A C T A U N I V E R S I T A T I S L O D Z I E N S I S ____________ FOLIA OECONOMICA 228, 2009
E w a Ja ło w ie c k a * , P io tr Jałow iecki**, A rk a d iu sz O rłow ski***
TRENDS IN CIGARETTES CONSUMPTION IN POLAND
ACCORDING TO EXPOTENTIAL SMOOTHING
AND AUTOREGRESSIVE MODELS
Abstract. Polish tobacco industry has been recently changing significantly due to accession of Poland to EU. It is one of the prime sector of polish economy. It generates every year about 7% of budget incomes on average. The aim of this paper is to compare some forecast methods of cigarettes consumption in 2006-2010. The models used expo-nential smoothing and autoregression theory. The forecasts were estimated on historical data from 1995-2005. The main attention was focused on the trends in prediction. Iden-tification, the most crucial stage in fitting autoregressive models exploited different approach such as the comer method and extended sample autocorrelations. The outlier selection techniques were also applied to get more reliable estimates. The results were compared to the predicted values obtained from Central Statistical Office and to the results of forecasts taking cigarettes production into consideration due to prewhitening technique. The advantages and drawbacks of different methods are discussed.
Key words: cigarettes consumption, forecasting, expotential smoothing models, autoregressive models, comer methods, prewhitening technique.
I. INTRODUCTION
Polish tobacco industry is a significant branch o f national economy, which generates 7.5% o f budget incomes. In 2004 the greatest Polish tobacco company - Phillip Morris has paid 4.4 billion PLN taxes (2.8% budget incomes). Accord-ing to AC Nielsen report from 2006, Polish tobacco industry has been divided by 6 foreign corporations: Philip Morris (38.9%), Scandinavian Tobacco (16.8%), British American Tobacco (16.3%), Imperial Tobacco (14.4%), Altadis Polska (8.7%), Gallaher (4.7%). Summary participation o f the greatest tobacco compa-nies in Polish market is situated on the level o f 99.8%. Participation in market o f
* M.Sc., Chair of Informatics, Warsaw University of Life Sciences. ** Ph.D., Chair of Informatics, Warsaw University o f Life Sciences. % % Ф
the greatest Polish tobacco company - Zakłady Tytoniowe w Lublinie S.A. is an about level o f 0.1%. In Poland, from among 5 main categories o f tobacco prod-ucts: cigarettes, cigars, cigarillos, cigarette tobacco and pipe tobacco, the great-est participation in market have cigarettes (about 90%) and cigarette tobacco (about 7%). The other tobacco products are bought in small amounts.
Nowadays, according to different estimations from 9 to 10 millions inhabi-tants o f Poland smoke cigarettes. A statistical smoker in Poland consumes 13 cigarettes daily, that is 4745 cigarettes yearly. A consumption o f cigarettes in Poland was amounted on the yearly level o f 2500-2650 cigarettes per statistical inhabitant in the first half o f 90s, 2300-2400 pieces in the second half o f 90s. Definitely decreasing o f cigarettes consumption level was observed after 2000 year, when an amount o f legal produced cigarettes consumed by statistical in-habitant fluctuated from 1920 to 2010 pieces in the year. According to AC Niel-sen reports, a consumption o f cigarettes in Poland in 2006 year in comparison to 2005 decreased by 3.5%.
Despite the fact that consumption o f cigarettes in Poland decreases, the smoking is still very serious problem. Eveiy year cigarettes-related diseases are the reason o f about 70000 premature deceases. It is more than the sum o f de-ceases related from AIDS, alcohol and drugs consumption together. In the other countries the cigarettes consumption is also very serious problem. According to WHO study results, more than 10 millions people dies due to cigarettes-related premature deceases (Zatoński et all., 2002).
II. A IM O F STUDY AND M ETH O D S
The aim o f this paper was a preparation o f cigarettes consumption in Poland forecasts based on 1970-2005 historical data in order to confirmation o f decreas-ing trend observed from 1995 to 2005. Forecasts were prepared accorddecreas-ing to expotential smoothing models for yearly and monthly data, autoregressive mod-els due to ARIMA (AutoRegressive Integrated Moving-Average) methodology for monthly data. Additionally, forecasts with taking cigarettes production into consideration due to prewhitening technique were prepared. Identification, the most crucial stage in fitting autoregressive models exploited different approach such as the comer method and extended sample autocorrelations. The outlier selection techniques were also applied to get more reliable estimates. Identified outliers are signed by white points on all figures. The main criterion o f model assessment were AIC (Akaike Information Criterion) and BIC (Bayesian Infor-mation Criterion). The auxiliary criterion was MAPE (Mean Absolute Percent Error). Calculations and results preparations were performed with using The SAS System and MS Excel software.
III. DATA SOURCE AND CH ARACTERISTICS
Time series used in cigarettes consumption forecasts were prepared on the basis o f historical data from Central Statistical Office. Data includes 36 yearly observations o f 1970-2005 years, and 120 monthly observations o f 1995-2005 years. Yearly data are publishing every year in Polish Statistical Yearbook. Monthly data originates from prepared every year data bases, which include characteristics, incomes and outcomes o f households. These data bases have been preparing from 1993 on the basis o f surveys in about 31000 polish house-holds. M onthly data were calculated by authors on the basis o f amount o f person and expenses for cigarettes. On the basis o f these data Households Budgets pub-lications are preparing every year.
IV. FO RECASTS ACCORDING TO EX PO TENTIAL SM OOTHING MODELS
From expotential smoothing forecasts prepared on the basis o f yearly data, the best assessment characteristics were for a forecast according to linear expo-tential smoothing Holt model (AIC = 339,61; MAPE = 3,41; R“ = 0,71) pre-sented on figure 1. According to forecast results, cigarettes consumption in Po-land in 2008 year is estimate on 1892, and in 2010 year on 1845 pieces for a person level.
Figure 2. Forecast results according to multiplicative Winters model for monthly data Source: Own preparation.
Figure 3. Forecast results according to Holt model for seasonal adjusted monthly data Source: Own preparation.
From expotential smoothing forecasts prepared on the basis o f monthly data, the best assessment characteristics were for a forecast according to seasonal multiplicative Winters model (AIC = 519,30; MAPE = 3,54; R2 = 0,88) pre-sented on figure 2 and according to Holt model for seasonal adjusted data (AIC = 498,15; MAPE = 2,90; R2 = 0,89) presented on figure 3. According to results o f monthly forecasts, cigarettes consumption in Poland in 2008 year is estimate from 108 to 129 pieces for a person due to multiplicative Winters model, and 120 pieces for a person due to Holt model.
V. IDENTIFICATIO N OF ARIM A M ODELS W ITH USING CORNER M ETHODS
An identification o f ARIMA models were prepared with using o f selected com er methods. In these methods a table o f successive autoregressive orders in columns on moving average orders in rows (Gourieroux et all., 1997). In each cell o f identification table there are values o f test function used in concrete method. In this paper, ESACF (Extended Sample Autocorrelation Function) [Tsay et all., 1984], SCAN (Smallest CANnonical autocorrelation) (Tsay et all., 1985) and MINIC (MINimal Information Criterion) (Hannan et all., 1982) meth-ods were used.
In all com er methods, the order o f ARIMA model is tentatively identified by finding o f left, upper comer o f pattem with statistically insignificant values (ESACF, SCAN methods) or maximal value o f concrete criterion (MINIC method). A few the best ARIMA models may be identified by using o f comer methods, then the final identification is doing according to selected information criterion. In this paper BIC (Bayesian Information Criterion) was used and A R IM A (l,l,l)s (0 ,l,l) model was identified. An identification o f ARIMA model is presented on figure 4.
The Extended Sample Autocorrelation Function (ESACF)
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The Smallest CANonical (SCAN) correlation w*t MAP M A I m 2 M AJ m * m s M l * Mi A B t A » i M M 0Ô939 DOOM 09W1 00!« 0020« 0Ш7 lo o ts » о « в г в о » ? о ю м ooora 9 0771 00030 од аг[$ Д '\оо14' e'aócäi DOžíS v<üm naijo 0«Ш ä«M 8 DO« v o m m i mmi ooosi w m o*?i
tS M m O B S » 0 0 (9 3 Ö.01SS 0.Ü<S3 »«SSO Critical value 0.05 of norm ál lis tr button C rtical value 0.003!) o f X 'stM tatlc
The MINimum Information Criterion (MINIC) u * t m , * т л ш г Щ Ш М- M A S A R » 4 , Ш 1 1 4 .Ш 4 П А Ш Ш а 4 т п 4 m m A R t 4 ш т 4 638344 4 61590« 4 Ш Щ Ą w t m 4 4*46^ № . г 4 w т п ш 4 л т т 4ЙМ1ФТ АЙЗ 4 М Ж $ *«13836 4 $ Ш М 4 ^ Ш 4 4 ш т A ft 4 Л4ШЯ « 4? 1*1 4 4SÍÔ2? 4«1803# ' 4 т т « 4 т т A R Í 4,«7131Í 4 510611 4.821778 4!&»Ш 4 Щ Ш 44Т4Ш Махатм! value o f BIC
Figure 4. ARIMA model identification with using of ESACF, SCAN and MINIC method Source: Own preparation.with using of SAS System.
VI. FORECASTS AC CO RD ING TO SELECTED AR IM A M ODEL
A forecast o f cigarettes consumption according to A R IM A (l,l,l)s(0 ,l,l) (AIC = 505,83; MAPE = 4,12; R2 = 0,80) is presented on figure 5. According to results o f monthly forecast, cigarettes consumption in Poland in 2008 is estimate from 98 to 120 pieces per person.
06.95 06.96 03.97 01.96 11.96 09.99 07.00 05.01 03.02 12.02 10.03 06.04 06.05 04.06 02.07 12.07 09.08
Figure 5: Forecast results according to ARIMA(l ,1,1 )s(0,1,1) model for monthly data Source: Own preparation.
According to Central Statistical Office data, from 2003 in Poland an obvious descending trend o f cigarettes consumption and ascending trend o f cigarettes production has been observing. A comparison with export, import and smug-gling levels indicates to significant surplus o f production over consumption. Then, it was interesting to prepare a consumption forecast with taking produc-tion into consideraproduc-tion due to prewhitening technique.
In the prewhitening technique ARIMA model is complemented by addi-tional variable or variables. Its values are simultaneously forecasted using an-other ARIMA model. In this paper a forecast o f cigarettes consumption accord-ing to selected ARIMA(0,1,1) model was prepared with additional variable, which were forecast results o f cigarettes production according to ARIMA(0,1,1) model for monthly data from 1995-2005 years. A comparison o f results o f fore-cast with the use o f prewhitening technique with results o f forefore-cast according to ARIMA( 1,1,1) model for seasonal adjusted monthly data is presented on figure 6.
s s 151 • 13C ... Model A ,i, — ---95% C.L. of A .« --- --- 95% C.L. of A 7i 8 Model P к Й 5 Й 05% C.L. Of P 9S% C L o fP
sie.95 сге.96 mar.97 sty.98 lis.98 wrz.99 maj.01 mar.02 gru.02 paź.03 sie.04 cze.05 kwl.06 lut.07 gru.07 wrz.08
Figure 6. Comparison o f forecasts results according to ARIMA( 1,1,1) model with (P) and without (A) the use o f prewhitening technique.
Source: Own preparation.
According to results o f forecast without the use o f prewhitening technique, a cigarettes consumption in Poland in 2008 year is estimate on the level o f 119 pieces per person monthly. According to results o f forecast with taking ciga-rettes production into consideration due to prewhitening technique, a cigaciga-rettes consumption is estimate on 134 pieces per person.
Forecasts prepared with using o f prewhitening technique often have a wider confidence intervals than analogous forecasts prepared only on the basis o f his-torical data like in case o f forecasts presented on figure 6. It is a consequence of consideration necessity o f additional variable variability. Nevertheless these forecasts enable to take into consideration the influence o f another variables. On figure 6, (lie results of forecast prepared with the use o f prewhitening technique are closer to average monthly cigarettes consumption level in 2006, which is situated on 167 pieces per a person and was calculated on the basis o f yearly data.
VII. CO N C LU SIO N S
The results o f all prepared forecasts confirm a descendent trend o f cigarettes consumption observed in last years. Potential reasons are: a growth o f cigarette prices connected with excise increases according to necessity o f adaptation its level till the end o f 2008 year to minimal level in European Union (64 EUR for 1000 pieces and 57% o f price) and powerful anti-smoking advertising
cam-paigns. The effects are giving up or limitation o f cigarettes consumption by smokers and a growth o f cigarettes smuggling number.
At the other side, Central Statistical Office data indicates to an unquestion-able growth trend o f cigarettes production in Poland in last years. An ascendent trend o f cigarettes production is confirmed by the results o f prepared earlier forecasts (Jałowiecka et all., 2006; Jałowiecka et all., 2007). The results of ciga-rettes consumption forecast taking a cigaciga-rettes production into consideration show a slower, but still significant descendent trend o f consumption. It means, that probably changes o f production level have relatively poor influence to changes of consumption in Poland.
A comparison o f production, import and smuggling o f cigarettes yearly level from one side with consumption and export indicates on obvious surplus o f pro-duction. In 2006 year 111 billions cigarettes were produced in Poland, 13.8 bil-lions mostly most expensive luxuries kinds were imported and 11.2 bilbil-lions mainly from former USSR countries were smuggled. A consumption o f ciga-rettes in Poland in 2006 year were estimated to 76.7 billions and exported were 22.2 billions o f cigarettes. A difference between supply and consumption and export is 12.1 billions o f cigarettes.
R E F E R E N C E S
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Zatoński W., Przewoźniak K. (2002), Przeciwko epidemii. Działania rządów a ekonomi-ka ograniczenia konsumpcji tytoniu, Bank Światowy / Wydawnictwo Medycyna Praktyczna. Kraków, Poland.
Ewa Jałowiecka, Piotr Jałowiecki, Arkadiusz Orłowski
B A D A N I E T E N D E N C J I S P O Ż Y C I A P A P I E R O S Ó W W P O L S C E Z W Y K O R Z Y S T A N I E M M O D E L I W Y R Ó W N A N I A W Y K Ł A D N I C Z E G O
I M O D E L I A U T O R E G R E S Y J N Y C H
Polski przemysł wyrobów tytoniowych przechodzi w ostatnich latach znaczące przemiany związane z akcesją Polski do Unii Europejskiej. Stanowi on ważny sektor polskiej gospodarki generując 7,5% dochodów budżetu państwa. W pracy porównano prognozy spożycia papierosów w latach 2006-2010 przygotowane w oparciu o wybrane modele wyrównywania wykładniczego oraz autoregresyjne na podstawie danych histo-rycznych z lat 1995-2005. Główną uwagę skoncentrowano na trendzie w prognozach. Identyfikację modeli autoregresyjnych przeprowadzono przy użyciu metod typu „cor-ner” oraz rozszerzonej funkcji autokorelacji. W celu zwiększenia wiarygodności, pro-gnozy przygotowano z uwzględnieniem zidentyfikowanych wartości odstających. Uzy-skane wyniki porównano z danymi szacunkowymi uzyskanymi z Głównego Urzędu Statystycznego oraz z wynikami prognoz uwzględniających jako dodatkową zmienną produkcję papierosów przygotowanymi z zastosowaniem techniki „prewhitening”. Prze-prowadzono dyskusję zalet i wad zastosowanych metod.
