تحلیل مانایی سری زمانی شاخص قیمت مصرف کننده در ایران و ارائه یک مدل ARIMA برای پیش بینی آن
محورهای موضوعی : مدیریت استراتژیکصمد کاظمی 1 , پوریا سوری 2 , مهدي غضنفري 3 , میرسامان پیشوایی 4
1 - دانشگاه علم و صنعت
2 - دانشگاه علم و صنعت
3 - دانشگاه علم و صنعت
4 - دانشگاه علم و صنعت
کلید واژه: سری زمانی آزمون ریشه واحد مانایی مدل خودرگرسیو انباشته با میانگین متحرک پیش بینی,
چکیده مقاله :
در این پژوهش برای تعیین مانایی یا غیر مانایی داده های سری زمانی شاخص قیمت مصرف کننده در ایران از سال 1359 تا 1391 به قیمت های ثابت سال 1383، پس از کشف روند تغییرات داده های سری زمانی و تعیین مرتبه خود رگرسیو، میانگین متحرک و میانگین متحرک خودرگرسیو سری زمانی، آزمون ریشه واحد را روی داده های سری زمانی انجام می دهیم و عدم مانایی سری مشخص می شود. در ادامه با انجام آزمون دیکی فولر تکمیل شده، مشخص می شود که سری زمانی تنها یک ریشه واحد دارد. پس از حصول اطمینان از داشتن تنها یک ریشه واحد، مدل فرایند خودرگرسیون انباشته با میانگین متحرک را برای این سری زمانی برآورد می کنیم. سپس کفایت مدل را با آزمون پورتمن تیو بررسی کرده و تصادفی خالص بودن سری زمانی مشخص می شود. در نهایت با استفاده از مدل به دست آمده، مقادیر آینده داده های سری زمانی را در دو فاصله اطمینان 80 و 95 درصد از سال 1392 تا 1401 پیش بینی می کنیم.
This study aims to determine stationarity or non-stationarity of time series data of consumer price index (CPI) in 1980-2012 (i.e. 1359-1391 based on Iranian calendar) time period where 2004 (i.e. 1383 Iranian calendar) is the base year. applying the appropriate methods to detect the trend of time series and determine the autoregressive, moving average and autoregressive moving average of CPI time series autoregressive, moving average and autoregressive moving average of CPI time series, we perform unit root test that results in non-stationarity of CPI time series. using the Augmented Dicky-Fuller test, it is concluded that the time series has only one unit root. therefore, an ARIMA model is developed for the time series data. using Portman-Teau test, the adequacy of the model and its pure randomness is proved. Finally, we use the proposed ARIMA model to forecast future data from 2013 to 2022 (i.e. 1392 to 1401 Iranian calendar) in 80 and 95 percent levels of confidence.
[1] G. C. Tiao, “Time Series: ARIMA methods,” Int. Encycl. Soc. Behav. Sci., pp. 316–321, 2015.#
[2] K. Chapman, “The Consumer Price Index: A History and Source List,” Ref. Serv. Rev., vol. 13, no. 4, pp. 47–51, 1985.#
[3] R. E. Abdel-Aal and A. Z. Al-Garni, “Forecasting monthly electric energy consumption in eastern Saudi Arabia using univariate time-series analysis,” Energy, vol. 22, no. 11, pp. 1059–1069, 1997.#
[4] Y. Wang, J. Wang, G. Zhao, and Y. Dong, “Application of residual modification approach in seasonal ARIMA for electricity demand forecasting: A case study of China,” Energy Policy, vol. 48, pp. 284–294, 2012.#
[5] V. Ş. Ediger, S. Akar, and B. Uğurlu, “Forecasting production of fossil fuel sources in Turkey using a comparative regression and ARIMA model,” Energy Policy, vol. 34, no. 18, pp. 3836–3846, 2006.#
[6] V. Ş. Ediger and I. Berk, “Crude oil import policy of Turkey: Historical analysis of determinants and implications since 1968,” Energy Policy, vol. 39, no. 4, pp. 2132–2142, 2011.#
[7] M. Tabesh, Z. Banafsheh, and A. J. Khoshkholgh, “Application of time series analyzing in forecasting daily demand of Tehran drinkable water,” in National Congress of Civil Engineering, 2004.#
[8] S. Barak and S. S. Sadegh, “Forecasting energy consumption using ensemble ARIMA–ANFIS hybrid algorithm,” Int. J. Electr. Power Energy Syst., vol. 82, pp. 92–104, 2016.#
[9] C. Yuan, S. Liu, and Z. Fang, “Comparison of China’s primary energy consumption forecasting by using ARIMA (the autoregressive integrated moving average) model and GM (1, 1) model,” Energy, vol. 100, pp. 384–390, 2016.#
[10] P. Narayanan, A. Basistha, S. Sarkar, and S. Kamna, “Trend analysis and ARIMA modelling of pre-monsoon rainfall data for western India,” Comptes Rendus Geosci., vol. 345, no. 1, pp. 22–27, 2013.#
[11] J. Jia, J. Zhao, H. Deng, and J. Duan, “Ecological footprint simulation and prediction by ARIMA model—A case study in Henan Province of China,” Ecol. Indic., vol. 10, no. 2, pp. 538–544, 2010.#
[12] R. O. Yusuf, Z. Zainon Noor, A. Halilu Abba, M. Ariffin Abu Hassan, M. Rafee Majid, and N. Idris Medugu, “Predicting methane emissions from livestock in Malaysia using the ARIMA model,” Manag. Environ. Qual. An Int. J., vol. 25, no. 5, pp. 585–599, 2014.#
[13] K. Taneja, S. Ahmad, K. Ahmad, and S. D. Attri, “Time series analysis of aerosol optical depth over New Delhi using Box–Jenkins ARIMA modeling approach,” Atmos. Pollut. Res., 2016.#
[14] H. Karbasi Yazdi, Y. Nourifard, and H. Chenari Bouket, “Study of regression toward the mean phenomenon in Tehran stock exchange using unit root test,” Knowl. Invest., vol. 4, pp. 87–103, 2013.#
[15] A. Jadevicius and S. Huston, “ARIMA modelling of Lithuanian house price index,” Int. J. Hous. Mark. Anal., vol. 8, no. 1, pp. 135–147, 2015.#
[16] Y. Du, Y. Cai, M. Chen, W. Xu, H. Yuan, and T. Li, “A Novel Divide-and-Conquer Model for CPI Prediction Using ARIMA, Gray Model and BPNN,” Procedia Comput. Sci., vol. 31, pp. 842–851, 2014.#
[17] C. N. Babu and B. E. Reddy, “A moving-average filter based hybrid ARIMA–ANN model for forecasting time series data,” Appl. Soft Comput., vol. 23, pp. 27–38, 2014.#
[18] A. Vosseler, “Bayesian model selection for unit root testing with multiple structural breaks,” Comput. Stat. Data Anal., 2014.#
[19] A. Hepsen and M. Vatansever, “Forecasting future trends in Dubai housing market by using Box-Jenkins autoregressive integrated moving average,” Int. J. Hous. Mark. Anal., vol. 4, no. 3, pp. 210–223, 2011.#
[20] S. Stevenson, “A comparison of the forecasting ability of ARIMA models,” J. Prop. Invest. Financ., vol. 25, no. 3, pp. 223–240, 2007.#
[21] I. Teymouri, M. Ahmadi, and K. Abolhassanzadeh, “Designing a mathematical model of railway passenger demand using time series-case study: Khorasan mainline,” in Rail Transportaion Conference, 2006.#
[22] S. L. Ho and M. Xie, “The use of ARIMA models for reliability forecasting and analysis,” Comput. Ind. Eng., vol. 35, no. 1, pp. 213–216, 1998.#
[23] C. Y. Lam, W. H. Ip, and C. W. Lau, “A business process activity model and performance measurement using a time series ARIMA intervention analysis,” Expert Syst. Appl., vol. 36, no. 3, pp. 6986–6994, 2009.#
[24] M. Z. Babai, M. M. Ali, J. E. Boylan, and A. A. Syntetos, “Forecasting and inventory performance in a two-stage supply chain with ARIMA (0, 1, 1) demand: Theory and empirical analysis,” Int. J. Prod. Econ., vol. 143, no. 2, pp. 463–471, 2013.#
[25] K. C. Gilbert and V. Chatpattananan, “An ARIMA supply chain model with a generalized ordering policy,” J. Model. Manag., vol. 1, no. 1, pp. 33–51, 2006.#
[26] M. Blanchard and G. Desrochers, “Generation of autocorrelated wind speeds for wind energy conversion system studies,” Sol. Energy, vol. 33, no. 6, pp. 571–579, 1984.#
[27] B. G. Brown, R. W. Katz, and A. H. Murphy, “Time series models to simulate and forecast wind speed and wind power,” J. Clim. Appl. Meteorol., vol. 23, no. 8, pp. 1184–1195, 1984.#
[28] G. Box and G. Jenkins, Time series analysis: forecasting and control. 1976.#
[29] Central Bank of Iran (CBI), Annual data of Consumer Price Index in Iran from 1359 to 1391: http://www.cbi.ir/datedlist/10807.aspx.#
