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1 Inernaional Nework for Economic Research Working Paper Modelling he Cyclical Behaviour of Wine Producion in he Douro Region Using a Time-Varying Parameers Approach by Mario Cunha (Universidade do Poro) & Chrisian Richer

2 Modelling he Cyclical Behaviour of Wine Producion in he Douro Region Using a Time-Varying Parameers Approach Mário Cunha and Chrisian Richer Faculdade de Ciências, Universidade do Poro, Campus Agrário de Vairão, Rua Padre Armando Quinas, Vairão, Porugal, mcunha@mail.icav.up.p School of Economics, Kingson Universiy, Kingson, KT1 EE, UK, Tel: +44-(0) , c.richer@kingson.ac.uk. Absrac: This paper invesigaes he cyclical behaviour of he wine producion in Porugal s Douro region during he period of 193 o 008. In general, wine producion is characerised by large flucuaions. These flucuaions may cover he exisence of deerminisic cycles. Hence, in his paper, we decompose he wine producion s variance in order o find he dominaing producion cycles In he nex sep we ry o explain hose cycles using a dependen variable, namely he medium spring emperaure for he period 1967 o 008. We esimaed a Time-Varying Auoregressive Model, which could explain 76% of wine variabiliy (R =0.76; n=69; p<0.000). When he emperaure was incorporaed he R-squared is much higher (R =0.98; n=36; p<0.000) and he Akaike crierion value is lower. Hence, medium spring emperaure causes a large amoun of hese cycles and he wine producion variaion reflecs his relaionship. In addiion o an upward rend, here is a clearly idenifiable cycle around he long erm rend in Douro wine producion. We also show how much of he producion cycle and wha cycle in paricular is explained by he medium spring emperaure. We use he shor ime Fourier Transform o decompose he link beween wine producion and emperaure. We find: i) wine producion is characerised by 4.8 and.5 year cycles; ii) by here is a srong link beween wine producion and he mean emperaure in spring; iii) his link is no consan, bu sable. In paricular, he emperaure is responsible for 5. and.4 year cycles which has been happening since he 1980s, iv) he spring emperaure can also be used o as an indicaor for he six year and one year cycles of wine producion. Keywords: Specral Analysis, Time-varying specra, Kalman filer, Wine forecas, Por Wine, Climae variabiliy

3 1. INTRODUCTION Regional wine producion is characerized by large flucuaions wih adverse consequences for everybody involved wih vineyards and he winery indusry as a whole. Moreover, he impac of hese flucuaions have consequences concerning inpu use, land use and hus, indirecly, he environmen. These have conribued o he developmen and accepance of public inervenion and secorial regulaions aimed a reducing income variabiliy ha have no parallel in oher crops (COM, 008). Invesigaing a poenial cyclical naure of wine producion is herefore vial for everyone, from he vinners and grape growers, o he invesors, policy makers and all hose whose business relies on wine supply chain. I is essenial for efficien harves organisaion, regional pricing negoiaions, invesmen in new winery capial equipmen and he developmen of markeing sraegies for boh domesic and expor markes (Cunha e al., 010). Governmen can use forecass on wine grape supply cycles o implemen regulaors mechanisms provided under he Common Organizaion of he Marke (COM) in wine, for moderaing he effecs cyclical wine producion: vineyard resrucuring/conversion, modernizaion of he producion chain, innovaion, suppor for green harves, price policy, sock managemen, assign economic aid, producion quoas, disillaion schemes and oher insrumens o reconcile supply and demand (COM, 008). Various crop modeling approaches are proposed in he agriculural economics lieraure focusing on invesigaing he cyclical facors associaed wih crop producion and sudying how his crop cycles should be characerized and measured. The modelling approach ranges from non-parameric o parameric (Capianio and Adinolfi, 009; Chen and Chang, 005; Ferris, 006; Gemmil, 1978; Goodwin and Ker, 1998; Zhu e al., 008). The radiional approach o modeling he cyclicaliy of wine producion in large economeric models is o assume normal weaher and projec crop yields as linear exension of pas rend (Ferris, 006; Zhu e al., 008). Alhough his linear rend describes he overall long-erm rend in producion, i does no reflec he inheren cyclicaliy in producion and he informaion conained herein. Appropriae saisical es showed ha using regression analysis he explanaory power of a linear model is less han 50 percen (European Commission, 1997; Phares, 000), meaning ha we can have similar forecasing wine producion resuls if we simply flipped a coin. The cyclical paern of regional wine producion is he resul of inricae dynamic fusion of agronomic, poliical and economic decisions as well as he erraic influence of a number of

4 environmenal facors. Hence, he oal adjusmen of he regional wine producion in any given year is he ne effec of all he planing decisions (echnologies includes) ha modify boh he regional vineyard area and he age composiion of grapevine composiion sock. This model was esimaed by Kalman filer and applied o he Florida grapefrui indusry. One of he drawbacks of vineyard cyclical analysis a regional level is he lack of deailed regional daa on new planings, replaning, removal and age composiion of vineyard. However any approach based on specific regional daa can be very cosly when a high number of years is involved in he analysis. To work wih hese regional problems, Kalaizandonakes and Shonkwiler (199) developed a dynamic unobserved componens mehod where separae esimaion of he srucural equaion is possible wihou deailed daa on new planings and replaning. In his conex, i is criical o undersand he limiaions of any regional wine cyclical model ha is developed and used since hey are necessarily gross simplicaions of complex sysems. One oher hand, he perennial naure of grapevine means ha every year is physiologically dependen in several ways on he previous years (Gladsones, 199; May, 004). The permanen srucures of grapevine provide reserves of carbon and nuriens, bu also carry effecs from year o year. Therefore, developing muliple years models is very difficul as many of he imporan carry-over effecs on growh or cropping are no well undersood. Gladsones (199) found ha, afer accouning for echnology, climae is main conrol on he yield grapevine variabiliy because hey are no irrigaed, low ferilized, minimally geneically engineered, and long-lived (>50 years). Climae regulaes nearly every sep of wine producion from selecion of a suiable grape variey o he ype and qualiy of wines produced (Gladsones, 199). The link beween wine producion and in-season meeorological daa has been sudied rough many research aricle (Bindi e al., 001; Cunha e al., 003; Folwell e al., 1994; Jones, 007; Jones and Davis, 000; Lobell e al., 006). However long ime cyclical analysis is affeced by vineyard srucural and climae variabiliy and here are no regional wine cyclical analyses ha co-inegrae hese wo sources of informaion.these are he changes we wish o es for here. Enhanced producion and climae effecs will come in several pars: obviously, meeorological affecs producion via grapevine growh convergence (coherence, correlaion); bu producion mehods have changed hemselves and here is a non-consan impac (or spillovers) of weaher ono wine producion; which ranslaes ino sronger lead/lag relaionships beween producion and weaher. We examine all hree in his conex; focusing 3

5 on measures of coherence and gain respecively. We can hen ask: o wha exen are growh cycles becoming more correlaed weaher? We are herefore engaged in an exercise in idenifying he linkages beween weaher and wine producion using ime-varying mehods. We are no aware ha his has been aemped before. In his paper we show how o use a ime-varying specral analysis o deermine he degree of impac a differen frequencies and cycles, even where daa samples are small and where srucural breaks and changing srucures are a par of he sory. The inconclusive resuls obained in he pas, may have been he resul of using a correlaion analysis which averages he degree of conemporaneous impac across all frequencies. Tha is problemaic because wo variables could share a rend or shor erm shocks, bu show no coherence beween heir cycles. Tha would imply low or possibly negaive conemporaneous correlaions, and give no picure of he rue linkage or dependence beween hem. A common feaure of all he sudies cied above is ha he resuls are sensiive o: i) he choice of coherence measure (correlaion, concordance index); ii) he choice of cyclical measure (classical, deviaion or growh cycles); and iii) he derending measure used (linear, Hodrick-Presco filer, band pass ec). This sensiiviy o he derending echnique is a serious difficuly highlighed in paricular by Canova and Dellas (1993) and Canova (1998). The advanages of using a ime-frequency approach are herefore: i) I does no depend on any paricular derending echnique, so we are free of he lack of robusness found in many recen sudies. ii) iii) iv) These mehods also do no have an end-poin problem no fuure informaion is used, implied or required as in band-pass or rend projecion mehods. There is no arbirary smoohing parameer, such as in he HP algorihm, equivalen o an arbirary band-pass selecion (Aris e al., 004). We use a coherence measure which generalises he convenional correlaion and concordance measures. Any specral approach is ied o a model based on a weighed sum of sine and cosine funcions. However, ha is no resricive. Any periodic funcion may be approximaed arbirarily well over is enire range, and no jus around a paricular poin, by is Fourier expansion (a suiably weighed sum of sine and cosine erms) and ha includes nondiffereniable funcions, disconinuiies and sep funcions. Hence, once we have ime-varying weighs, we can ge almos any cyclical shape we wan. Therefore, a ime-varying specral 4

6 approach, capable of separaing ou changes a differen cyclical frequencies in he regional wine producion, will be needed o provide he flexibiliy o capure hese feaures. Similarly, a ime varying approach will be necessary if we are o accommodae he srucural breaks which mus be expeced wih wine producion mehods and meeorological variabiliy. However, if hese changes argue for a ime-varying approach o measuring he coherence beween variables, hen hey also argue for a decomposiion of he differen cycles ha make up wine producion performance. Hence our choice of a ime-frequency approach. This paper invesigaes he cyclical behaviour of he wine producion in Porugal s Douro region by using ime-varying specral mehods (Shor Time Fourier Transform) o decompose he link beween wine producion and a number o meeorological facor. The paper is srucured as follows: he nex secion gives a shor descripion of world wine indusry and he Douro wine region. This secion also presens he ime series of Douro wine producion and climae daa used. Secion 3 gives a brief inroducion in he ime-frequency approach and explains our echnique wih respec wine cycle relaionships. Secion 4 and 5 presens and discuss he main resuls of long and shor-erm wine cycles for he singular and cross specral analysis. Finally, secion 6 concludes.. WINE INDUSTRY, DOURO REGION AND SAMPLE DATA Grapevines are he number one frui crop planed, wih more han seven million hecares of vineyard grown worldwide, ranging from 50ºN la, rough he ropics, o 43ºS la, in all coninens excep Anarcica. Vineyards occupy 0.5% of he world agriculural area, bu represens abou 3.5% of agri-food world rade and 0.4 of he household expendiure. Alhough grapevines grow from emperae o ropical regions, mos vineyards are planed in areas wih emperae climaes, wih he mos concenraed culures occurring in Europe. The European Union represens 45% (4.8 millions ha) of he world s vineyard area, and almos 65% (175 millions hl) of wine producion, 57% of global consumpion (30 L/year per-capia) and 70% of expors in global erms (EU, 006). Porugal is number five in he European wine producers ranking and he number en worldwide (OIV, 010) and i accouned for 4% of EU-15 producion. Porugal accouned for 7% ( ha) vineyard surface and around 4% (7.1 milions hl) of he oal wine producion in he EU-15. The wine yield of Porugal (9 Lha -1 ) represens less han a half of wine yield in France or Ialy (61 Lha -1 ). Wine indusry represens 8.3% in he value of agriculural producion in Porugal (OIV, 010). Boh domesic (30 Lyear -1 per-capia) and expor 5

7 markes (7 h larges in erms of world expor marke share) performed exremely well conribuing significanly o he Porugal economy by way of generaing revenue from expors as well as generaing and encouraging local business, mainly in Douro region. The Douro Region, locaed in Norheas Porugal, has an area of 5000 ha and vineyards cover approximaely 15.4% of all he land in he region. Viiculure, he main aciviy of mos farmers in he region, akes place under paricularly rigorous climaic condiions, on sony soil ha canno be pu o any oher use (IVDP, 010). Ou of he enire amoun of land used as vineyards in he Douro region, only 6000 ha (68%) are auhorized for he producion of Por Wine. The vines which are considered appropriae for his wine ype, are seleced according o a crieria of qualiy based on a Scoring Mehod (considers soil, climaic, varieies, age of he vines), and classified according o a scale of qualiy ha ranges from A o F. The regulaing insiuion of he secor (IVDP) sipulaes annually he quaniy of grapes produced in Douro Region ha can be used for he producion of Por wine. This ypical quoa policy, called benefício coefficien, is aribued annually among he vineyard ha have ha propery righ (classificaion A o F). On average of 55% of he annual grapes is used for he producion of Por wine and almos 90% is expored. Por Wine is a forified wine (abou 19% of brandy), as defined in EU legislaion. This brandy is impored according he auhorized for Por Wine defined annually by IVDP. This is an imporan business and he informaion provided by modeling cyclical wine producion can be used for accurae quaniy acquiremen and sock of his brandy. For our analysis, we use he annual wine producion daa (193 o 008) for he Douro Region obained from he Insiuo dos Vinho do Douro e Poro (IVDP, 010). The regional climae of Douro is Medierranean and Douro s vineyards is one of he mos non-irrigaed arid regions of he Europe and a srong waer sress is normally observed. These siuaions are especially frequen in summer and appear as a consequence of he low soil waer conen, due o he low rainfall and he elevaed gradiens of he waer vapor pressure beween he leaves and he air. The meeorological observaions for he years 1967 o 008 were colleced in saion of Peso da Régua (41º10 N; 7º47 W, 139 m above sea level), locaed wihin he Douro region and has no been relocaed over he period of record. The meeorological daa consis of daily observaions mean emperaure (Tm) and precipiaion (R), ha are summed (R) or averaged (Tm) by seasons (Spring and Summer). 6

8 3. EMPIRICAL TECHNIQUES 3.1. Esimaion in he Time Domain We esimae he bilaeral links beween he cycles. In order o allow for he possible changes in he parameers, we will employ a ime-varying model AR(p) by applying a Kalman filer o he chosen model as follows: y 9 = α 0, + α i,y i +ε i= 1 wih i, i, 1 i, and i, ( εη, ) ε, η ~ i.i.d. 0, σ, for i= i (.1) α =α +η, for i=0...9 (.) In order o run he Kalman filer we need iniial parameer values. The iniial parameer values are obained esimaing hem by Ordinary Leas Squares (OLS) using he enire sample (see also Wells, 1996). Of course, using he enire sample implies ha we neglec possible srucural breaks. The iniial esimaes migh herefore be biased. The Kalman filer however correcs for his bias since, as Wells (1996) shows, he Kalman filer will converge o he rue values independenly of eh iniial values. Hence, our sar values have no effec on he parameer esimaes, ie.e our resuls are robus. Given hese saring values, we can hen esimae he parameer values using he Kalman filer. We hen employ a general o specific approach o obain a final specificaion for (eq..1), eliminaing insignifican lags using he sraegy specified in he nex paragraph below. The maximum number of lags was deermined by he Akaike Crierion (AIC), and was found o be nine in each case. Each ime we ran a new regression we used a new se of iniial parameer values. Then, for each regression we applied a se of diagnosic ess, shown in he ables in he following secions, o confirm he final specificaion found. The final parameer values are herefore filered esimaes, independen of heir sar values. Using he specificaion above implies ha we ge a se of parameer values for each poin in ime. Hence, a paricular parameer could be significan for all poins in ime; or a some periods bu no ohers; or i migh never be significan. These parameer changes are a he hear of his paper as hey imply changes in he lag srucure and hence changes in he specral resuls. We herefore employed he following esing sraegy: if a paricular lag was never significan hen his lag was dropped from he equaion and he model esimaed again. If he AIC crierion was less han before, hen ha lag was excluded alogeher. If a parameer was 7

9 significan for some periods bu no ohers, i was kep in he equaion wih a parameer value of zero for hose periods in which i was insignifican. This sraegy minimised he AIC crierion, and leads o a parsimonious specificaion. Finally, we esed he residuals in each regression for auo-correlaion and heeroscedasiciy. The final specificaion (eq..1 and.) was hen validaed using wo differen sabiliy ess. Boh ess check for he same null hypohesis (in our case a sable AR(9) specificaion) agains differing emporal insabiliies. The firs is he flucuaions es of Ploberger e al. (1989), which deecs discree breaks a any poin in ime in he coefficiens of a (possibly dynamic) regression. The second es is due o LaMoe and McWorher (1978), and is designed specifically o deec random parameer variaion of a specific uni roo form (our specificaion). We found ha he random walk hypohesis for he parameers was jusified for each model (resuls available on reques). We also es for auocorrelaion of he residuals. For his purpose we use he Ljung-Box es, which allows for auocorrelaed residuals of order p. In all our regressions, we could rejec he hypohesis of auocorrelaion. Finally we chose he flucuaions es for deecing srucural breaks because he Kalman filer allows srucural breaks a any poin and he flucuaions es is able o accommodae his. I should be noed, ha all our ess of significance, and significan differences in parameers, are being conduced in he ime domain, before ransferring o he frequency domain. This is because no saisical ess exis for calculaed specra (he daa ransformaions are nonlinear and involve complex arihmeic). Sabiliy ess are imporan here because our specra are sensiive o changes in he underlying parameers. Bu, given he exensive sabiliy and specificaion ess conduced, we know here is no reason o swich o anoher model ha fails o pass hose ess. Once his regression is done, i gives us a ime-varying AR(p) model. From his AR(p) we can hen calculae he shor ime Fourier ransform as oulined below, and as originally suggesed by Gabor (1946), in order o calculae he associaed ime-varying specrum. 3.. Specra analysis As a firs sep we analyse he power specral densiy funcion of Douro region. The power specral densiy funcion (PSD) shows he srengh of he variaions (energy) of a ime series a each frequency of oscillaion. In oher words, i decomposes he variance of a ime series ino is periodiciies. In a diagram i shows a which frequencies variaions are srong/powerful, and a which frequencies he variaions are weak (expressed in energy ). The uni of measuremen in he PSD is energy (variance) per frequency, frequency band or 8

10 cycle lengh. For example, if a ime series X, where ~ iid...( 0, ) ime, he power specrum would look like he figure 1. =ε ε σ and consan over Figure 1: Power Specrum of a Whie Noise Process As one can see from Figure 1, a whie noise process is characerised by he fac ha no specific frequency has a bigger impac han any oher frequency, for ω= 0,..., π. However, if he daa were dominaed by long cycles or producion cycles, hen he diagram would have higher power (variances) a he low or middle frequency bands respecively; and lower power a he high frequencies 1. In order o calculae he specrum from an esimaed represenaion of (eq..1), we use he Fas Fourier Transform. The Fas Fourier Transform is an efficien algorihm for compuing a discree Fourier ransformaion, or in our case a Discree Time Fourier Transform (DTFT) for discree poins in ime. In our case i creaes a frequency domain represenaion of he original ime domain represenaion of he daa (eq..1). Hence, our analysis of he specra and coherences ha follow are based on a regression done in he ime domain, bu hen ransformed ino a frequency domain funcion by he Fourier ransform. However, in his paper we also allow he coefficiens of our regressions o vary over ime. Therefore we derive one DTFT for each poin in ime. These calculaions define a sequence of shor ime Fourier ransformaions (STFT). In discree ime, his means he daa o be ransformed has been broken up ino frames (which usually overlap each oher). Each frame is hen Fourier ransformed, and he (complex) resul added o a marix which records is magniude, phase and frequency a each poin in ime. This can be expressed as: 1 In he specral diagrams ha follow, we use he erm power raher han energy o denoe relaive variances.

11 { [ ]} (, ω ) = [ ] [ ] STFT xn X m xnwn me jωn (.3) n= In his case, m and n are differen poins in ime; ω is he frequency and is coninuous; and j = -1. Bu in mos ypical applicaions he STFT is performed using he Fas Fourier Transform, so all variables are discree and n-m would be he esimaion window. In our applicaion he window is no consan, bu increasing wih each new observaion. Moreover, we derive he STFT using Kalman filer esimaes of (eq..1): see secion.3 below. The squared magniude of he STFT hen yields he specrogram of he funcion: specogram x { } X (, ) τω (.4) The remaining quesion is wha algorihm do we use o calculae he Fas Fourier Transform? One algorihm ofen used o calculae he Fas Fourier Transform is he Bluesein algorihm (Bluesein, 1968), which is also called he chirp z-ransform algorihm. In paricular, i can compue any ransform of he form: N 1 nk Xk = xnz, where k = 0,..., M 1 (.5) n= 0 for an arbirary complex number z and for differing numbers N and M of inpus and oupus (see also: Rabiner e al., 1969). Hence, he algorihm we apply o calculae he Fas Fourier Transform is a well-esablished algorihm and widely used in engineering (Boashash, 003; Boashash and Reilly, 199). I is no commonly used in economics however. Finally Boashash and Reilly (199) have shown heoreically ha, once eq. (.) has been esimaed, is coefficiens α i, can be used o calculae he shor ime Fourier Transform and he power specra direcly (by applying he Bluesein algorihm). Tha has he convenien propery ha he radiional formulae for he PSD are sill valid and may sill be used, bu hey have o be recalculaed a each poin in ime. The ime-varying specrum of he growh rae series can herefore be calculaed as follows (see also: Lin, 1997): P ( ) ω = 9 i= 1 i, σ ( ) 1+ α exp jωi (.6) where ω is angular frequency and j is a complex number. The main advanage of his mehod is ha, a any poin in ime, a power specrum can be calculaed insananeously from he 10

12 updaed parameers of he model. Hence, we are able o generae a power specrum even if we have a shor ime series and even if ha ime series conains srucural breaks. Thus, when we presen our empirical resuls below, hey are based on he ime-varying STFT calculaions. The only difference from figure 1 is ha we have o add a ime dimension o show how he specra have changed over ime. The resul is hen a 3-dimensional diagram Cross-Specra Analysis In his paper we also invesigae he linkage beween differen wine producion cycles. In he frequency domain, he naural ool o do ha is he coherence. The specral coherence ( K XY ) is a saisic ha can be used o examine he relaion beween wo signals or daa ses. Values of he coherence will always saisfy 0 K XY 1. For a sricly proporional linear sysem wih a single inpu x and single oupu y, he coherence will equal one. If x and y are compleely unrelaed hen he coherence will be zero. If K XY is less han one bu greaer han zero i is an indicaion ha oupu y is being produced by inpu x as well as by oher inpus. Hence, he coherence is nohing else han he R in he frequency domain. Since we are calculaing he coherence using he shor ime Fourier ransform, he coherence may also be ime-varying. So we have o exend K by a ime index. For he res of his paper we will wrie K. XY Suppose now we are ineresed in he relaionship beween wo variables{ y } and{ x }, where { y } is he wine growh rae and { x } ha hey are relaed in he following way: XY, is he emperaure variabiliy for example. We assume ( ) ( ) ( ) V L y = A L x + u, u ~ i.i.d. 0, σ (.7) where A(L) and V(L) are filers, and L is he lag operaor such ha Lz = z -1. Noice ha he lag srucure, A(L), is ime-varying. Tha means we need o use a sae space model (we use he Kalman filer again) o esimae he implied lag srucure. Tha is i, i, 1 i, i, i, i, 1 i, i, ( ε ) i ( η ) v = v +ε, for i = 1,..., p and ε ~ 0, σ a = a +η, for i = 0,..., q and η ~ 0, σ i (.8) As before, we es for he random walk propery using he LaMoe-McWorher es. And for srucural breaks, we employ he flucuaions es (Ploberger e al., 1989). Finally, we use our previous general o specific approach o esimae (.5); saring off wih lag lenghs of nine and p=q, and dropping hose lags which were never significan (as we did before). 11

13 Having esimaed he coefficiens in (eq..7), we can calculae he gain, coherence and cross specra based on he ime-varying specra jus obained. This allows us o overcome a major difficuly in his kind of analysis: namely ha a very large number of observaions would usually be necessary o carry ou he necessary frequency analysis by direc esimaion. Tha would be a paricular problem in he case of srucural breaks, since he sub-samples would ypically be oo small o allow he associaed specra o be esimaed direcly. In Hughes Halle and Richer (00; 003a; 003b; 004; 006; 009a; 009b; 009c) we use he fac ha he ime-varying cross specrum, f YX (ω), using he STFT can be wrien as: YX ( ) ( ) ( ) f ω = T ω f ω (.9) where T(ω) is he ransfer or filer funcion is defined by (eq..9) and calculaed as follows: XX T ( ) q ( ω ) a exp j b b, b= 0 ω = p ( ω ) 1 vi, exp j i i= 1, for = 1,..., T (.10) The las erm in (eq..9), f XX (ω), is he specrum of predeermined variable. This specrum may be ime varying as well. However, in his paper we are ineresed in he coherence and in he composiion of he changes o ha coherence over ime. So we need o esablish expressions for he coherence and gain beween x and y o show he degree of associaion and size of impac of x on y. The specrum of any dependen variable is defined as (Jenkins and Was, 1968; Laven and Shi, 1993; Nerlove e al., 1995; Wolers, 1980): ( ) ( ) ( ) ( ) f ω = T ω f ω + f ω (.11) YY XX vv From (eq.6) we ge he ime varying residual specrum f ( ) ω = vv p i= 1 f uu i, ( ω) 1 v exp ( jωi) (.1) and he gain as A( ω ) = T( ω). Finally, given knowledge of f YY (ω), ( ) we can calculae he coherence a each frequency as: T ω, and f XX (ω), K = { 1+ fvv ( ω) ( T( ω) fxx ( ω) ) } YX, 1 (.13) 1

14 The coherence is equivalen o he R saisic, and he gain he regression coefficien, impac or ransmission effec of x on y, in he ime domain. Thus he coherence measures, for each frequency, he degree of fi beween x and y : equivalenly he R beween each of he corresponding cycles in x and y. Hence A( ω) and K YX, measure he link beween wo variables a ime. For example, if he coherence has a value of 0.6 a frequency 1., hen i means ha he emperaure cycle a frequency of 1. deermines wine producion cycle a ha poin in ime by 60%. Similarly a gain of 0.5 means ha half he variance in emperaure cycle a ha frequency is ransmied o he wine producion cycle. In his paper, we are concerned wih he coherence and gain, no wih measuring he phase shif elemens as such. Bu we are able o deec changes in phase relaionships from changes in he relaive imporance of differen cycles in he cross-specral componens. 4. RESULTS In his secion and he nex, we sudy he specra and cross-specra of wine oupu in he Douro region. In he nex wo secions, we firs presen he ime-varying specrum and hen he coherence and gain. One can see from hese figures ha he specra change. However, one canno infer direcly from hose figures ha he changes in he specra are also saisically significan. The figures for he ime-varying specra/cross-specra have o be accompanied by he flucuaion es resuls. Once a srucural break has been idenified by he flucuaions es, he resuls will show up as a significan change in he associaed specrum or coherence or gain Single specra of Douro wine producion The resuling daa are hen fied o an AR(p) or auoregressive disribued lags model ADL(p,q) model as described above, and esed for saionariy, saisical significance, and a baery of diagnosic and specificaion checks before being convered o he specra and crossspecra ha we need. Figure shows he ime series of wine producion in he Douro Region from 1940 o 008. For mos of he sample his ime series shows a lo of variaion, which can be caused by srucural breaks. In any case, his variaion makes a common regression very difficul, as i does no really capure he variaion. In conras, ime-varying parameer approaches can capure hose parameer changes in a sysemaic way. 13

15 Wine Producion (hl * 1000) Year Figure. Wine Producion in he Douro Region Table 1 shows he regression resuls for he series producion. This AR(5) model is he basis for he specrum shown in he figures 3 and 4. As one can see he regression is robus as here is no auocorrelaion. The AIC crierion seems o be high. However, one should keep in mind ha he AIC crierion is based on he sandard error of he regression. Since he underlying ime series has quie large values, so has he AIC crierion. For he chosen model, his was in fac, he lowes value. The R-squared is relaively high wih 76%, bu here is a lo of unexplained variance. Alhough he firs four lags are saisically no significan a he end of he sample, hey were no a oher sample poins in ime, which is why we kep hem in he regression (Table 1). Hence, his able only shows he final regression for he las observaion for reason of resriced space. All regressions are available on reques. Table 1. Kalman filer parameer esimaes and summary saisics for ime-varying specral model of he Wine Producion in he Douro Region. Dependen Variable PRD Annual Daa From 1940 o 008 Variable Coeff. Sd Error -values Obs 69 Df 64 Consan R Sd Error y PRD(1) Mean SSr PRD() SE LjB Tes PRD(3) AIC PRD(5) Obs.- Usable observaions; df- Degrees of Freedom; PRD- Douro wine producion R - Uncenered coefficien of deerminaion; AIC- Akaike Crierion; LjB es- Ljung-Box Tes: Q*(16) SSr- Sum of Squared residuals; Sd Error y- Sandard error of dependen Variable and of esimae (SE) -value- Significance level for 64 df: >1.670 (p<0.05); >.387 (p<0.01); > 3.44 (p<0.0005)

16 The regressed series models he variaion of he original series fairly well (Fig.3). Bu he peaks are someimes no as high as in he original series. This calls for an invesigaion of oher deerminans of he dynamic behaviour of he series. However, before we come o ha, i is worhwhile o highligh he dynamic properies of he wine producion series. Wine Producion (hl * 1000) Year Figure 3. Original Time Series (black) and Regressed Time Series (scaered) of Wine Producion in Douro Region. The ime-varying specrum, which is based on above regression shows he dynamic characerisics of he wine producion. Over he enire frequency band, here are hree disincive peaks: a 0.1, 1.3 and.5 (Fig. 4). A frequency of 0.1 basically represens he long run rend. For he las five years, all hree frequencies have he same imporance (specral densiy). Tha was no always he case, for example during he 1990s. Hence, currenly wine producion is characerised by a long run rend and wo shorer cycles of 4.8 years and.5 years, respecively. In oher words wine producion is following an (upwards) rend. Around ha rend here are wo flucuaions of equal srenghs: one has a lengh of 4.8 years and here is a shorer one of.5 years. Since boh have he same specral densiy, i.e. have he same impac ha makes i difficul o disinguish beween he wo when considering he ime series only. For example he upswing of he five year cycle could be dampened by he downurn of he wo year cycle. Unforunaely, wha his model does no provide is a way o predic where you are in he cycle. This deficiency is undersandable given he complexiy in analyzing no jus he long erm rend and shor-erm cyclical flucuaions of wine producion. 4.. Cross specra of Douro wine producion Having esablished wha characerises he producion cycles he nex quesion is wha causes hem. The specrum in iself canno answer his quesion. I is purely descripive.

17 Power Frequency :1 004:1 001:1 1998:1 1995:1 199:1 1989:1 1986:1 1983:1 1980:1 1977:1 Time 1974:1 1971:1 1968:1 1965:1 196:1 1959:1 1956:1 1953:1 1950:1 Figure 4. Time Varying Specrum of he Wine Producion We had he choice of several exogenous variables which may have an impac on wine producion. Noably, we have ime series of rainfalls and emperaure for he period 1967 o 008. The aim was o find a deerminan ha can explain he observed producion paern and herefore he mos imporan variable. As i urned ou among all models conaining differen variables, he one ha produced he lowes AIC value was he one conaing mean emperaure in spring. Figure 5 show he ime series of mean spring emperaure. Like he wine producion series, i conains large variaion. On eyesigh i seems here are hree regimes: i) one regime ha sars he beginning of he sample unil This period is characerised by a relaively high level of emperaure variaion (mean 16.0ºC; σ 0.76). ii) he nex period is from 1984 unil 1994, where he variance is relaively low (mean 16.6ºC; σ 0.47) and he las regime iii) from 1994 o 008 he variaion is increasing again, bu also he mean emperaure is higher (mean 17.9ºC; σ 0.76) han in he previous periods. Given hese srucural breaks, i makes sense o incorporae emperaure ino our AR(5) model in a ime-varying manner. Table shows he regression resuls for he final poin in ime (008). In comparison o he able 1, he R- squared is now much higher (98%) and he AIC value is lower.

18 Temperaure ºC Year Figure 5. Mean spring emperaure in Douro region for he period 1973 o 008. The following figure shows he behaviour of he Tm_Sp coefficien. As one can see, he coefficien varies a lo hroughou he sample. However, owards he end of he sample, he coefficien sabilises on a relaively high level (149). Hence, a one degree increase in he Tm_Sp will increase mean wine producion in he same year by 13.4% (14938 hl, Table). Over ime hough afer hree years, an increase in emperaure will reduce mean wine producion by 6.0% (6679 hl, Table ). Table. Kalman filer parameer esimaes and summary saisics for he ime-varying model of Wine Producion on emperaure Dependen Variable PRD Annual Daa From 1973 o 008 Variable Coeff. Sd Error -value Obs 36 Df 3 Consan R Sd Error y PRD(5) Mean SSr Tm_Sp SE LjB Tes Tm_Sp(3) AIC Obs.- Usable observaions; df- Degrees of Freedom; PRD- Douro wine producion; Tm_Sp- Mean Temperaure during he spring season R - Uncenered coefficien of deerminaion; AIC- Akaike Crierion; LjB es- Ljung-Box Tes: Q*(16) SSr- Sum of Squared residuals; Sd Error y- Sandard error of dependen Variable and of esimae (SE) -value- Significance level for 3 df: >1.695 (p<0.05); >.45 (p<0.01); > (p<0.0005)

19 Parameer Value [ ] Year Figure 6. Immediae Impac of Spring Temperaure The original idea o use emperaure was o check wheher his variable can explain he wine producion cycles. Figure 7 shows he gain. Wha his figure is showing ha if he emperaure changes i causes wo major cycles: on he one hand here is he cycle a a frequency of 1. or 5.4 years and a frequency of.6 or.41 years. Those cycles are indeed very close o he producion cycles. Alhough he wo mos imporan cycles of he gain have always been he mos imporan cycles, heir impac is no consan as once can see from he figure 7. Neverheless, he 5.4 year cycles have always been he mos imporan one. This resul is in conras o he previous resuls where he specrum of he wine producion was characerised by an equal impac of hese cycles. Temperaure on is own does no cause cycles of equal srengh. Hence, emperaure alone canno fully explain he dynamic behaviour of wine producion. Oher impacs could come from meeorological variables no esed, grape prices or marke regulaors mechanisms, for example.

20 Power Frequency Time Figure 7. Gain Temperaure on Producion Having esablished ha he spring emperaure causes a dynamic behaviour of wine producion close o he specrum, he nex quesion is wha can we learn from he acual behaviour of he emperaure? For ha we consider he coherence which gives he curren impac of emperaure on wine producion. The coherence shows ha emperaure explains up o 50% of he 5 year cycle of wine producion and abou 40% of he curren shor run rend of producion. Temperaure also explains abou 0% of curren.4 year cycle. The conclusion is wofold: 1) Temperaure does have a conemporary effec on wine producion. However, his impac is no more han 50%. ) Given ha he conemporary effec is raher low, emperaure is a process ha is leading he curren wine producion. Also, here mus be oher variables which explain he conemporary behaviour of wine producion. However, given ha wine producers may be ineresed in he predicive power of emperaure, furher research is needed on how srong his predicive power is.

21 Percen/100 Time Frequency Figure 8. Coherence beween wine producion and Spring emperaure 5. DISCUSSION From growing season wine producion in Douro region has been subjeced o cycles bu here has been a rend oward a coninued increased producion. While some of he rend in high producion can undoubedly be aribued o vineyard srucure changes and/or beer viiculural and wine praices, climae exer profound influence in producion variabiliy. As previously saed, he linear model currenly used by indusry analyss accouns for less han 50 percen of he variaion of grape producion; our model spring emperaure based accouns for approximaely 98 percen explanaion in wine producion variabiliy. According o his ime varying model, he spring emperaure has he meeorological variable wih more explanaion of he cyclicaliy of Douro wine producion. Despie he grea imporance of rainfall on grapevine producion in Medierranean climaes (Bindi e al., 001; Jones, 007), mainly during he summer period, no significan influence on wine producion cycles was repored in his sudy. In Douro region, summer rainfall is consisen low over he years and i is difficul o consider an imporan facor o explain he grea variabiliy of wine producion (Cunha e al., 003). On he oher hand, high spring emperaure is usually combined wih high sunshine, low precipiaion levels and soil moisure.

22 Remarkably, spring emperaure can be used o forecas he acual shor erm variaion of wine producion. Mean spring emperaure explains up o 35% of shor erm variaion of wine producion (Fig. 8). Moreover i also explains up o 37% of he curren 5 year cycle and i sill explains 15% of he curren year cycle (Fig. 8). Hence, if one follows he mean emperaure, his informaion can be used o esablish a wha sae of he cycle wine producion is. This informaion is useful when i comes o forecass concerning wine producion in he curren year. The influence of previous and in-season spring emperaure on he shor erme wine cyclical producion founded in his sudy is consisen wih previous sudies on he grapevine ecophysiology behaviour and yield. As a perennial and deciduous plan, environmenal condiions influence is vegeaive and reproducive growh. The condiions of he previous year are imporan componens of he wine producion variabiliy. This influence relaes no only o he season in which he crop is produced, bu also o pas seasons, mainly he las wo seasons before he one in which harves ake place (Cunha e al., 010; May, 004). As one of he premises for grape yield, grapevine bud fruifulness has been he focus of many sudies. Mos of hese sudies have consisenly deermined ha ligh and emperaure are he mos imporan climaic facors during he bud differeniaion in he season before he one in which harves akes place (Cunha e al., 010; May, 004). These sudies suppor he posiive impac of spring emperaure of he curren year producion cycle founded in our work. Ho spring emperaures are favorable, direcly or indirecly, for phoosynheic assimilaion, grapevine pollinaion/ferilizaion and resul in high frui-se (ex. Cunha e al., 003; May, 004). Moreover, ho and dry spring condiions are generally associaed o low impacs of grape diseases on producion level. One he oher hand, he earlier phenology developmen, associaed o ho spring (Jones and Davis, 000; May, 004), allows he grapevine o be rain fed and capialize on diminishing soil waer from winer rains. All of hese effecs are in accordance wih posiive impac of in-season spring emperaure on he Douro wine producion level observed in our sudy. However, in Medierranean climae no irrigaed vineyard (like Douro region) submied o consecuives ho springs could reduce he soil moisure as well as depleing accumulaed reserves of carbon and nuriens in he permanen srucures (ex. May, 004). These reserves can play a criical role in poenial producion of grapevine, mainly in years wih unfavourable 1

23 meeorological condiions during he spring. Modeling work suggess negaive relaionship beween wine producion and he spring emperaures in he previous 5 five year. Modelling cyclical wine producion wih his ime-varying model allows for accurae shorerm as well long-erm forecass, providing long-erm growh raes, shor-erm cycle lengh and inensiy by differen periods and climae scenarios. While hese long erm cycles do no necessarily mean ha perennial grapevine is more vulnerable han oher crops, hey argue for effecive inegraion of climae science wih agriculural pracice. The projecions of fuure climaes in combinaion wih he developed model of cyclical behavior of wine producion can provide a powerful ool for assessing poenial fuure responses of viiculure and wine indusry o climaic variabiliy, and allow saisical confidence limis o be aached o esimaed responses. Wih respec o he fuure, we can expec climae risks o inensify in he Medierranean (IPCC, 007). Based on he mos recen and comprehensive ensembles of global and regional climae variabiliy simulaions, he Medierranean may experience subsanial warming (emperaure increases of 3 5ºC) by 080; a he same ime, iner-annual variabiliy is projeced o increase, especially in he spring period (Giorgi and Lionello, 008). Premium wine producions are coming for viiculural regions locaed in narrow climaic niches ha are very vulnerable from boh shor-erm climae variabiliy and long-erm climae change (Jones, 007). Due o he economic and social imporance of wine indusry, i behooves us o pay aenion o his phenomenon, and especially o pu effor ino undersanding how viiculure and wine indusry will respond and adap o informaion abou climae generally and forecas in paricular. 6. CONCLUSIONS This paper has aken a close look a he accuracy of measuring he cyclical behaviour of wine producion in he Douro region using a long ime series. Paricular aenion was devoed o he fac ha he vineyard srucural producion and meerological facors migh have changed during he sample period. Using differen srucural breaks ess, we indeed found several break poins for he individual series and even more for he co-inegraing relaionship. When modelling wine producion research is complicaed by he large variance and he srucural changes of he ime series. A ime invarian approach canno capure boh effecs simulaneously. In conras our approach can model he large variance, precisely because he

24 underlying daa generaing process is no bound o be consan. Moreover, using he shor ime Fourier ransform allows o decompose he observed variance ino is componens. We could deec several imporan deerminisic cycles, which can be used o analyse curren wine producion. The model presened here provides a deailed picure of he cyclical behavior of wine producion in Douro region ha akes ino consideraion boh vineyard srucural and spring emperaure, idenifying he long-erm rend as well as he shor erm cyclicaliy. Modeling work suggess a srong dependence on he shor-erm wine producion on he Spring emperaures. We show ha he variabiliy of wine producions in Douro region increased in he las wo decades. I may be ha he changes in climae variabiliy during he same period, repored on he lieraure, have conribued o his increased in variabiliy as show in oher regions. Farmers, policy developers and insurers are ineresed in undersanding and quanifying he risk of climae variabiliy and is ineracion wih oher producion risks. The developed model of cyclical behavior of wine producion can be coupled wih projecions of fuure climaes in order o explore poenial changes in wine producions ha could accompany fuure spring emperaure changes in he Medierranean vineyards. The simpliciy, accuracy and early capabiliy of he cyclical wine producion model developed and he comparison of marginal informaion coss wih respec o he benefis jusify is use for he viiculure and wine indusry for boh economic and echnical reasons. REFERENCES Aris M., Marcellino M., Prioriei T. (004) Daing he Euro Area Business Cycle, in: L. Reichlin (Ed.), The Euro Area Business Cycle: Sylised Facs and Measuremen Issues, Cenre for Economic Policy Research, London. Bindi M., Fibbi L., Migliea F. (001) Free Air CO Enrichmen (FACE) of grapevine (Viis vinifera L.): II. Growh and qualiy of grape and wine in response o elevaed CO concenraions. European Journal of Agronomy 14: Bluesein L.I. (1968) A linear filering approach o he compuaion of he discree Fourier ransform. Norheas Elecronics Research and Engineering Meeing Record Boashash B. (003) (Ed.)^(Eds.) Time Frequency Signal Analysis and Processing, Elsevier, Oxford. pp. Pages. Boashash B., Reilly A. (199) Algorihms for ime-frequency signal analysis, in: B. Boashash (Ed.), Time-Frequency Signal Analysis - Mehods and Applicaions, Longman- Cheshire, Melbourne. pp

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