From noise to turning points: A new framework for seasonal adjustment in Armenia

Minasyan, Ge o g; Schippe , S e an; Khacha yan, Lusya; Mo sisyan, Seda; Lapi an,
Pamela
Wo king Pape
F om noise o u ning poin s: A new amewo k o
seasonal adjus men in A menia
ADB Economics Wo king Pape Se ies, No. 786
P o ided in Coope a ion wi h:
Asian De elopmen Bank (ADB), Manila
Sugges ed Ci a ion: Minasyan, Ge o g; Schippe , S e an; Khacha yan, Lusya; Mo sisyan, Seda;
Lapi an, Pamela (2025) : F om noise o u ning poin s: A new amewo k o seasonal adjus men in
A menia, ADB Economics Wo king Pape Se ies, No. 786, Asian De elopmen Bank (ADB), Manila,
h ps://doi.o g/10.22617/WPS250242-2
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/322379
S anda d-Nu zungsbedingungen:
Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen
Zwecken und zum P i a geb auch gespeiche und kopie we den.
Sie dü en die Dokumen e nich ü ö en liche ode komme zielle
Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich
machen, e eiben ode ande wei ig nu zen.
So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen
(insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en,
gel en abweichend on diesen Nu zungsbedingungen die in de do
genann en Lizenz gewäh en Nu zungs ech e.
Te ms o use:
Documen s in EconS o may be sa ed and copied o you pe sonal
and schola ly pu poses.
You a e no o copy documen s o public o comme cial pu poses, o
exhibi he documen s publicly, o make hem publicly a ailable on he
in e ne , o o dis ibu e o o he wise use he documen s in public.
I he documen s ha e been made a ailable unde an Open Con en
Licence (especially C ea i e Commons Licences), you may exe cise
u he usage igh s as speci ied in he indica ed licence.
h ps://c ea i ecommons.o g/licenses/by/3.0/igo/
ASIAN DEVELOPMENT BANK
ASIAN DEVELOPMENT BANK
6 ADB A enue, Mandaluyong Ci y
1550 Me o Manila, Philippines
www.adb.o g
ADB ECONOMICS
WORKING PAPER SERIES
NO. 786
June 2025
F om Noise o Tu ning Poin s
A New F amewo k o Seasonal Adjus men in A menia
This pape e alua es he ansi ion o he X13-ARIMA-SEATS amewo k o he seasonal adjus men o
A menia’s qua e ly na ional accoun s, highligh ing i s ole in de ec ing economic u ning poin s. The pape
discusses bes p ac ices o seasonal adjus men and s a egies o accu a e eal- ime economic analysis.
Abou he Asian De elopmen Bank
ADB is a leading mul ila e al de elopmen bank suppo ing inclusi e, esilien , and sus ainable g ow h ac oss
Asia and he Paci ic. Wo king wi h i s membe s and pa ne s o sol e complex challenges oge he , ADB
ha nesses inno a i e inancial ools and s a egic pa ne ships o ans o m li es, build quali y in as uc u e,
and sa egua d ou plane . Founded in 1966, ADB is owned by 69 membe s—50 om he egion.
FROM NOISE TO TURNING POINTS
A NEW FRAMEWORK FOR SEASONAL ADJUSTMENT
IN ARMENIA
Ge o g Minasyan, S e an Schippe , Lusya Khacha yan, Seda Mo sisyan, and Pamela Lapi an
F om
he People o Japan
ASIAN DEVELOPMENT BANK
The ADB Economics Wo king Pape Se ies
p esen s esea ch in p og ess o elici commen s
and encou age deba e on de elopmen issues
in Asia and he Paci ic. The iews exp essed
a e hose o he au ho s and do no necessa ily
e lec he iews and policies o ADB o
i s Boa d o Go e no s o he go e nmen s
hey ep esen .
ADB Economics Wo king Pape Se ies
Ge o g Minasyan, S e an Schippe ,
Lusya Khacha yan, Seda Mo sisyan,
and Pamela Lapi an
No. 786 | June 2025
Ge o g Minasyan (gminasyan.consul an @adb.o g)
is a consul an ; S e an Schippe (sschippe @adb.o g)
is a p incipal s a is ician; and Pamela Lapi an
([email p o ec ed]g) is a s a is ics o ice a he
Economic Resea ch and De elopmen Impac
Depa men , Asian De elopmen Bank.
Lusya Khacha yan (na ional_acc[email p o ec ed])
is head o Mac oeconomic Indica o s and he
Na ional Accoun s Di ision and Seda Mo sisyan
(seda_mo sis[email p o ec ed]) is a senio specialis a
he S a is ical Commi ee o he Republic o A menia.
F om Noise o Tu ning Poin s: A New F amewo k o
Seasonal Adjus men in A menia
C ea i e Commons A ibu ion 3.0 IGO license (CC BY 3.0 IGO)
© 2025 Asian De elopmen Bank
6 ADB A enue, Mandaluyong Ci y, 1550 Me o Manila, Philippines
Tel +63 2 8632 4444; Fax +63 2 8636 2444
www.adb.o g
Some igh s ese ed. Published in 2025.
ISSN 2313-6537 (p in ), 2313-6545 (PDF)
Publica ion S ock No. WPS250242-2
DOI: h p://dx.doi.o g/10.22617/WPS250242-2
The iews exp essed in his publica ion a e hose o he au ho s and do no necessa ily e lec he iews and policies
o  he Asian De elopmen Bank (ADB) o i s Boa d o Go e no s o he go e nmen s hey ep esen .
ADB does no gua an ee he accu acy o he da a included in his publica ion and accep s no esponsibili y o any
consequence o hei use. The men ion o speci ic companies o p oduc s o manu ac u e s does no imply ha hey
a e endo sed o ecommended by ADB in p e e ence o o he s o a simila na u e ha a e no men ioned.
By making any designa ion o o e e ence o a pa icula e i o y o geog aphic a ea in his documen , ADB does no
in end o make any judgmen s as o he legal o o he s a us o any e i o y o a ea.
This publica ion is a ailable unde he C ea i e Commons A ibu ion 3.0 IGO license (CC BY 3.0 IGO)
h ps://c ea i ecommons.o g/licenses/by/3.0/igo/. By using he con en o his publica ion, you ag ee o be bound
by he e ms o his license. Fo a ibu ion, ansla ions, adap a ions, and pe missions, please ead he p o isions
and e ms o use a h ps://www.adb.o g/ e ms-use#openaccess.
This CC license does no apply o non-ADB copy igh ma e ials in his publica ion. I he ma e ial is a ibu ed
oano he sou ce, please con ac he copy igh owne o publishe o ha sou ce o pe mission o ep oduce i .
ADB canno be held liable o any claims ha a ise as a esul o you use o he ma e ial.
Please con ac pubsma ke [email protected] g i you ha e ques ions o commen s wi h espec o con en , o i you wish
oob ain copy igh pe mission o you in ended use ha does no all wi hin hese e ms, o o pe mission o use
heADB logo.
Co igenda o ADB publica ions may be ound a h p://www.adb.o g/publica ions/co igenda.
ABSTRACT
This pape e alua es he ansi ion om X12-ARIMA o X13-ARIMA-SEATS o he seasonal
adjus men o A menia’s qua e ly na ional accoun s (QNA). We analyze he me hodological
ad ancemen s and hei impac on key economic indica o s, ocusing on he p ecision and
eliabili y o seasonally adjus ed da a. Ou indings sugges ha he indi ec seasonal adjus men
me hod, despi e la ge e isions, is p e e able, gi en po en ial a ia ions in seasonal pa e ns
among g oss domes ic p oduc componen s and s ong use p e e ences o p ese ing
accoun ing ela ionships. Fu he mo e, a pa ial concu en upda e s a egy achie es a be e
balance be ween accu acy and e ision minimiza ion compa ed o cu en o ully concu en
me hods. Finally, de i ing seasonally adjus ed p ice de la o s om seasonally adjus ed olume
and cu en p ice da a aligns mo e closely wi h he unde lying economic s uc u e o A menian
QNA, gi en ha QNA da a is a ailable p ima ily in nominal e ms. These esul s emain
consis en ac oss a ious sensi i i y checks, suppo ing ou me hodological app oach o
analyzing A menia's QNA se ies.
Keywo ds: A menia, JDeme a+, na ional accoun s, seasonal adjus men , X13-ARIMA-SEATS
JEL codes: C22, C32, C5
_________________________
The g an und o his s udy was ecei ed om he Japan Fund o P ospe ous and Resilien Asia and he
Paci ic inanced by he Go e nmen o Japan h ough he Asian De elopmen Bank.

1. INTRODUCTION
Economic a iables exhibi sys ema ic and ecu ing wi hin-yea pa e ns in luenced by a a ie y
o ac o s, such as wea he , ins i u ions, and social cus oms and adi ions. When hese seasonal
a ia ions domina e changes in he o iginal se ies om one pe iod o ano he , iden i ying
nonseasonal e ec s, including long- e m mo emen s, cyclical a ia ions, and i egula ac o s—
in o ma i e economic signals—becomes challenging. Timely iden i ica ion o u ning poin s in
key mac oeconomic a iables, like he qua e ly na ional accoun s (QNA), equi es he emo al
o seasonal and calenda e ec s om ime se ies da a. This p ocess in ol es u ilizing analy ical
echniques o b eak down he se ies in o unobse ed componen s, based on a p io i assump ions
ega ding hei expec ed beha io .
Remo ing he epea ed impac o seasonal e ec s is impo an o bo h his o ical business cycle
analysis and assessing cu en economic condi ions. This helps in iden i ying undamen al long-
un mo emen s and sho - un luc ua ions in he ime se ies, he eby enhancing he
in e p e a ion o economic a iables and con ibu ing o in o med decision making. Howe e , he
challenge o p ecisely de ining seasonali y means ha he di e en app oaches may esul in
di e en ou comes. Analys expe ise emains essen ial o ine uning he seasonal adjus men
p ocedu es and e i ying he accu acy o he adjus ed s a is ics. Expe -d i en judgmen is
pa icula ly impo an in he cu en economic landscape, whe e linea il e s a e ypically applied
o seasonal componen ex ac ion despi e he p e alence o unce ain ies and nonlinea ends
in many economic se ies.
The S a is ical Commi ee o he Republic o A menia (ARMSTAT) ini ia ed i s i s seasonal
adjus men o QNA in 1998, using he au o eg essi e in eg a ed mo ing a e age (ARIMA) X11
me hod de eloped by he Uni ed S a es Census Bu eau. In 2013, ARMSTAT shi ed o he X12-
ARIMA me hod and he Deme a+ p og am,1 aligning wi h ecommenda ions om he
In e na ional Mone a y Fund (IMF) and he Uni ed Na ions Economic Commission o Eu ope.
Howe e , X12-ARIMA, while ep esen ing an ad ance on ea lie me hods, elies hea ily on
linea models, limi ing i s abili y o cap u e he nonlinea ends inc easingly p esen in mode n
economies. Recognizing his limi a ion, ARMSTAT ansi ioned o he X13-ARIMA-SEATS
me hod and he JDeme a+ so wa e in 2022, aligning wi h he Eu opean S a is ical Sys em
(ESS) 2015 guidelines on seasonal adjus men and he IMF's QNA 2017 manual.
X13-ARIMA-SEATS o e s se e al ad an ages o e i s p edecesso s. Fi s , i inco po a es he
SEATS (signal ex ac ion in ARIMA ime se ies) me hod, speci ically designed o handle
nonlinea ends and s uc u al b eaks in ime se ies da a. Second, X13-ARIMA-SEATS p o ides
a mo e ad anced oolki o diagnosing he quali y and s abili y o seasonal adjus men models.
Thi d, X13-ARIMA-SEATS can e icien ly p ocess mul iple se ies simul aneously. In addi ion,
JDeme a+ includes a mo e e sa ile in e ace compa ed o Deme a+, enabling use s o apply
ools such as nowcas ing, empo al disagg ega ion, and benchma king. Impo an ly, JDeme a+
p o ides common analysis op ions o di e en seasonal adjus men me hods, allowing o easy
compa ison o esul s ac oss hese algo i hms.
1 ARIMA is a s a is ical me hod o analyzing and o ecas ing ime se ies da a by modeling i s empo al s uc u e, and
Deme a+ is ee so wa e de eloped by he Na ional Bank o Belgium o seasonal adjus men using
TRAMO/SEATS and X12-ARIMA me hods.
2
In his pape , we examine he implica ions o ansi ioning om he X12-ARIMA o he X13-
ARIMA-SEATS me hod o he seasonal adjus men o A menia's QNA se ies. Ou analysis
ocuses on assessing he me hodological ad ancemen s and hei impac on he in e p e a ion
o key economic indica o s, wi h a pa icula emphasis on he p ecision and eliabili y o
seasonally adjus ed da a in cap u ing unde lying economic ends. Addi ionally, we conduc a
wide ange o ad anced quali y diagnos ics o alida e he unde lying assump ions o he new
seasonal adjus men amewo k and he majo decisions ega ding a ious aspec s o he
me hodology.
Ou indings sugges ha he new amewo k yields signi ican insigh s, pa icula ly in he con ex
o di ec e sus indi ec adjus men s, upda e s a egies, and he ela ionship be ween p ice,
olume, and alue indices. While bo h di ec and indi ec app oaches p oduce simila ends,
no able disc epancies eme ge, especially du ing c isis pe iods. The indi ec me hod, despi e i s
suscep ibili y o la ge e isions, appea s p e e able, gi en he po en ial o di e gen seasonal
pa e ns among g oss domes ic p oduc (GDP) componen s and use demand. Addi ionally, ou
explo a ion o upda e s a egies highligh s he ad an ages o a pa ial concu en adjus men
me hod, which balances accu acy wi h he minimiza ion o e isions. Finally, he indings on he
ela ionship be ween seasonally adjus ed p ice, olume, and alue indices indica e ha de i ing
esiduals om seasonally adjus ed olume and cu en p ice da a, a he han di ec ly adjus ing
p ice de la o s, aligns be e wi h he unde lying economic s uc u e o he A menian QNA. These
esul s emain obus ac oss a ious sensi i i y checks, ea i ming he alidi y o ou
me hodological app oach and i s applicabili y o he analysis o he A menian QNA se ies.
The emainde o his pape is s uc u ed as ollows: Sec ion 2 e iews he li e a u e on seasonal
adjus men me hods, Sec ion 3 de ails he me hodology employed, Sec ion 4 p esen s indings,
Sec ion 5 discusses quali y diagnos ics, Sec ion 6 add esses he p e-adjus men o QNA du ing
he co ona i us disease (COVID-19) c isis, and Sec ion 7 concludes wi h a summa y.
2. LITERATURE REVIEW
Seasonal adjus men me hods all in o h ee b oad ca ego ies: (i) nonpa ame ic me hods, which
ely on linea smoo hing il e s o adjus he da a; (ii) pa ame ic me hods, whe e seasonal
adjus men is achie ed h ough explici speci ica ion and es ima ion o unobse ed componen s
wi hin he da a; and (iii) and semipa ame ic me hods, which combine aspec s o bo h explici and
implici modeling o each componen (see Figu e 1).
3
Figu e 1: Classi ica ion o Seasonal Adjus men Me hods
Sou ce: Eu os a (2018).
2.1. Nonpa ame ic Models
The mos common seasonal adjus men me hods use mo ing a e ages o linea smoo hing
il e s o adjus da a sequen ially by adding and sub ac ing indi idual obse a ions. A pionee in
his ield was he Uni ed S a es Census Bu eau’s X11 p og am, eleased in 1965 (Shiskin,
Young, and Musg a e 1967). This was he esul o o e a decade o de elopmen , beginning
wi h Me hod I in 1954 and ollowed by 12 expe imen al a ian s o Me hod II (X0, X1, e c.),
culmina ing in he elease o X11 (Shiskin 1978).
Building on he ounda ion o X11, he Aus alian Bu eau o S a is ics in oduced SEASABS
(Seasonal Analysis a he Aus alian Bu eau o S a is ics) in 1987 (Eu os a 2018). This
knowledge-based algo i hm e ains eco ds o p e ious se ies analyses, enabling compa isons
o X11 diagnos ics and insigh s in o he pa ame e s ha p oduced accep able adjus men s.
Young (1992) de eloped ano he e sion, GLAS (Gene al Linea Abs ac ion o Seasonali y), a
he Bank o England o seasonally adjus ing mone a y a iables. This me hod es ima es and
smoo hs end and seasonal componen s wi h a iangula -shaped weigh ing pa e n in a mo ing
a e age o da a, and i inco po a es Lane’s (1972) minimum e ision algo i hm. O he simila
ools include SABL (Seasonal Adjus men -Bell Labo a o ies) (Cle eland, Dunn, and Te penning
1978), a obus al e na i e o X11 ha ackles ou lie s and smoo hs ends wi hou igid da a
assump ions. STL (seasonal and end decomposi ion using Loess), de eloped by Cle eland e
al. (1990), unc ions simila ly o GLAS by applying localized smoo hing echniques o es ima e
end and seasonal componen s, using adap able polynomial i s o model bo h linea and
nonlinea pa e ns.
4
2.2. Pa ame ic Models
Some c i ics exp essed conce ns abou nonpa ame ic seasonal adjus men me hods based on
linea il e s o mo ing a e ages. Slu sky (1927) and Yule (1927) no ed he po en ial o hese
models o in oduce a i icial cycles, while o he s c i icized he use o ad hoc empi ical p ocedu es
when mo e igo ous ma hema ical ools we e a ailable. This g owing dissa is ac ion wi h
nonpa ame ic app oaches led o he de elopmen o explici model-based me hodologies o
seasonal adjus men . The e a e wo main ca ego ies o hese model-based app oaches: (i) hose
ha ely on de e minis ic amewo ks, and (ii) hose g ounded in s ochas ic modeling.
Ea ly model-based me hods elied on eg ession analysis. Pionee ing wo ks by Fishe (1937)
and Mende shausen (1939) used leas squa es o i polynomials and isola e seasonali y. The
1960s saw a ise in mul iple eg ession echniques, d i en by econome ic model de elopmen
and compu ing ad ancemen s. No able con ibu ions include wo ks by Rosenbla (1965) and
Lo ell (1963), which i componen s using pa ame ic unc ions and o dina y leas squa es.
Howe e , hei inabili y o cap u e he s ochas ic na u e o se ies has limi ed hei use. Ex ensions
wi h local eg essions, like DAINTIES (Fische 1995) and BV4 (Nou ney 1984), ha e seen some
de elopmen , hough hey ace limi a ions like phase shi s and iden i ica ion p oblems.
Unlike de e minis ic me hods, s ochas ic me hods ely on speci ying unobse ed componen
ARIMA models and applying signal ex ac ion echniques. A key di ec ion is he ARIMA Model-
Based (AMB) app oach, which models he obse ed ime se ies using a seasonal ARIMA model,
while componen s a e de i ed om he model’s s uc u e using spec al es ima ion echniques.
Pionee ing wo ks in his a ea include con ibu ions by Ma a all and Pie ce (1987), Bell (1984),
Hillme and Tiao (1982), and Bu man (1980). Howe e , while powe ul, ARIMA models a e
suscep ible o inaccu acies caused by ou lie s and may s uggle o co ec ly es ima e
de e minis ic componen s. To add ess his limi a ion, de elopmen s like TRAMO-SEATS
(Gómez and Ma a all 1995) use he Wiene -Kolmogo o il e o ex ac he componen s om
he spec um o a i ed ARIMA model by minimizing he mean squa ed e o be ween he
es ima ed and ac ual componen s. Compa ed wi h X11, TRAMO-SEATS p oduces mo e s able
seasonal componen s by using a canonical decomposi ion me hod ha maximizes he a iabili y
o he i egula elemen while minimizing ha o he seasonal ac o s. Howe e , i elies hea ily
on a well- i ing ARIMA model, and esul s a e pa icula ly sensi i e o pa ame e unce ain y,
especially in e y sho o long ime se ies.
2.3. Semipa ame ic Models
Building upon he wo k o Box and Jenkins (1970) on ARIMA models in he 1970s (see Box e
al. 2015), Dagum (1980) p oposed a new X11 a ian called X11-ARIMA. This ep esen ed an
imp o emen o e he o iginal X11 p og am and was u he au oma ed a S a is ics Canada.
The key imp o emen lies in X11-ARIMA's abili y o ex end p edic ions beyond he obse ed da a
and es ima e alues p io o he s a o he se ies. This capabili y add esses missing da a a he
se ies' ends, allowing o less asymme ic il e s. In con as , he o iginal X11 simply ex apola ed
missing alues a bi a ily, leading o signi ican e isions when he missing da a e en ually
became a ailable. Ano he ex ension o X11 is he Uni ed Kingdom e sion, which inco po a ed
o ecas s based on he Kenny-Du bin au o eg ession echnique (Kenny and Du bin 1982),
hough Fische (1995) ound ha X11-ARIMA deli e ed mo e accu a e o ecas ing esul s. The
Du ch Cen al Bu eau o S a is ics also in oduced an ex ension known as CPBX11 so wa e
11
(L). Howe e , mos end-cycle componen s show insigni ican co ela ions. This sugges s ha
di ec ly adjus ing GDP may mask impo an seasonal a ia ions wi hin indi idual sec o s,
po en ially comp omising he quali y o he seasonally adjus ed GDP.
Figu e 3: Chain-Linked Volume Indices (2012 = 100)
Sou ce: Au ho s’ calcula ions based on QNA da a om ARMSTAT.
Figu e 4: Yea -on-Yea G ow h Ra es o G oss Domes ic P oduc
Sou ce: Au ho s’ calcula ions based on QNA da a om ARMSTAT.
60
80
100
120
140
160
180
200
220
Index
O iginal Di ec Indi ec
-15
-10
-5
0
5
10
15
20
%
Di ec - Indi ec Di e ence (pe cen age poin s) Di ec Indi ec

12
Figu e 5: Co ela ion Ma ix o T end-Cycle Componen s o Sec o al Value-Added
Sou ce: Au ho s’ calcula ions.
To u he in es iga e he implica ions o hese me hods, we conduc ed a e ision analysis on yea -
on-yea GDP g ow h a es. We employed a ecu si e es ima ion app oach o e he pe iod om
2013Q1 o 2022Q4 and subsequen ly inco po a ed addi ional da a poin s up o 2023Q4. The
esul ing e isions o 2021, 2022, and 2023 indica e ha bo h di ec and indi ec me hods
in oduce changes o he seasonally adjus ed GDP se ies. Howe e , he magni ude o e isions
ends o be ma ginally la ge unde he indi ec me hod, which is e idenced by he highe Mean
Squa ed E o (MSE) alues o indi ec adjus men ac oss analyzed pe iods. The la ge e isions
unde he indi ec app oach likely esul om he ampli ica ion o noise and inconsis encies a ising
om he independen adjus men o componen se ies. In con as , he di ec me hod, which
ope a es on agg ega e da a, may bene i om a smoo hing e ec , leading o mo e s able
es ima es. Despi e he highe e ision suscep ibili y o he indi ec me hod, we p e e ed i o
A menia, gi en he po en ial o di e gen seasonal pa e ns among GDP componen s and he
s ong use demand o p ese ing accoun ing and agg ega ion ela ionships in he QNA da a.
13
Table 3: Compa ison o Re isions Unde Di ec and Indi ec Seasonal Adjus men
(yea -on-yea changes in seasonally adjus ed g oss domes ic p oduc )
2021 2022 2023
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4
Di ec Adjus men
Un il
MSE
2022Q4
-2.5
9.2
3.4
11.1
8.3
13.1
15.2
12.5
0.86
2023Q1
-2.5
9.3
3.4
11.1
8.3
13.1
15.2
12.5
11.2
2023Q2
-2.5
9.3
3.4
11.1
8.3
13.1
15.2
12.5
11.2
9.5
2023Q3
-2.6
9.2
3.5
11.1
8.2
13.0
15.3
12.5
11.1
9.4
7.8
2023Q4
-2.6
9.2
3.5
11.1
8.2
13.1
15.4
12.5
11.0
9.5
7.8
7.6
Indi ec Adjus men
Un il
MSE
2022Q4
-2.5
8.6
3.9
12.4
7.9
12.0
15.8
13.9
1.21
2023Q1
-2.8
8.7
4.0
12.4
7.7
12.1
15.7
13.8
11.3
2023Q2
-2.9
8.9
3.9
12.4
7.7
12.3
15.7
13.8
11.3
9.0
2023Q3
-2.9
9.0
3.8
12.4
7.6
12.4
15.7
13.8
11.3
8.9
7.5
2023Q4
-2.9
9.0
4.1
12.1
7.8
12.4
15.9
13.5
11.4
9.1
7.8
6.6
MSE = mean squa ed e o .
Sou ce: Au ho s’ calcula ions.
4.2. S a egies o Upda ing Seasonal Adjus men
Seasonal adjus men p ocedu es can ollow di e en upda ing app oaches, depending on he
equency wi h which he adjus men models and hei se ings a e e-e alua ed as new o e ised
da a become a ailable. Two main app oaches a e mos ly used: concu en o cu en adjus men .
In he concu en app oach, he model, i s con igu a ion, and pa ame e s a e e-es ima ed e e y
ime new o e ised da a poin s a e added. This ensu es ha he adjus ed se ies e lec he la es
seasonal pa e ns and s uc u al changes, ypically esul ing in he mos accu a e es ima es.
Howe e , his s a egy ends o p oduce mo e equen e isions o he adjus ed da a due o
ongoing upda es o he unde lying model and pa ame e s. In con as , he cu en adjus men
app oach upda es he model and i s componen s only du ing p ede e mined e iew windows –
usually held annually o when signi ican changes occu in he sou ce da a. Be ween hese e iew
pe iods, he model s uc u e and es ima ed pa ame e s emain unchanged. Adjus ed alues a e
gene a ed by applying p ojec ed seasonal and calenda ac o s o he incoming da a. As a esul ,
e isions o he seasonally adjus ed se ies a e concen a ed wi hin he e iew pe iods, wi h no
adjus men s made du ing he in e im unless his o ical sou ce da a a e modi ied.
A comp omise be ween he concu en and cu en seasonal adjus men s a egies is he pa ial
concu en app oach. In his me hod, he choice o models and adjus men se ings is ixed du ing
14
scheduled e iew pe iods – usually once pe yea o ollowing subs an ial da a e isions – and
emains cons an un il he nex e iew. Howe e , he pa ame e s o he model a e e-es ima ed
e e y ime he se ies is upda ed wi h new da a. While he model and adjus men se ings a e
gene ally kep unchanged be ween e iews, hey may be e ised in esponse o a e o
excep ional ci cums ances ha demand special ea men . Ou side o such e en s, any e isions
o he seasonally adjus ed da a a ise solely om he upda ed pa ame e es ima es. This s a egy
o e s a balanced app oach by main aining a high le el o accu acy in he adjus men s while
educing he equency and magni ude o e isions.
In Figu e 6, we compa e he magni udes o e isions o yea -on-yea GDP changes ac oss he
h ee app oaches. As an icipa ed, he pa ial concu en me hod gene a es ewe e isions in
es ima es compa ed o he cu en and concu en app oaches, which lead o la ge e isions.
Fo ins ance, he second qua e o 2023 expe ienced a 0.3 pe cen age poin e ision in he yea -
on-yea GDP change using he cu en app oach, a mo e subs an ial 1.1 pe cen age poin e ision
wi h he concu en app oach, and a mino -0.1 pe cen age poin e ision wi h he pa ial
concu en app oach. Consequen ly, ARMSTAT adop ed his la e me hod o seasonally
adjus ing QNA in A menia. The model, il e s, and ou lie s wi hin his app oach a e e ised
annually, while seasonal ac o s and calenda e ec s a e upda ed wi h each new da a elease.
This app oach aligns wi h he ESS guidelines and he IMF manual on QNA, bo h o which
ecommend pa ial concu en adjus men o accoun o new in o ma ion and minimize he size
o e isions esul ing om he seasonal adjus men p ocess.
Figu e 6: Cu en Ve sus Concu en Ve sus Pa ial Concu en Adjus men
( e isions o yea -on-yea g oss domes ic p oduc g ow h a es, pe cen age poin s)
Sou ce: Au ho s’ calcula ions.
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
2022Q1 2022Q2 2022Q3 2022Q4 2023Q1 2023Q2 2023Q3 2023Q4
Pe cen age poin
Pa ial Concu en Concu en Cu en
15
4.3. Re ision Pe iod
Ano he c i ical aspec o e isions policy is de e mining he e ision pe iod o QNA publica ions,
which de ines he numbe o p e iously eleased qua e ly obse a ions subjec o e ision. In a
pa ial concu en app oach, he en i e seasonally adjus ed se ies is modi ied whene e a new
obse a ion is added o an exis ing one is e ised. Re isions can be subs an ial o yea s nea he
las e ised obse a ion in he o iginal se ies, bu end o be mino o mo e dis an obse a ions.
This pa e n a ises because seasonal adjus men il e s assign g ea e weigh o ecen
obse a ions compa ed o hose u he in he pas .
Acco ding o he IMF’s QNA manual, a pa ial concu en adjus men s a egy manda es e ising
seasonally adjus ed se ies o a leas 2 comple e yea s p io o modi ying he o iginal da a. This
pe iod enables he inclusion o upda ed eg ession coe icien s and newly de ec ed ou lie s in o
he la es seasonally adjus ed da a. Main aining a minimum o 2 ull yea s is c ucial o accu a ely
calcula ing qua e - o-qua e g ow h a es o he cu en and p eceding yea using consis en ly
adjus ed da a. Seasonally adjus ed da a published be o e his 2-yea window can emain
unchanged unless a i icial b eaks eme ge in he se ies. Simila ly, he ESS guidelines
ecommend se ing he s a ing poin o he ea lies seasonally adjus ed da a e ision a he
beginning o a yea , 3 yea s be o e he unadjus ed da a e ision pe iod.
To de e mine an app op ia e e ision pe iod o A menia, Figu e 7 compa es e isions o yea -on-
yea GDP g ow h a es ollowing he addi ion o new obse a ions o each qua e o 2023. The
analysis e eals ha , while ecen da a signi ican ly impac s he mos ecen es ima es, ea lie
obse a ions emain ela i ely s able. Based on hese indings, ARMSTAT adop ed a e ision
policy ha upda es he p e ious 3 yea s o da a wi h each new obse a ion, while p ese ing
es ima es o ea lie pe iods. The only excep ion o his e ision policy occu ed when ARMSTAT
ansi ioned o a new seasonal adjus men amewo k a he end o 2022. Du ing his pe iod, he
en i e se ies was upda ed compa ed o he p e ious me hodology, aligning wi h ESS
ecommenda ions o majo e isions.
Figu e 7: Changes in Seasonally Adjus ed Es ima es by Adding New Obse a ions
( e isions o yea -on-yea g oss domes ic p oduc g ow h a es, pe cen age poin s)
Sou ce: Au ho s’ calcula ions.
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Pe cen age poin
2023Q1 2023Q2 2023Q3 2023Q4
16
4.4. Rela ionship Be ween P ice, Volume, and Value Indices o Seasonally Adjus ed Se ies
Seasonally adjus ed es ima es o na ional accoun s p ice indices, olume measu es, and cu en
p ice da a can be ob ained by ei he adjus ing each se ies independen ly o adjus ing wo and
de i ing he hi d as a esidual, assuming all h ee exhibi seasonal pa e ns. Gi en nonlinea i ies
in seasonal adjus men p ocesses, hese me hods p oduce di e en esul s, al hough he
di e ences a e ypically mino . As he IMF sugges s, deciding which se ies o de i e esidually
should be de e mined on a case-by-case basis based on which app oach yields he mos
easonable ou come.
Theo e ically, seasonali y in cu en p ice da a is gene a ed by seasonali y om p ice and olume
e ec s. The e o e, he bes app oach appea s o be applying seasonal adjus men o he p ice
and olume se ies and hen indi ec ly de i ing seasonally adjus ed da a in cu en p ices.
Howe e , di ec ly adjus ing da a in cu en p ices may be p e e ed when he main da a sou ce is
a ailable in nominal e ms.
Be o e 2022, ARMSTAT seasonally adjus ed only he olume indices. Howe e , since adop ing
he new amewo k, bo h olume measu es and cu en p ice da a a e seasonally adjus ed, while
p ice de la o s a e de i ed as esiduals. This decision is in luenced by he ac ha he unde lying
da a o QNA is collec ed in nominal e ms in A menia, and olume indices a e subsequen ly
de i ed using QNA se ies a he p e ious yea ’s p ices h ough he double de la ion me hod.
5. QUALITY DIAGNOSTICS
In his sec ion, we e alua e he quali y o he seasonally adjus ed se ies using bo h pa ame ic
and nonpa ame ic c i e ia. To e i y he absence o esidual seasonali y, we begin by conduc ing
seasonali y es s on he di ec ly adjus ed se ies and hei i egula componen s. The esidual
seasonali y es s used in JDeme a+ a e de i ed om he se o diagnos ics o iginally c ea ed o
X12-ARIMA. Among hese, we p ima ily ely on he F- es , which uses seasonal dummy a iables
(including a mean e ec and h ee seasonal dummies o qua e ly da a) o de e mine whe he
hey a e join ly s a is ically insigni ican .
The ejec ion h esholds and es esul s o his analysis a e p esen ed in Tables 4a and 4b. As
indica ed, he p- alues o mos se ies exceed 0.05, con i ming he absence o esidual
seasonali y in he indi idual GDP componen s. Since he seasonally adjus ed QNA se ies a e
de i ed indi ec ly by agg ega ing he co esponding subcomponen s, we also pe o m simila es s
on he agg ega ed se ies. As shown in Appendix C, all agg ega ed se ies a e ee om esidual
seasonali y. Addi ionally, we conduc analogous es s on he p ice de la o s calcula ed om
seasonally adjus ed olume measu es and cu en p ice da a, wi h esul s in Appendix C
suppo ing ha hese se ies a e also de oid o esidual seasonali y.

17
Table 4a: C i ical Values o In e p e ing F-Tes Resul s
P- alue
JDeme a+ de aul se ings
<0.01
Se e e
[0.01, 0.05)
Bad
[0.05, 0.1)
Unce ain
≥0.1
Good
Sou ce: JDeme a+ Re e ence Manual (h ps://jdeme adocumen a ion.gi hub.io/JDeme a-
documen a ion/).
Table 4b: Resul s o he F-Tes o he P esence o Residual Seasonali y and T ading-Day
E ec s
NACE
Code
Residual Seasonali y
Residual T ading-Day E ec s
Seasonally
adjus ed se ies
I egula
componen
Seasonally
adjus ed se ies
I egula
componen
A
Good (0.668)
Good (0.418)
Good (0.079)
Good (0.405)
B
Good (0.921)
Good (0.832)
Good (0.101)
Good (0.134)
C
Good (0.477)
Good (0.446)
Good (0.429)
Good (0.269)
D
Good (0.513)
Good (0.635)
Good (0.905)
Good (0.058)
E
Good (0.768)
Good (0.569)
Good (0.207)
Good (0.779)
F
Good (0.321)
Good (0.222)
Good (0.172)
Good (0.650)
G
Good (0.382)
Good (0.187)
Good (0.493)
Good (0.091)
H
Good (0.985)
Good (0.781)
Good (0.639)
Good (0.240)
I
Good (0.959)
Good (0.568)
Good (0.607)
Good (0.292)
J
Good (0.895)
Good (0.973)
Good (0.371)
Good (0.598)
K
Good (0.938)
Good (0.541)
Good (0.966)
Good (0.328)
L
Good (0.953)
Good (0.958)
Good (0.804)
Good (0.436)
M
Good (0.898)
Good (0.403)
Good (0.255)
Good (0.756)
N
Good (0.728)
Good (0.487)
Good (0.235)
Unce ain (0.024)
O
Good (0.422)
Good (0.446)
Good (0.059)
Good (0.124)
P
Good (0.812)
Good (0.477)
Good (0.131)
Good (0.976)
Q
Good (0.717)
Good (0.633)
Good (0.216)
Good (0.304)
R
Good (0.814)
Good (0.557)
Good (0.160)
Good (0.059)
S
Good (0.593)
Good (0.397)
Good (0.489)
Good (0.799)
T
Good (0.723)
Good (0.781)
Good (0.091)
Unce ain (0.017)
Sou ce: Au ho s’ calcula ions.
We nex e alua e he speci ied RegARIMA models om he p e-adjus men phase using se e al
es s o no mali y, independence, andomness, and linea i y o esiduals. Ensu ing esiduals a e
no mally dis ibu ed is impo an o he accu acy o o ecas p edic ion in e als. To es his, we
use he Doo nik-Hansen es , which e alua es skewness and ku osis in mul i a ia e da a
ans o med o achie e independence. The co esponding p- alues om his es a e p esen ed
in column (1) o Table 5. The indings show ha esiduals om all RegARIMA models con o m o
a no mal dis ibu ion, indica ing no addi ional model e inemen is equi ed.
18
To check he independence o esiduals, we apply he Ljung-Box and Box-Pie ce Q-s a is ics,
calcula ed o bo h egula and seasonal lags. The egula lag es s e alua e au oco ela ion o e
he i s 16 lags, while seasonal lag es s ocus on he i s wo seasonal lags. Assuming he
esiduals a e andom, hei es s a is ics should ollow a chi-squa e dis ibu ion, wi h deg ees o
eedom equal o he numbe o model pa ame e s. The esul s o hese es s a e shown in
columns (2) and (3) o Table 5. Since mos p- alues exceed 0.05, we do no ejec he null
hypo hesis ha esiduals a e independen ly and iden ically dis ibu ed, suppo ing he
independence assump ion.
The andomness o he esiduals' signs is e alua ed using he Wald-Wol owi z es , also called
he Run es . This es analyzes da a cen e ed on he mean by coun ing he numbe and leng h
o uns – de ined as consecu i e alues all abo e o all below he mean. An up un consis s o
successi e alues abo e he mean, while a down un consis s o successi e alues below i . The
es examines whe he hese up and down uns a e e enly dis ibu ed o e ime, since bo h an
excess and a sho age o uns a e unlikely in uly andom sequences. I also es s whe he he
leng hs o hese uns occu andomly. The ou comes shown in columns (4) and (5) o Table 5
demons a e ha , in ou case, he esiduals exhibi andomness bo h in e ms o he numbe o
uns a ound he mean and hei a e age leng h.
Finally, he linea i y o esiduals es p o ides e idence o whe he he e is au oco ela ion in
esiduals o no . Signi ican alues o he Ljung-Box and Box-Pie ce Q-s a is ics o he squa ed
esiduals indica e andom a ia ion in he coe icien s o ime- a ying condi ional a iances,
leading o lowe eliabili y o he es s a is ics and o ecas co e age in e als. The esul s in
columns (6) and (7) o Table 5 show ha , in ou da ase , he null hypo hesis o no au oco ela ion
canno be ejec ed, which means he esiduals do exhibi a linea s uc u e.
Table 5: P-Values o RegARIMA Residual Tes s
NACE
Code
No mali y Independence Randomness Linea i y
Doo nik-
Hansen
Ljung-
Box
Box-
Pie ce
Runs
a ound
mean
numbe
Runs
a ound
mean
leng h
Ljung-Box
on
squa ed
esiduals
Box-Pie ce
on squa ed
esiduals
(1)
(2)
(3)
(4)
(5)
(6)
(7)
A
0.765
0.753
0.903
0.901
1.000
0.893
0.972
B
0.947
0.543
0.753
0.989
1.000
0.623
0.802
C
0.712
0.637
0.894
0.205
1.000
0.616
0.886
D
0.903
0.587
0.824
0.368
1.000
0.047
0.202
E
0.797
0.943
0.989
0.871
1.000
0.365
0.616
F
0.540
0.971
0.993
0.796
1.000
0.061
0.278
G
0.218
0.867
0.964
0.510
1.000
0.767
0.937
H
0.567
0.586
0.820
0.300
1.000
0.469
0.707
I
0.911
0.473
0.743
0.407
1.000
0.581
0.803
J
0.954
0.562
0.821
0.067
0.984
0.680
0.843
K
0.430
0.915
0.985
0.698
1.000
0.737
0.907
L
0.230
0.911
0.959
0.447
1.000
0.966
0.990
M
0.585
0.075
0.307
0.950
1.000
0.824
0.931
N
0.844
0.648
0.884
0.203
1.000
0.455
0.709
Con inued on he nex page
19
NACE
Code
No mali y Independence Randomness Linea i y
Doo nik-
Hansen
Ljung-
Box
Box-
Pie ce
Runs
a ound
mean
numbe
Runs
a ound
mean
leng h
Ljung-Box
on
squa ed
esiduals
Box-Pie ce
on squa ed
esiduals
(1)
(2)
(3)
(4)
(5)
(6)
(7)
O
0.401
0.836
0.935
0.638
1.000
0.003
0.057
P
0.275
0.357
0.621
0.003
0.023
0.792
0.931
Q
0.813
0.442
0.683
0.531
1.000
0.130
0.372
R
0.703
0.091
0.292
0.183
1.000
0.403
0.630
S
0.244
0.600
0.847
0.948
1.000
0.136
0.456
T
0.236
0.348
0.652
0.901
1.000
0.888
0.961
Sou ce: Au ho s’ calcula ions.
A e ensu ing all o he c i ical assump ions a e sa is ied in he p e- ea men s age, we analyze
he quali y o he seasonal adjus men esul s using a se o “M diagnos ics” p oduced by
JDeme a+. The a ious indica o s assess di e en aspec s o he seasonal adjus men p ocess,
such as how much he i egula componen con ibu es o he o e all a iance (M1, M2, and M3),
he andomness o he i egula componen (M4), he signi icance o changes in he end and
i egula componen s (M5), he a io o annual changes in he i egula componen o he seasonal
componen (M6), he p esence o iden i iable seasonali y (M7), and he s abili y o sho - and
long- e m a ia ions (M8, M9, M10, and M11). In addi ion, JDeme a+ p oduces wo composi e
indica o s (Q and Q − M2), which assess he o e all quali y o he models. Values exceeding 1
sugges possible p oblems wi h he adjus men , while alues anging om 0 o 1 a e conside ed
sa is ac o y.
The M-diagnos ic indica o s o all sec o s, p esen ed in Table 6, sugges he seasonal adjus men
p ocess is gene ally sa is ac o y o mos sec o s. Howe e , a ew sec o s exhibi po en ial issues
in speci ic indica o s. In pa icula , some sec o s, like mining and qua ying (B), manu ac u ing
(C), and in o ma ion and communica ion (J), ha e p oblems wi h mo ing seasonali y, as indica ed
by M10 and M11 s a is ics exceeding he accep able alue o 1. Simila ly, se e al sec o s ha e a
high i egula componen , such as eal es a e ac i i ies (L), adminis a i e and suppo se ice
ac i i ies (N), and o he se ice ac i i ies (S). Howe e , o all sec o s, he wo composi e
indica o s ha e alues less han 1, con i ming ha , o e all, he seasonal adjus men p ocess
appea s o be adequa e.
20
Table 6: The M-Diagnos ics
NACE
Code M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11
Q Q-M2
A
0.0
0.0
1.3
1.2
1.0
1.2
0.1
0.3
0.2
0.3
0.3
0.5
0.5
B
0.6
0.1
0.2
0.5
0.2
0.3
0.6
1.0
0.7
1.5
1.4
0.5
0.6
C
0.1
0.1
0.5
0.2
0.7
0.9
0.3
0.8
0.6
1.5
1.5
0.5
0.5
D
0.7
0.4
1.3
0.6
1.3
0.8
0.4
1.4
0.8
1.6
1.6
0.9
0.9
E
0.8
0.1
0.6
0.5
0.5
0.5
0.4
0.8
0.5
0.8
0.7
0.5
0.6
F 0.0 0.0 0.3 0.6 0.6 1.1 0.1 0.3 0.2 0.5 0.4
0.3
0.3
G 0.0 0.0 0.0 0.3 0.2 1.0 0.3 0.5 0.5 0.4 0.4
0.2
0.3
H 0.8 0.3 0.4 0.9 0.4 0.9 0.2 0.2 0.1 0.2 0.2
0.4
0.4
I 0.1 0.0 0.0 0.2 0.2 0.7 0.3 0.7 0.1 0.6 0.4
0.2
0.2
J
1.1
0.2
0.3
0.7
0.2
0.1
0.4
1.1
0.9
1.2
1.2
0.6
0.6
K
0.1
3.0
0.0
0.7
0.2
0.3
0.4
1.1
0.4
0.9
0.7
0.7
0.4
L
1.2
0.9
1.0
0.5
1.0
0.5
0.5
1.2
0.9
1.6
1.5
0.9
0.9
M
0.3
0.3
0.9
0.3
0.7
0.3
0.3
0.6
0.3
0.9
0.9
0.5
0.5
N
0.7
1.1
1.2
1.0
1.0
0.1
0.3
0.6
0.2
0.7
0.7
0.7
0.6
O
0.7
0.8
1.8
0.3
1.5
0.1
0.4
0.8
0.7
0.4
0.4
0.7
0.7
P 0.1 0.1 1.1 1.2 0.9 0.3 0.2 0.4 0.3 0.4 0.4
0.5
0.5
Q 0.3 0.2 0.8 0.6 0.9 0.5 0.3 0.9 0.6 0.7 0.7
0.6
0.6
R 0.2 0.0 0.0 0.7 0.2 0.9 1.0 2.1 0.5 2.1 2.0
0.7
0.8
S
1.2
0.5
1.0
0.7
0.9
0.1
0.4
0.9
0.3
0.8
0.4
0.7
0.7
T
0.1
0.1
0.9
0.2
0.8
0.3
0.1
0.4
0.3
0.7
0.7
0.4
0.4
Sou ce: Au ho s’ calcula ions.
Seasonally adjus ed ime se ies should emain consis en , showing minimal a ia ion when a ew
obse a ions a e added o emo ed om he o iginal da a. To e alua e his s abili y, we use
sliding spans analysis, which examines how seasonal adjus men esul s luc ua e when di e en
po ions o he o iginal da ase a e used. This me hod speci ically assesses he es ima ed
seasonal ac o s and he qua e - o-qua e changes in he seasonally adjus ed se ies, p o iding
wa nings i he e is oo much a iabili y o he same qua e o i he coun o uns able seasonal
ac o s o changes su passes accep able h esholds.
In JDeme a+, a h eshold o 3% o he es s a is ics is used o iden i y abno mal alues.
Following IMF guidelines, seasonal adjus men esul s a e deemed s able when uns able
seasonal ac o s accoun o less han 15% o all obse a ions, and when abno mal qua e - o-
qua e a ia ions in he seasonally adjus ed se ies ep esen less han 35% o he o al
obse a ions. This is also consis en wi h he ecommenda ions o Findley e al. (1990), who
p o ide simila accep able h esholds o hese measu es. Figu es 8a and 8b show he sha e o
abno mal seasonal ac o s and qua e - o-qua e changes, espec i ely, in he case o A menian
QNA se ies. As can be seen, in mos cases, hese sha es a e below he espec i e h esholds,
meaning he seasonal adjus men esul s emain oughly cons an in di e en speci ica ions wi h
a ying numbe s o obse a ions.
27
REFERENCES
Bell, William. 1984. “Signal Ex ac ion o Nons a iona y Time Se ies.” The Annals o S a is ics 646–
664.
Box, Geo ge, Gwilym Jenkins, G ego y Reinsel, and G e a Ljung. 2015. Time Se ies Analysis:
Fo ecas ing and Con ol. John Wiley & Sons.
Bu man, J. Pe e . 1980. “Seasonal Adjus men by Signal Ex ac ion.” Jou nal o he Royal S a is ical
Socie y Se ies A: S a is ics in Socie y 143 (3): 321–337.
Cas les, Ian. 1987. “A Guide o Smoo hing Time Se ies-Es ima es o ‘T end’.” In o ma ion Pape .
Canbe a: Aus alian Bu eau o S a is ics.
Cen al Bu eau o S a is ics. 1976. “The Seasonal Adjus men o Se ies Conce ning he Labo
Ma ke .” Social Maands a is iek 24 (1): 4–12.
Cen al Bu eau o S a is ics. 1981. “A New Me hod o Seasonal Adjus men Conce ning he Labo
Ma ke .” Social Maands a is iek 29 (3): 66–78.
Cle eland, William, Douglas Dunn, and I ma Te penning. 1978. “SABL: A Resis an Seasonal
Adjus men P ocedu e wi h G aphical Me hods o In e p e a ion and Diagnosis.” In A nold
Zellne (ed.). Seasonal Analysis o Economic Time Se ies (pp. 201–241). Na ional Bu eau o
Economic Resea ch.
Cle eland, Robe , William Cle eland, Jean McRae, and I ma Te penning. 1990. “STL: A Seasonal-
T end Decomposi ion.” Jou nal o O icial S a is ics 6 (1): 3–73.
Dagum, Es ella. 1980. “The X-11-ARIMA seasonal Adjus men Me hod.” S a is ics Canada.
Da né, Oli ie , Lau en Fe a a, and Dominique Ladi ay. 2018. “A B ie His o y o Seasonal
Adjus men Me hods and So wa e Tools.” No. hal-03754072.
Eu os a . 2018. “Handbook on Seasonal Adjus men .” 2018 Edi ion.
h ps://ec.eu opa.eu/eu os a /documen s/3859598/8939616/KS-GQ-18-001-EN-N.pd
Findley, Da id, B ian Monsell, Holly Shulman, and Ma ian Pugh. 1990. “Sliding-Spans Diagnos ics
o Seasonal and Rela ed Adjus men s.” Jou nal o he Ame ican S a is ical Associa ion 85
(410): 345–355.
Findley, Da id, B ian Monsell, William Bell, Ma k O o, and Bo -Chung Chen. 1998. “New
Capabili ies and Me hods o he X-12-ARIMA Seasonal Adjus men P og am.” Jou nal o
Business and Economic S a is ics 16: 127–152.
Fishe , A ne. 1937. “B ie No e on Seasonal Va ia ion.” Jou nal o Accoun ancy 64 (3): 174–199.
Fische , Bjo n 1995. “Decomposi ion o Time Se ies: Compa ing Di e en Me hods in Theo y and
P ac ice.” Eu os a .
Gómez, Vic o , and Agus ín Ma a all. 1995. P og ams TRAMO and SEATS. Eu opean Uni e si y
Ins i u e.
Hillme , S e en, and Geo ge Tiao. 1982. “An ARIMA-Model-Based App oach o Seasonal
Adjus men .” Jou nal o he Ame ican S a is ical Associa ion 77 (377): 63–70.

28
Kenny, Pe e , and James Du bin. 1982. “Local T end Es ima ion and Seasonal Adjus men o
Economic and Social Time Se ies.” Jou nal o he Royal S a is ical Socie y Se ies A:
S a is ics in Socie y 145 (1): 1–28.
Lane, R. O. D. 1972. “Minimal Re ision T end Es ima es”. Resea ch Exe cise No e 8 (72). Cen al
S a is ical O ice.
Lo ell, Michael. 1963. “Seasonal Adjus men o Economic Time Se ies and Mul iple Reg ession
Analysis.” Jou nal o he Ame ican S a is ical Associa ion 58 (304): 993–1010.
Ma a all, Agus ín, and Pie ce, Da id. 1987. “A P o o ypical Seasonal Adjus men Model. Jou nal o
Time Se ies Analysis 8(2): 177–193.
Mende shausen, Ho s . 1939. “Elimina ing Changing Seasonals by Mul iple Reg ession Analysis.”
The Re iew o Economics and S a is ics 21 (4): 171–177.
Nou ney, Ma in. 1984. “Seasonal Adjus men by F equency De e mined Fil e P ocedu es.”
S a is ical Jou nal o he Uni ed Na ions Economic Commission o Eu ope 2 (2): 161–168.
Rosenbla , Ha y. 1965. Spec al Analysis and Pa ame ic Me hods o Seasonal Adjus men o
Economic Time Se ies. Volume 3. Uni ed S a es Depa men o Comme ce, Bu eau o he
Census.
Shiskin, Julius. 1978. “Seasonal Adjus men o Sensi i e Indica o s.” In A nold Zellne (ed.).
Seasonal Analysis o Economic Time Se ies (pp. 97–104). Na ional Bu eau o Economic
Resea ch.
Shiskin, Julius, Allan Young, and John Musg a e. 1967. “The X-11 Va ian o he Census Me hod II
Seasonal Adjus men P og am.” Technical Pape 15. Uni ed S a es Depa men o
Comme ce, Bu eau o he Census.
Slu sky, Eugen. 1927. “The Summa ion o Random Causes as he Sou ce o Cyclic P ocesses.”
P oblems o Economic Condi ions 3 (1). Conjunc u e Ins i u e.
Uni ed S a es Bu eau o he Census. 2000. “X-12-ARIMA: Re e ence Manual.” Ve sion 0.2.6. Time
Se ies S a S a is ical Resea ch Di ision, Bu eau o he Census.
Van de Hoe en, H., and Anco Hundepool. 1986. “A Me hod o Seasonally Adjus ing Time Se ies
wi h Va ia ion in he Seasonal Ampli ude.” Jou nal o Business & Economic S a is ics 4 (4):
455–471.
Young, Tim. 1992. Seasonal Adjus ing o Flow o Fund Ma ices. Bank o England.
Yule, Geo ge. 1971. “On a Me hod o In es iga ing Pe iodici ies in Dis u bed Se ies wi h Special
Re e ence o Wol e ’s Sunspo Numbe s.” S a is ical Pape s o Geo ge Udny Yule, 389–420.
Ha ne P ess.
ASIAN DEVELOPMENT BANK
ASIAN DEVELOPMENT BANK
6 ADB A enue, Mandaluyong Ci y
1550 Me o Manila, Philippines
www.adb.o g
ADB ECONOMICS
WORKING PAPER SERIES
NO. 786
June 2025
F om Noise o Tu ning Poin s
A New F amewo k o Seasonal Adjus men in A menia
This pape e alua es he ansi ion o he X13-ARIMA-SEATS amewo k o he seasonal adjus men o
A menia’s qua e ly na ional accoun s, highligh ing i s ole in de ec ing economic u ning poin s. The pape
discusses bes p ac ices o seasonal adjus men and s a egies o accu a e eal- ime economic analysis.
Abou he Asian De elopmen Bank
ADB is a leading mul ila e al de elopmen bank suppo ing inclusi e, esilien , and sus ainable g ow h ac oss
Asia and he Paci ic. Wo king wi h i s membe s and pa ne s o sol e complex challenges oge he , ADB
ha nesses inno a i e inancial ools and s a egic pa ne ships o ans o m li es, build quali y in as uc u e,
and sa egua d ou plane . Founded in 1966, ADB is owned by 69 membe s—50 om he egion.
FROM NOISE TO TURNING POINTS
A NEW FRAMEWORK FOR SEASONAL ADJUSTMENT
IN ARMENIA
Ge o g Minasyan, S e an Schippe , Lusya Khacha yan, Seda Mo sisyan, and Pamela Lapi an
F om
he People o Japan
JFPR
Japan Fund o P ospe ous and
Resilien Asia and he Paci ic