. 2

13 ε a. France Year ε b. Greece Year c. Ialy ε ε d. Porugal Year Year ε e. Span Year Fgure Kalman Fler Esmaes of Compensaed Own-Prce Elasces ( ε ) n he Unresrced TVP-LR-LAIDS ( ) 3

14 SUMMARY Ths paper has nroduced some of he laes developmens of economerc approaches n oursm forecasng. The error correcon mechansm and he TVP forecasng echnque have been ncorporaed n boh sngle-equaon and sysem of equaons (represened by LAIDS) frameworks. The emprcal evdence shows ha more advanced forecasng mehods are lkely o generae more accurae forecass of oursm demand. Furher developmens and applcaons of economerc forecasng approaches should be herefore encouraged. I should be noed ha he above models are suable where he annual oursm demand s concerned. In oher words, her model specfcaons accommodae annual daa well, bu do no consder he seasonal paerns of oursm demand. In pracce, shorer-erm forecass, such as monhly or quarerly forecass, are of more neress o oursm busnesses n he prvae secor. I has been observed ha he seasonaly ended o be feaured n shor-erm oursm demand n mos desnaons and oursm ndusres. To mee he need for seasonal oursm forecasng, furher developmens of economerc forecasng mehods should pay more aenon o he seasonal paerns of oursm demand, and ncorporae seasonal componens n he TVP sngle-equaon or TVP-LAIDS specfcaons. Consderng he mers of he TVP echnque, he varous seasonaly-augmened TVP models are lkely o generae accurae forecass of shor-erm demand for oursm. 4

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