Methodological description of the Trend indicator of Output

Transcription

1 1(17) Mehodological of he Trend indicaor of Oupu Chaper 1 Chaper 2 Chaper 3 Chaper 4 Overview of he Trend Indicaor of Oupu Publicaion imeable, revisions policy and disseminaion of he Trend Indicaor of Oupu Compilaion of he Trend Indicaor of Oupu Quarerly flash esimae of GDP

2 2(17) Chaper 1 Overview of he Trend Indicaor of Oupu 1.1 Organisaion The Trend Indicaor of Oupu is compiled by he Naional Accouns Uni of Saisics Finland s Deparmen. The compiling is performed by one full-ime person (summariser) and beween one and hree oher naional accouns expers. 1.2 Publicaion imeable, revisions policy and disseminaion The Trend Indicaor of Oupu is published some 65 days (he firs wo monhs of a quarer) or 45 days (las monh of a quarer) from he end of he saisical reference monh. A calendar showing all fuure release daes for he curren year can be found on he web pages of he Trend Indicaor of Oupu: hp://ilasokeskus.fi/il/kkk/julk_en.hml. Trend Indicaor of Oupu daa become revised afer heir firs release. I is, herefore, advisable o always rerieve he laes version from he Trend Indicaor of Oupu web pages when using ime series. 1.3 Compilaion of he Trend Indicaor of Oupu 1.4 Benchmarking The calculaion of he Trend Indicaor of Oupu is based on monhly indicaors. These indicaors are used because, in conras o annual accouns, exhausive monhly daa on he values of he differen ransacions are generally no available. Daa a curren prices are mainly calculaed by means of exrapolaion of indicaor changes, i.e. he monhly Trend Indicaor of Oupu daa from welve monhs back are muliplied wih he year-onyear change in he indicaor. Daa a curren prices are deflaed according o he average prices of he year before. This produces volume figures a previous year's prices, in which he previous year is always he base year. Volume changes a previous year's prices are used o chain a coninuous volume series a reference year 2000 prices wih he so-called annual overlap mehod. This series is published as he Trend Indicaor of Oupu. Chained volume series are benchmarked o he quarerly naional accouns value added series using he proporional Denon mehod. 1.5 Seasonal adjusmen and working day correcion In he Trend Indicaor of Toal Oupu seasonal adjusmen and working day correcions are performed wih he TRAMO/SEATS mehod by using he Demera sofware. The daa are calculaed as original and adjused for working days for he whole economy and for hree main indusries. A seasonally adjused and a rend series are also calculaed for he whole

3 3(17) economy. Seasonally adjused, working day correced and rend ime series are no benchmarked o quarerly or annual accouns afer adjusmen.

4 4(17) Chaper 2 Publicaion imeable, revisions policy and disseminaion of he Trend Indicaor of Oupu 2.1 Release imeable and revisions o daa 2.2 Conens published 2.3 Special ransmissions The Trend Indicaor of Oupu is published some 65 days (he firs wo monhs of a quarer) or 45 days (las monh of a quarer) from he end of he saisical reference monh. A calendar showing all fuure release daes for he curren year can be found on he web pages of he Trend Indicaor of Oupu: hp://ilasokeskus.fi/il/kkk/julk_en.hml. The Trend Indicaor of Oupu is no published beween calculaion rounds even if some daa have changed in some oher saisics included in naional accouns, such as quarerly or annual accouns. Such changes will show up in he nex regular publicaion of he Trend Indicaor of Oupu. Trend Indicaor of Oupu daa become revised afer heir firs release. I is, herefore, advisable o always rerieve he laes version from he Trend Indicaor of Oupu web pages when using ime series. The revisions can be divided ino hose arising from revisions in he source daa and revisions caused by benchmarking o quarerly annual accouns. Revisions arising from revisions in he monhly source daa occur wihin roughly one year of he iniial publicaion. In each calculaion round he ime series are recalculaed saring from he 1996 daa. However, in he revisions of Trend Indicaor of Oupu daa from earlier han he mos recen 1 o 3 monhs, he benchmarking o quarerly naional accouns is more significan han he revisions arising from revisions in he source daa. The publicaion forma of he Trend Indicaor of Oupu is a free online release comprising a brief release ex and ime series accessible via he Tables link. The enire daa conen is included in he ables of he online release. The ime series sar from January The ables can illusrae he original index series of he whole naional economy and he hree main indusries, namely primary producion, secondary producion and services, he working-day correced index series as well as change percenages for boh when compared wih he respecive monh of he year before. Seasonally-adjused and rend series are available as index series for he whole economy as well as heir change percenages form he previous monh. The ime series and change percenages included in he online release of he Trend Indicaor of Oupu are also delivered o he ASTIKA service.

5 5(17) The quarerly accouns flash esimae for he naional economy, which is based on he Trend Indicaor of Oupu and no published separaely, is sen o Eurosa a a lag of 43 days from he end of a quarer. 2.4 Meadaa The of he Trend Indicaor of Oupu is available on he home page of he saisics a hp://ilasokeskus.fi/il/kkk/mea_en.hml. A qualiy (in Finnish only) is also available on he home page of he Trend Indicaor of Oupu a: hp://ilasokeskus.fi/il/kkk/laa.hml.

6 6(17) Chaper 3 Compilaion of he Trend Indicaor of Oupu 3.1 Overall compilaion approach Calculaion sysem of he Trend Indicaor of Oupu The calculaion of he Trend Indicaor of Oupu is based on monhly indicaors. Indicaors refer o such quickly released saisics or oher source daa ha are considered o correlae wih or develop in he same direcion as a cerain naional accouns ransacion. These indicaors are used because, in conras o annual accouns, exhausive monhly daa on he values of he differen ransacions are generally no available. Even if exhausive daa were available monhly a some ime lag, i would be very rare for hem o be available in he imeable required by he Trend Indicaor of Oupu, i.e. wihin 40 or 60 days from he end of a monh. Daa a curren prices are calculaed by means of exrapolaion of indicaor changes, i.e. he monhly Trend Indicaor of Oupu daa from welve monhs back are muliplied wih he year-on-year change in he indicaor. For he ime being, inermediae consumpion is no esimaed separaely, bu he developmen of indusries is esimaed on he basis of he developmen of oupu indicaors. Example 1: Exrapolaion wih one indicaor Time period Indicaor Value, EUR million Exrapolaed value, EUR million 2006 Jan , Feb , March , Apr , Jan (102.7/100.0)*1,478 = 1, Febr (104.0/101.4)*1,499 = 1, March (103.5/102.1)*1,530 = 1, Apr (105.2/103.9)*1,590 = 1,610 Daa on volume are obained by deflaing he curren priced figure wih he price index change from previous year s average price and by chaining hus obained volumes a he previous year s prices ino values a reference year 2000 prices wih he Annual overlap mehod (see 3.2). In he Trend Indicaor

7 7(17) of Oupu he chained volume series are benchmarked o correspond o he value added series of quarerly naional accouns. Working day correcions and seasonal adjusmens are performed on benchmarked ime series. Seasonally adjused and working day correced series are no benchmarked again, which means hey do no follow exacly he developmen of quarerly naional accouns Trend Indicaor of Oupu daa sources The source daa used in he calculaion of he Trend Indicaor of Oupu cover mos of he daa used in quarerly naional accouns. The calculaion uses 64 sources o describe boh value daa and price developmen. The calculaion is performed a he 2-digi level of he classificaion of indusries bu no by a breakdown by secor as in quarerly naional accouns. Inermediae consumpion is no esimaed separaely eiher. For manufacuring and privae services he primary sources of value daa are preliminary daa from urnover indices and for public services preliminary daa from wage and salary indices, while producer price indices and indices of wage and salary earnings are used as sources for price daa. The source daa for primary producion derive from informaion on volumes of milk received by dairies, slaugherhouse saisics, crop producion saisics, daa on marke fellings, and uni price daa corresponding wih hese uni volume daa Esimaion in preliminary daa Esimaes based on saisical predicion models or exper esimaes are used in he esimaion of some sub-series when an indicaor describing he developmen of he sub-series is no available, ypically because of he release imeable. In ime series benchmarking and seasonal adjusmen saisical models are, of course, used. 3.2 Volume daa Trend Indicaor of Oupu volume daa are published as chained series a reference year 2000 prices. The chaining is performed wih he Annual overlap mehod Chaining wih he Annual overlap mehod in he Trend Indicaor of Oupu Calculaion of volume daa sars wih he so-called deflaion in which ime series a curren prices are convered o series a he average prices of he previous year by dividing monhly curren price figures wih a deflaor. The simples deflaor is he raio beween he index poin figure for one calculaion monh and he previous year s average of he index, which expresses he price level of he calculaion monh relaive o he average price level of he previous year. Several price indices which receive heir weighs from curren priced daa are used in he deflaion of one published series. Deflaion is performed a he level of sub-series, so weighing is auomaic when he deflaed sub-

8 8(17) series are summed o main indusries a he publicaion level where he chaining akes place.

9 9(17) Example 2: Deflaion wih one price index (NB his produces as he average for he price index of 2006) Time period Esimae a curren prices Price index Deflaor Volume a previous year s average price 2006 Jan 1, Feb 1, March 1, Apr 1, Jan 1, / = Feb 1, / = March 1, / = Apr 1, / = ,518 / = 1,524 1,537 / = 1,537 1,551 / = 1,545 1,610 / = 1, Chaining and benchmarking When he previous year s average priced volumes have been calculaed, hey are chained ino reference year 2000 prices. The chaining is done by firs calculaing change in he volume (a previous year s average prices) of each monh from he curren priced average of he previous year. This monhly change in he volume is used o muliply he average of he previous year s volume, which produces a chained monhly volume series. In chained series he reference year means ha volumes are expressed relaive o he curren priced level of he reference year. Because he price weighs change annually in chained series, we canno acually claim ha chained volume series would be a he prices of The drawback of chained series is loss of addiiviy, in oher words, he series canno be summed up ogeher. For example, he chained volume of oal value added or oal oupu does no exacly equal he sum of is componens. Chained volume series are benchmarked o quarerly naional accouns wih he proporional Denon mehod (see 3.3). This procedure differs from he quarerly naional accouns benchmarking, in which volumes a he previous year's prices are benchmarked using he pro raa mehod and curren priced

10 10(17) values are benchmarked using he proporional Denon mehod before chaining Chaining and seasonal adjusmen Chained and benchmarked volume series are seasonally adjused wih he TRAMO/SEATS mehod using he Demera sofware. Each chained volume series is adjused separaely (so-called direc approach) because chained series canno be summed up ogeher. The daa are calculaed as original and working day adjused series for he whole economy and for hree main indusries. In addiion, a seasonally adjused series and a rend series are calculaed for he whole economy. Seasonally adjused, working day correced and rend ime series are no benchmarked o quarerly or annual accouns afer adjusmen. 3.3 Benchmarking wih quarerly naional accouns The Trend Indicaor of Oupu is benchmarked o correspond o he mos recen quarerly naional accouns. Afer benchmarking he rend developmen of he monhly ime series corresponds o ha of he quarerly naional accouns ime series. Time series are benchmarked before heir working day and seasonal adjusmen. Trend Indicaor of Oupu ime series are benchmarked o quarerly naional accouns wih he proporional Denon mehod 1 which is basically mechanical and aims o jus o mainain he originaliy of he rend developmen beween he monhs. If an observaion in an original series a poin in ime is denoed wih i and an observaion in he benchmarked series a poin in ime wih x, he sum of squares T x x i i = , where T denoes he las monh of he ime series, is minimised under he condiion ha he sum of all he monhs in a quarer is he value obained from quarerly naional accouns. The benchmark o indicaor raio BI = x, i will hus be esimaed for every monh, which, when he enire ime series considered, deviaes as lile as possible from he BI raio of he previous poin in ime. There are also various benchmarking mehods ha are based on ime series models and in which he original ime series is used as he exernal regressor. A simple example of his is Chow-Lin 2, and if suiably formulaed, he Denon mehod can also be regarded as a special case of his 1 Denon, F.T. (1971), Adjusmen of monhly or quarerly series o annual oals: An approach based on quadraic minimizaion. Journal of he American Saisical Associaion, 82, Chow, G.C. Lin, A.-L. (1971), Bes Linear Unbiased Inerpolaion, Disribuion and Exrapolaion of Time Series by Relaed Series. The Review of Economics and Saisics, 53 (4) s

11 11(17) kind of a model. Wih he excepion of cases of paricularly problemaic series, he Denon mehod and mehods based on simple ime series modelling produce in pracice he same benchmarked series, and no reasons for changing he mehod have emerged from he examinaions performed. In addiion, he proporional version of he Denon mehod is recommended by he IMF 3. More complex models would make i possible o sudy ineresing connecions wih e.g. seasonal adjusmen, bu hen he benchmarking proper would no necessarily succeed equally reliably. Furher reading abou ime series model-based mehods is available in he maser s hesis wrien a Saisics Finland (Hakala, 2005) Seasonal adjusmen and working day correcion Background informaion on seasonal adjusmen Time series of he Trend Indicaor of Oupu show srong variaion beween he observaions periods of a year, which is ypical of ime series on economic rends. This is known as seasonal variaion. The reasons for his variaion could be he cycle of seasons, changes in he observed phenomenon caused by sales seasons favourable for differen producs and he iming of ransacions. In addiion o he variaion beween winer and summer monhs, consumpion over he Chrismas and Easer seasons, paymens of ax refunds and back axes ha in Finland fall due in December, as well as companies paymens of dividends in spring afer he closing of accouns are examples of causes of seasonal variaion in monhly and quarerly series. Seasonal variaion in a rend series makes i difficul o deec urning poins relaive o he previous observaion. The direcion and shape of developmen in he longer erm are also difficul o deec from an original series. Indeed, in a ime series conaining observaions a inervals shorer han one year, seasonal variaion is ofen seen as a nuisance which has very lile o do wih he picure of developmen over a longer ime period. The conclusion mus no be drawn from his ha seasonal adjusmen would be sandard or deerminisic, and ha is modelling or adjusmen would be a rivialiy in he way of bigger hings. (See also Takala 1994, pp ) When analysing monhly ime series on he naional economy, i would be beneficial o compare an observaion wih he previous one as well as o calculae he change from he respecive monh one year previously. Turning 3 hp:// 4 Hakala, Samu (2005), Aikasarjojen äsmäyäminen (Benchmarking ime series). 5 Much of his chaper is based on he aricle Aikasarjan ARIMA-mallipohjaisesa kausiasoiuksesa (On he ARIMA model-based seasonal adjusmen of a ime series) by Aro Kokkinen ja Faiz Alsuhail (2005). The Finnish Economic Journal, Issue 4/2005, Volume 101 (hp:// as well as on he maerials of Saisics Finland s courses on seasonal adjusmen (2006) (Kokkinen). 6 Takala, K. (1994): Kahden kausipuhdisusmeneelmän verailua; X11 ja STAMP (Comparing o mehods of seasonal adjusmen; X11 and STAMP), in Suhdannekäänne ja aloudellise aikasarja (Turns in economic rends and economic ime series), pp , Saisics Finland. Sudies 210, Helsinki.

12 12(17) poins in he examined variable can be observed by comparing developmen since he previous observaion. To be able o do his, a ime series mus be broken down o is componens and seasonal variaion wihin he year evened ou. I is ofen suggesed ha ime series on economic rends ha conain more frequen han annual observaions should be broken down o four componens: rend (developmen over an exended ime period), business cycle (medium-erm variaion caused by economic rends), seasonal variaion (variaion wihin one year) and irregular variaion. The las one of hese is presumed o be random whie noise wih no informaion ha would be useful o he analysis of he series. Because making an unambiguous and clear disincion beween he rend and he business cycle is difficul, hese componens are usually esimaed ogeher, and his combinaion is referred o as he rend cycle. When he concep of rend is used in his mehodological i refers o he rend cycle as is ypical in analyses of ime series on economic rends. When seasonal variaion is evened ou, a seasonally adjused series is obained which conains he rend cycle and irregular variaion TRAMO/SEATS The ARIMA model-based TRAMO/SEATS mehod recommended by Eurosa is used in seasonal adjusmens of monhly and quarerly naional accouns series. The ARIMA model-based (ARIMA Model Based (AMB)) seasonal adjusmen sars by modelling he variaion in he observaion series by means of he ARIMA model. The obained ARIMA model is uilised in breaking down he variaion in he ime series ino he rend, seasonal and irregular componens. The division ino he componens is done so ha he obained componens can be presened wih ARIMA models. The mos significan difference from he ad hoc approach (e.g. mehods X11/X12, Dainies, Sabl, BV4) is ha in TRAMO/SEATS own, series-specific filer formulas are formed for each ime series for he adjusmen of he daa. The mehod also conains an efficien means for making correcions for working and rading days and for idenifying oulying observaions. TRAMO/SEATS also enables he calculaion forecass, sandard errors and confidence inervals by componen. The sofware and mehod have been developed ino heir curren form by Maravall and Gomez 7. Whenever a ime series is being adjused, he auocorrelaion srucure of he original series is inerfered wih. If he used filer (be i a common ad hoc filer or one based on an unsuiable model) fails o screen ou expressly and only he seasonal adjusmen frequencies of a ime series, or rend frequencies when a rend is being esimaed, he auocorrelaion srucure of he original ime series becomes skewed wih he emporally repeaed characerisics of he original phenomenon. 7 See e.g. V. Gomez, and A. Maravall (1996): Programs TRAMO and SEATS. Insrucions for he User, (wih some updaes). Working Paper 9628, Servicio de Esudios, Banco de España.

13 13(17) The ARIMA model-based seasonal adjusmen and he TRAMO/SEATS mehod offer one analyical soluion o his problem. In he TRAMO par, he original series is pre-adjused for e.g. oulying observaions and variaions in numbers of working and rading days so ha he pre-adjused series can be ARIMA-modelled. This modelling of he auocorrelaion srucure of he enire pre-adjused series is uilised when variaion in he ime series a differen frequencies is broken down o is componens in he SEATS par. The poin of deparure in he decomposiion is ha each componen should only describe he precise par of he auocorrelaion srucure of he whole series and he variaion ha relaes o i, i.e. he componens are muually orhogonal. Inerpreaionally his means ha he reasons ha cause seasonal variaion (such as ime of year) in a ime series are uncorrelaed wih he reasons behind a long-erm rend, such as invesmens or R&D aciviy. In addiion i is presumed ha a ime series is made up of componens ha are realisaions of linear sochasic processes. Then each componen (wih he excepion of he irregular erm) can be described wih an ARIMA model. Boh he pre-adjused series and is componens are ARIMA modelled while respecing he dynamic characerisics of he original series which recur in ime. Finally he deerminisic facors, ouliers and variaion caused by working or rading days ha are observed in he pre-adjusmen are assigned o he componens as follows: exreme observaions of level change (level shif (LS)) o rend, variaion caused by numbers of working days and rading days (working day/rading day effecs (WD/TD)) o seasonal variaion, and individual oulying observaions (addiive ouliers (AO)) and momenary oulying observaions lasing for he duraion of several observaions (ransiory ouliers (TC)) o random variaion. Thus he variaion in he enire original ime series becomes disribued o he componens of final rend cycle, final seasonal variaion and final irregular variaions. Because he said componens are iniially unobservable in he original ime series hey can be formed in many ways. In he TRAMO/SEATS mehod a soluion is sough in he decomposiion of a pre-adjused ime series where he variance of random variaion is maximised. This soluion is known as canonic decomposiion and i produces an unambiguous decomposiion of a ime series. When comparing he variance of he random variaion facor (and he componen of irregular variaion) produced by means of canonical decomposiion wih oher mehods, such as he oher model-based mehod, STAMP, and he aforemenioned ad hoc mehods, i is good o bear in mind ha:

14 14(17) 1. The modelling of a pre-adjused series is made wih diverse (pdq)*(pdq) models 8 of he seasonal ARIMA model family which produce quie small random variaion proven as random variance. 2. The idenificaion of a seasonal ARIMA model for a pre-adjused series is based on he Bayesian Informaion Crierion (BIC) 9 according o which he selecion of he model is deermined by as small a variance as possible in random variaion achieved wih as small a number of esimaed parameers as possible. Thus when a series pre-adjused in he SEATS phase is divided ino is componens, he variance of random variaion (residual of ARIMA model) produced by he seasonal ARIMA model fied o a ime series is very small. This minimising of he random variaion of an enire ime series in oher componens of he SEATS phase, and he assignmen of mos of i expressly o he variance of he random variaion componen canno be assumed o lead o any greaer variance of he random variaion componen (and he irregular componens) han in he menioned oher mehods in which he whole ime series is no firs modelled wih a model of he seasonal ARIMA model family. By conras, he combinaion of he deerminisic modelling of working and rading day variaion ofen leads o a greaer variance of he seasonal componen in TRAMO/SEATS. The sochasic modelling sraegy of seasonal variaion also works well on seasonal variaion ha ransforms in ime, which helps no only he capure of working and rading day effecs bu also ha of seasonal variaion. In order o reduce he revision of he laes adjused observaions, a projecion a few observaions forward mus be produced in all seasonal adjusmen mehods. I is usually done basing on an ARIMA model, such as X11-/X12 ARIMA, even if he seasonal adjusmen filer were no conneced wih he model concerned in any way. One logical jusificaion of ARIMA model-based seasonal adjusmen is ha he filer used in he adjusmen of a series is based on he same series-specific ARIMA model wih which he forward projecion is made. In all evenualiies, in all mehods he laes 1 o 3 adjused observaions will become revised agains new saisical observaions. Wih sandard regression and ARIMA model symbols, he phased TRAMO/SEATS mehod can be presened as follows: 8 Symbols p,d,q refer o he basic ARIMA par of he models and symbols P,D,Q o he seasonal ARIMA par, where p (or P) is an ar-parameric number, d (D) a differeniaed number, q (Q) a ma-parameric number. The T/S model selecion is based on he following maximum limis p=3,d=2,q=2; P=1,D=1,Q= Min BIC (p, q) = logσ + log( p + q) T logt, where p and q are he numbers of ar- and ma-parameres in he model and T he number of observaions in he ime series. When T approaches infiniy BIC locaes he model which has produced he ime line on he basis of simulaions.

15 15(17) Tramo (I) / Seas (II): I) y = x ' β + z Pre-adjusmen regressions Pre-adjused remainder - working/rading day effecs according o he ARIMA model (WD/TD) - oulying observaions (LS, AO, TC) II) z = p + s + u θ ( B) z φ( B) θ p ( B) = a φ ( B) p p + θ s ( B) a φ ( B) s s + u Residual of ARIMA modelling, random (WN) (pre-adjused = (iniial) rend + (iniial) seasonal + random series componen variaion) Finally he deerminisic facors of par I and he sochasic facors of par II are combined and he original series is divided ino is final componens: y p ( + LS ) + s ( + WD / TD) + u ( AO, TC) = Final Irregular + observaion = rend + seasonal + irregular series componen componen Policy for seasonal adjusmen The above final decomposiion shows ha when he seasonal componen is being removed, calendar effecs are also eliminaed in seasonal adjusmen. In he Trend Indicaor of Oupu he seasonally adjused ime series and he rend series are published a he level of he whole economy as a chained volume series a year 2000 prices. Time series chained ino reference year prices are adjused direcly, which means ha ime series are adjused separaely, and e.g. a seasonally adjused series for he whole economy is no produced by summing ogeher hree main indusries. Apar from his publicly available mehodological, he users also receive informaion abou he implemenaion of seasonal adjusmen on courses organised by Saisics Finland and simply by asking abou i. The policies

16 16(17) applied in describing he modelling of ime series are openness and sharing of informaion. The governing principle in seasonal adjusmens is o make he modellings carefully once a year and keep boh he deerminisic pre-adjusmen facors and he idenified ARIMA model fixed beween annual reviews of he modelling, ye so ha he parameer values are re-esimaed on each calculaion round. An excepion o his are oulying observaions mid-way hrough he year, such as a labour dispue, for example. The model migh, however, be adjused if he modelling no longer fis he daa due o new observaions. The main principle is o keep he adjusmen filers formed wih he model idenified for a series (apar from he esimaion of parameer values) unchanged so ha adapion of filers does no cause revisions o he hisory of a seasonally adjused series on every round. The aim in he updaing of parameer values is o produce forward projecions wih as full informaion as possible on he pas on every calculaion round. The objecive in his is o reduce revisions o he laes observaions in adjused series when new observaions become available Policy for working day correcion Working day correced (more generally calendar adjused) ime series are published as chained volume series a reference year 2000 prices. The main principle in he working or rading day correcion (inclusive of adjusmens for leap years, Easer and naional public holidays) is he esing of saisical significance during several modelling rounds. Working or rading day correcion facors (inclusive of omission of working day correcion of a series) are no changed mid-way hrough he year beween modelling rounds. In he bes case, based on experiences of several years modelling over a longer erm, a logical and sable soluion in erms of he conen of each individual series is sough for performing working or rading day correcions.

17 17(17) Chaper 4 Flash esimaes 4.1 Quarerly flash esimae of GDP A quarerly flash esimae of gross domesic produc is calculaed as Trend Indicaor of Oupu. The flash esimae is no published bu produced for Eurosa only. The calculaion of he flash esimae is based as exhausively as possible on he same daa sources as he quarerly naional accouns. Due o he fas release imeable, compleely idenical daa canno be used, and indusries are no spli ino differen secors. Inermediae consumpion as well as axes and subsidies on producs are no esimaed in he compilaion of he flash esimae, bu quarerly GDP is carried forward wih an annual change based on indicaors of oupu. Apar from he aforemenioned excepions, he same mehods are used in he calculaion of he flash esimae as in he calculaion of quarerly naional accouns. Developmen in he value and price of oupu is mainly esimaed basing on daa describing urnover and corresponding indices of produce prices, or daa on wage and salary sums and indices of wage and salary earnings. The calculaion is performed monhly wih he annual overlap mehod. Excep for he currenly calculaed quarer, chained ime series are benchmarked o correspond o quarerly and annual accouns. Monhly series are summed up o quarerly series. Quarerly series are seasonally adjused wih he TRAMO/SEATS mehod.