The Impact Analysis on Motor Gasoline Consumption in Taiwan Shu-Chuan Lin, Chiu-Lin Tseng, Yih-Luen Wu, Maw-Wen Lin Planning Division, Chinese Petroleum Corporation 3, SongRen Road, Taipei Abstract The motor gasoline consumption in Taiwan has reached more than 8 thousand KL per day and will continue to grow, with about 99% consumed by on-land transportation sector. The oil market in Taiwan had been fully liberalized. At the end of 004, there are,47 gas stations, including 640 gas stations owned by Chinese Petroleum Corporation. The research on gasoline consumption pattern in Taiwan has just yet attracted more attentions, and this information will be valuable for marketing strategy formulation. The factors influence gasoline consumption including economic growth, war, terrorist attacks, government policy, traffic demand, seasonality, weekend and holiday etc. In this research, the motor gasoline daily consumptions from the gas stations owned by the Chinese Petroleum Corporation, starting from January of 998 to April of 004, are analyzed for the case study. The time series analysis method is used to establish the gasoline consumption ARIMA model. Base on the model, the multiple interventions analysis is applied to evaluate the impacts by the trading day effect, the Chinese Lunar New Year holidays effect, the promotion activities sponsored by the Chinese Petroleum Corporation and the 003 SARS event in Taiwan. The outcomes are as follows:. The consumption has distinct trading day pattern. The consumers have the tendency to refill the vehicles for the weekend. The sales volume on Saturday increases 5.% on daily basis.. The sales volume during 9 days period of the Lunar New Year vacation increases 7.8% on daily basis. 3. During two promotion periods, the sales volume increases 5.6% on daily basis. 4. The 003 SARS event causes only a marginal increase in consumption with.5% increase on daily basis. Keywords: Gasoline sales volume, Calendar Effects, ARIMA, Intervention Analysis / 6
. Research Purpose Facing the trend of global liberalization of market, the oil market in Taiwan is inevitably opened up to competitions. The Formosa Petrochemical came into the market on September, 000 and the Esso entered in May, 00 as well. Although Esso backed out from the Taiwan oil market quietly two years later, leaving the market with two dominant suppliers, namely, The Chinese Petroleum Corporation and The Formosa Petrochemical, the market competition is still very intensive. The oil products are the main sources of the Chinese Petroleum Corporation revenues. The oil products consumptions are strongly affected by macroeconomic conditions. It is essential to conduct analysis on the macroeconomic factors to evaluate its impact on the oil market. In this research the daily sales volumes of the Chinese Petroleum Corporation owned gas stations from January, 998 to April 30, 004 are used for the case study. The time series analysis methods are applied to analyze the consumption patterns for the purpose of understanding the consumers behaviors and the formulation for marketing strategies.. Methodology and Data () Methodology Dr. Yule invented the time series analysis method during 90s. In the early of 970s, Dr. Box and Dr. Jenkins published the ARIMA model (Auto-Regression Integrated Moving Average Model). Afterwards, this analytical method is widely applied on economics, engineering, Natural and Social Sciences. Box and Tiao (975) proposed that if the intervention factors are known during the observation period, these factors can be brought into the time series model to assess the interference or the effect of the / 6
factors. The intervention variables are expressed in dummy forms. The known intervention periods are expressed with and the non-intervention periods are expressed with 0. The method of time series intervention is widely applied in the analysis on the effects of different promotions to the sales, the impacts of certain event or policy or regulation changes to the commercial or economic time series. The general form of dynamic intervention function can be written: Ζ = C+ f( k, ξ, t) + N t f( k, ξ, t) = The fixed effect given by exogenous variable, the time function with parameter k. N t = The random interference series t The dynamic model of effect of ξ can be written: w ( B) f( δ, w, ξ, t) = Y = { } ξtj ( B) k k j tj j= j= δ j () Ytj = The dynamic transformation from () k = Replaced by δ and rj (3) δ j( B) = δ jb... δ rij B and j( B) = 0j jb... B sij B Polynomials of rj and s j (4)Assumption: the root of ( B) resides outside of the unit circle, and the root of δ ( B) resides on or outside of unit circle. j j ξ tj sj In this article, the dummy variables are used in the intervention model for four different effects, which are the trading day effect, the Chinese Lunar New Year effect, the promotion activities sponsored by 3 / 6
the Chinese Petroleum Corporation and the 003 SARS event in Taiwan. In the time series analysis, Auto-correction Function (ACF) and Partial Auto-correction Function (PACF) are used for the identification for the model and classify into the following models: Auto-Regression, (AR),Moving Average (MA), Auto-Regression Moving Average (ARMA) or Auto-Regression Integrated Moving Average (ARIMA). According to the described model, the SCA (Scientific Computing Associates) time series software is used for analysis to assess the coefficients and the statistical significant of four intervention variables. The built-in SCA Intelligent Auto-Regression Integrated Moving Average function (IARIMA) can efficiently solve the problem of model identification and deal with the external interferences and outliers in the data. With the auto-detection, modification, the modified prediction model are established. ().Data Description The Petroleum Management Law was passed on September 7, 00 and came into effect on October, 00, which was one of the milestones of the liberalization of Taiwan oil market. During the process of liberalization of the Taiwan oil market, the retailing, refining and trading businesses are opened to private sectors accordingly. The important opening events include: retail gas station in 987, refining in 996, partial international trading in 999, the Formosa Petrochemical franchise gas station in 000, the pass of the Petroleum Management Law in 00, and the full scale of international trading on December 6, 00. After the permission of the first private owned gas station on February 988, till the end of 004 there are,83 private gas stations are in business. The number is far exceeding 640 gas stations owned by the Chinese Petroleum Corporation. Due to the difficulty in collecting the data from all the gas stations, the daily sales volumes of 4 / 6
these 640 gas stations owned by the Chinese Petroleum Corporation are used for the case study. The time period of the data starts from January, 998 to the April 30 of 004, with the total of,3 records. At that moment, there were,777 private gas stations and 63 CPC-owned gas stations, with the ratio of 74 to 6. 6,500 KL 4,500,500 0,500 8,500 6,500 4,500 998// 998/4/ 998/7/ 998/0/ 999// 999/4/ 999/7/ 999/0/ 000// 000/4/ 000/7/ 000/0/ 00// 00/4/ 00/7/ 00/0/ 00// 00/4/ 00/7/ 00/0/ 003// 003/4/ 003/7/ 003/0/ 004// 004/4/ Y/M/D Figure: The Daily Sales Volumes of CPC-Owned Gas Stations 3. The Establishment of the Time Series Model () ARIMA Model According the model construction sequence of Box and Jenkins, the data of daily sales volumes of CPC-Owned gas stations are defined as Z t (t=,,,3). When examining the Auto Correlation Function (ACF, Graph ), It was found that Z t needed to be differentiated for stabilization. After reviewing the graphics (Graph 3) of the first and the seventh order of differentiation, it came to the following equation: 5 / 6
(-B 7 )Z t = (-0.8749B 7 )/(-0.785B) t () (84.8) (49.54) ^ σ a = 38.4 R = 0.933 Figure : The ACF of the Series () Trading Day Effects The selection of timing to refill for the vehicles can be habitual. It may be because of the location of home, or route to the office, or the time of the office hours, or the weekday and weekend. The consumers habitual behaviors affect the fluctuations of the gasoline sales volumes. The trading day effect is analyzed to describe the consumption pattern. 6 / 6
i i=, 7 to present the trading days effects of Monday, Tuesday, to Sunday Wi i=, 7 to present the dummy variables for individual weekdays, for Monday W=, otherwise 0 The total trading day effects can be written as: f (,..., W,... W = iw 7 7 ) 7 i = i () In order to avoid the problems of highly correlation tendency and the multi-co linearity for to 7, only to 6 were used in the model. 6 Z t = C + W +at...(3) i = it it The estimations are as follows: Coef. C 3 4 5 6 Est. 037.7-9.3-537.3-467.4-563.5-5.0 3.6 t Test 5.5 -.53-4.8-3.7-4.49-0..57 From the estimation, we found the coefficient of W 6 positive and the W to W 5 are negative. The constant is the sales volume of Sunday. to 6 is the difference from Monday to Saturday relative to the Sunday. The rankings of sales volumes of the trading days accordingly are Saturday, Sunday, Friday, Monday, Wednesday, Tuesday and Thursday. It shows that consumers go to gas stations for refill more often during the weekend than the weekdays. Starting from January in 998, Taiwan has two days leaves for the weekend. People are more intend to use their own vehicles for traveling. For the consideration that we will take a first order of differentiation 7 / 6
in the final integrated model, we use another forms of dummy variables in the analysis. In the following paragraphs, we explain the transformation of the dummy variables: For a series with seven dummy variables (W, W, W3, W4, W5, W6 and W7): Y t = ß 0 + ß D t + ß D t + ß 3 D 3t + ß 4 D 4t +ß 5 D 5t + ß 6 D 6t +ε t u = ß 0 + ß u = ß 0 + ß u 3 = ß 0 + ß 3 u 4 = ß 0 + ß 4 u 5 = ß 0 + ß 5 u 6 = ß 0 + ß 6 u 7 = ß 0 Assumption: u +u +u 3 +u 4 +u 5 +u 6 +u 7 = 0 u 7 = -u -u -u 3 -u 4 u 5 -u 6 ( In our case W 7 =-) Y t = u+u D t +u D t +u 3 D 3t +u 4 D 4t +u 5 D 5t +u 6 D 6t +ε t W E(Y)= u+u W E(Y)= u+u W3 E(Y)= u+u 3 W4 E(Y)= u+u 4 W5 E(Y)= u+u 5 W6 E(Y)= u+u 6 W7 E(Y)= u-u -u -u 3 -u 4 -u 5 -u 6 u = The mean of the whole time series The original series of dummy variables of W-W6 are transformed 8 / 6
from: Time W W W3 W4 W5 W6.............. Mon. 0 0 0 0 0 Tues. 0 0 0 0 0 Wed. 0 0 0 0 0 Thurs. 0 0 0 0 0 Fri. 0 0 0 0 0 Sat. 0 0 0 0 0 Sun. 0 0 0 0 0 0 Mon. 0 0 0 0 0.............. Into: Time W W W3 W4 W5 W6....... Mon. 0 0 0 0 0 Tues. 0 0 0 0 0 Wed. 0 0 0 0 0 Thurs. 0 0 0 0 0 Fri. 0 0 0 0 0 Sat. 0 0 0 0 0 Sun. - - - - - - Mon. 0 0 0 0 0.............. After using the transformed dummy variables series, the estimations of trading day effect are in the follows: Coef. C 3 4 5 6 Est. 0030. 5. -39.7-59.9-356.0 9.5 530. t Test 98.9 0.8-4.0-3.6-4.33 -.34 6.45 The constant is total mean of the series, which is 0,030.KL. to 6 is the difference from Monday to Saturday relative to the total mean. In the original estimation, we found the mean of Sunday was 9 / 6
037.7. From there, we can calculate the mean of each date of the week as follows: Actual Means Monday 037.7+(-9.3)=0045.4 Tuesday 037.7+(-537.3)= 9700.5 Wednesday 037.7+(-467.4)= 9770.3 Thursday 037.7+(-563.5)= 9674. Friday 037.7+( -5.0)=0.7 Saturday 037.7+( 3.6)=0560.3 These estimations from these calculations are consistent with the direct averaging from the raw data as follows: Monday Tuesday Wednesday Thursday Friday Saturday Sunday 0045.4 9700.5 9770.3 9674. 0.7 0560.3 038. In the direct observations from the ratio to the total mean in the each date of the weeks in the raw data, we found the rankings of the sales volumes are the same as those from the estimations. Monday Tuesday Wednesday Thursday Friday Saturday Sunday.0 0.96 0.97 0.96.0.05.0 (3) Holiday Effect Due to the effect of the Chinese Lunar New Year, the consumption of gasoline may increase. In the past six years, the dates of the Chinese Lunar New Year are spread across January 4 to February 6. Assuming that there is nine days for vocations and evenly divided by the first day of Chinese New Year, a dummy 0 / 6
variable is defined as Newt. The First Day of the Chinese Lunar New Year Year Date 998 January 8 999 February 6 000 February 5 00 January 4 00 February 003 February The model considering the holiday effect was formulated as Z t ()= ( β )NEWY t ()+ (- B - B 3 B 3 )/(-φ 7 B 7 ) t Coefficients Estimation and t Value Considering Holiday Effect Coef. β 3 φ 7 Esti. 760.69 0.33 0.38 0. 0.38 t Test 8.95 6.5 9.3 0.8 9.0 ^ σ a = 46. R = 0.94 In the estimation, it was found that the holiday effect is significant and the coefficient is positive. It shows that the trips for sightseeing and family reunion are very active during holidays, which increase the sales of gasoline. (4) Promotion Activities In the periods of November 5 to December 3, 000 and March 8 to March 3 00, the Chinese Petroleum Corporation initiated two promotion activities. To study the impact of promotion activities to the gasoline sales, the dummy variable PROMO t was introduced. / 6
PROMO t = t = November 5 to December 3, 000 t = March 8 to March 3, 00 0 t = Others The model considering the promotion effect was formulated as Z t ()= ( β ) PROMO t ()+ (- B - B 3 B 3 )/(-φ 7 B 7 ) t Coefficients Estimation and t Value Considering Promotion Effect Coef. β 3 φ 7 Esti. 477.3 0.30 0.38 0.3 0.38 t Test 3.7 4.69 9.47.33 8.83 ^ σ a = 4. R = 0.93 From the estimation, the variable Prom is proved to be significant and the coefficient is positive. It shows there were incentives for the consumers to shop at the CPC-Owned gas stations. (5) SARS Event During the first half year of 003, Asia is under the shadow of SARS event. Not only the international traveling was greatly dampened, but also was the domestic traffic are heavily affected. People avoided taking the public transportation system and the economic activities are depressed. So did the sales of gasoline. The impact of SARS event to the sale of gasoline is analyzed, which took place during the period from March to June of 003. The dummy variable SARS t was introduced. SARS t = t = March 5 to June 30, 003 0 t = Others The model considering the SARS effect was formulated as Z t ()= ( β 3 ) SARS t ()+ (- B - B 3 B 3 )/(-φ 7 B 7 ) t Coefficients Estimation and t Value Considering SARS Effect / 6
Coef. β 3 3 φ 7 Esti. 93.6 0.30 0.38 0.3 0.38 t Test 0.48 4.8 9.47.33 8.8 ^ σ a = 43.0 R = 0.93 From the estimation, the coefficient of Sars was positive. It implies during that period people prefer driving their own car to instead of using public transportation system, which can increase the sale of gasoline. But from the statistical point of view, it is not significant. 0,000 9,500 9,000 8,500 8,000 7,500 7,000 6,500 6,000 KL 003/3/ 003/3/8 003/3/5 003/3/ 003/3/9 003/4/5 003/4/ 003/4/9 003/4/6 003/5/3 003/5/0 003/5/7 003/5/4 003/5/3 003/6/7 003/6/4 003/6/ 003/6/8 Fighue 3: The Sales of Gasoline in the CPC-Owned Gas Stations 4. The Integrated ARIMA Model After the discussion of the individual intervention factor, a integrated model was formulated for fully presentation. Z t ()= C+( )D t ()+ ( ) D t ()+ ( 3 ) D 3t ()+ ( 4 ) D 4t () 3 / 6
+ ( 5 ) D 5t ()+( 6 ) D 6t () + ( β )NEWY t ()+ ( β ) PROMO t ()+ ( β 3 ) SARS t () + (- B - B 3 B 3 )/(-φ 7 B 7 ) t (5) Coefficients Estimation and t Values Coef. C 3 4 5 6 Esti. -.46 8.78-36.6-57.9-358.30 9.39 54.6 t Test -0.99 0.96-6.64-3. -8.7 9.8 6.73 Coef. β β β 3 3 φ 7 Esti. 799.7 53.30 77.45 0.3 0.36 0. 0.05 t Test 9.7 3.86 0.4 5. 7.45 7.53.56 ^ σ a = 366.87 R = 0.95 Examining the coefficients of each variables, besides the constant term is not significant, we found that the coefficients of 3 and φ 7 were 0.5 and 0.05. To the sample size of,3, relative to, the coefficients were too small. removed from the model. The corresponding parameters were The final estimations are as follows: The Final Coefficients Estimation and t Values Coef. 3 4 5 6 Esti. 9.08-36.34-55.69-356.09 9.47 53.67 t Test.06-8. -4. -9.79 0.64 9.08 Coef. β β β 3 Esti. 785.78 559.37 53.69 0.35 0.39 t Test 9.48 3.89 0.76 7.97 0.39 ^ σ a = 37. R = 0.95 The results of the integrated model are identical with individual analysis of the impact factors. 4 / 6
5. Conclusions From the research, we have the following findings: () The consumption has distinct trading day pattern. The consumers have the tendency to refill the vehicles during weekend. The sales volume on Saturday increases 5.% on daily basis. () The sales volume during 9 days period of the Lunar New Year vacation increases 7.8% on daily basis. (3) During two promotion periods, the sales volume increases 5.6% on daily basis. (4) The 003 SARS event causes only a marginal increase in consumption with.5% increase on daily basis. The application of time series analysis can evaluate the consumption pattern of gasoline in Taiwan, which provides important implications for the formulations of the marketing strategies. If the time series of private gas stations can be compared with CPC-Owned gas stations, it will provide more insights and accuracy in the analysis of the gasoline consumers behaviors in the Taiwan gas stations. Acknowledgements We wish to think Lon-Mu Liu for helpful comments on an earlier draft of this article. Reference:. Bell, W. R., and Hillmer, S.C.(983). Modeling time series with calender variation. J. Amer. Stat Assoc., 78, pp.56-534.. Box G.E.P.,Jenkins GM, Reinsel GC. Time Series Analysis:Forecasting and Control.(3 rd Ed) 994; New Jersey: Pretice-Hall 3. Box G.E.P.& Tiao, G. C.(975) Intervention analysis with application to economic and environmental problems. Journal of the American Statistical Association, 70, 70-79. 4. Liu, L.M. & Chen, C.(99) Recent development of time series 5 / 6
analysis in intervention and environmental impact studies. Journal of Environmental Science and Health, A6, 7-5. 5. Liu, L.M., Hudak, G.B., Box, G.E.P., Muller, M.E.& Tiao, G.C.(99) Forecasting and Time Series Analysis Using the SCA Statistical System, vol. Chicago: Scientific Computing Associates Corporation. 6. Maw-Wen Lin. The Time Series Analysis and Forecasting.99 7. McCleary, R. & Hay, R.A.(980) Applied Time Series Analysis for the Socail Science. Beverly Hills, CA: Sage Publications. 6 / 6