Multi-Input Intervention Analysis for Evaluating of the Domestic Airline Passengers in an International Airport
Science Journal of Applied Mathematics and Statistics
Volume 5, Issue 3, June 2017, Pages: 110-126
Received: Apr. 5, 2017; Accepted: Apr. 18, 2017; Published: Jun. 3, 2017
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Salam Ali Wiradinata, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Rado Yendra, Department of Mathematics, State Islamic University of Sultan Syarif Kasim, Pekanbaru, Indonesia
Suhartono, Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia
Moh Danil Hendry Gamal, Department of Mathematics, University of Riau, Pekanbaru, Indonesia
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This article discusses multi-input intervention analysis to investigate the effect of interventions which may come from internal and/or external factors in time series data. The objective of this research is to obtain multi-input intervention analysis, which can explain the magnitude and periodic of each event effected to monthly types of the domestic airline passenger flight in Pekanbaru airport. The purpose of this study is to give a theoretical and empirical studies on the multi-input intervention analysis, particularly to develop and construct a model procedure of multi-input intervention cused by pulse and/or step function to evaluate the impact of these external and/or internal events in time series data. Monthly data comprising the number of the domestic airline passenger flight in Pekanbaru airport are used as the data for this case study. Generally, the forest fires, peatland, and illegal burning in Riau Province give a negative permanent impacts after four months. This study focuses on the derivation of some effect shapes, i.e. the temporary, gradually or permanent monthly airline passenger. In addition, the research also discusses how to assess the effect of an intervention in transformation data.
Time Series Data, Multi-input Intervention Analysis, Pulse Function, Step Function
To cite this article
Salam Ali Wiradinata, Rado Yendra, Suhartono, Moh Danil Hendry Gamal, Multi-Input Intervention Analysis for Evaluating of the Domestic Airline Passengers in an International Airport, Science Journal of Applied Mathematics and Statistics. Vol. 5, No. 3, 2017, pp. 110-126. doi: 10.11648/j.sjams.20170503.13
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
B. Abraham, Intervention analysis and multiple time series, Biometrika, 1 (1980), 73 - 78.
M. S. Atkins, A Case study on the use of intervention analysis applied to traffic accidents, Journal of the Operational Research Society, 7 (1979), 651 - 659.
P. J. Brockwell and R. A. Davis, Introduction to Time Series and Forecasting, Spinger-Verlag, New York, 1996.
B. L. Bowerman, R. T. O’Connell and A. Koehler, Forecasting, Time Series and Regression: An Applied Approach, 4th Edition, Duxbury Press, Belmont, California, 2004.
G. E. P. Box, G. M. Jenkins and G. C. Reinsel, Time Series Analysis Forecasting and Control, 5th Edition, John Wiley & Sons, Inc., Hoboken, New Jersey, 2016.
G. E. P. Box and G. C. Tiao, Intervention analysis with applications to economic and environmental problems, Journal of the American Statistical Association, 70 (1975), 70 - 79.
L. Bianchi, W. Gautschi, J. Jarrett and R. C. Hanumara, Improving forecasting for telemarketing centers by ARIMA modeling with intervention, International Journal of Forecasting, 14 (1998), 497 - 504.
M. N. Bhattacharyya and A. P. Layton, Effectiveness of seat belt legislation on the Queensland road toll – an Australian case study in intervention analysis, Journal of the American Statistical Association, 74 (1979), 596 - 603.
N. B. Chang and Y. T. Lin, An analysis of recycling impacts on solid waste generation by time series intervention modeling, Resources, Conservation and Recycling, 19 (1997), 165 - 186.
C. Chatfield, Time Series Forecasting, Chapman Hall, London, 2001.
J. D. Cryer and Kung-Sik Chan, Time Series Analysis with Applications in R, 2nd edition, Springer, New York, 2008.
K. Drakos and A. Kutan, Regional effects of terrorism on tourism in three Mediterranean countries. Journal of Conflict Resolution, 47 (2003), 621 - 641.
W. Enders, Applied Econometric Time Series, John Wiley & Sons, Inc., New York, 1995.
W. Enders, T. Sandler, and J. Cauley, Assessing the impact of terrorist thwarting policies: An intervention time series approach. Defense and Peace Economics, 2 (1990), 1 - 18.
A. Harvey and J. Durbin, The effects of seat belt legislation on British road casualties, Journal of the Royal Statistical Society, Series A, 4 (1986), 187 - 227.
J. D. Hamilton, Time Series Analysis, New Jersey: Princeton University Press, New York, 1994.
M. E. Hilton, The impact of recent changes in California drinking-driving laws on fatal accident levels during the first post intervention Year: An Interrupted time series analysis, Law & Society Review, 18 (1984), 605 - 627.
U. Helfenstein, The use of transfer function models, intervention analysis and related time series methods in epidemiology, International Journal of Epidemiology, 3 (1991), 808 - 815.
Z. Ismail, Suhartono, A. Yahaya and R. Efendi, Intervention model for analyzing the impact of terrorism to the tourism industry, Journal of Mathematics and Statistics, 5 (2009), 322 - 329.
[20] H. Jorquera, W. Palma, and J. Tapia, An intervention analysis of air quality data at Santiago, Chile. Atmospheric Environment, 34 (2000), 4073 - 4084.
Rising Fuel Price, Ministry of Finance of Republic of Indonesia,, accessed in May 10th, 2016 at 22.35 PM.
H. Luthkepohl, New Introduction Multiple Time Series Analysis, 2nd Edition, Springer, New York, 2005.
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 Systems with Applications, 36 (2009), 6986 - 6994.
J. Ledolter and K. S. Chan, Evaluating the impact of the 65-mph maximum speed limit on Iowa interstates. The American Statistician, 50 (1996), 79 - 85.
M. H. Lee, Suhartono and B. Sanugi, Multi-input intervention model for evaluating the impact of the Asian crisis and the terrorist attacks on tourist arrivals, Matematika, 26 (2010), 83 - 106.
D. C. Montgomery, C. L. Jennings and M. Kulahci, Introduction to Time Series Analysis and Forecasting, John Wiley & Sons, Inc., New Jersey, 2008.
J. P. Murry, A. Stam and J. L. Lastovicka, Evaluating an anti-drinking and driving advertising campaign with a sample survey and time series intervention analysis, Journal of the American Statistical Association, 2 (1993), 50-56.
A. J. McSweeny, The effects of response cost on the behavior of a million persons: Charging for directory assistance in Cincinnati, Journal of Applied Behavioral Analysis, 2 (1978), 47 - 51.
D. C. Montgomery and G. Weatherby, Modeling and Forecasting Time Series Using Transfer Function and Intervention Methods, AIIE Transactions, 12 (1980), 289 - 307.
S. Makridakis and M. Hibon, The M3-Competition: Result, Conclusions and Implications, International Journal of Forecasting, 16 (2000), 451 - 476.
P. W. Novianti and Suhartono, Modeling of Indonesia consumer price index using multi-input intervention model, Bulletin of Monetary Economics and Banking, 12 (2009), 75 - 96.
Polusi Asap 2015 (Smoke Pollution),, accessed in April 18th, 2016 at 21.30 PM.
Pemilu 2014 (General Election),, accessed in April 18th, 2016 at 22.35 PM.
S. Rezeki, Suhartono and Suyadi, Multi-input intervention model for analyzing the impact of the Asian crisis and the terrorist attacks on tourist arrivals in Bali, Applied Mathematical Sciences, 7 (2013), 6715 - 6727.
R. S. Tsay, Analysis of Financial Time Series, 2nd Edition, John Wiley & Sons, Inc., New Jersey, 2005.
Tim Pusdatinmas BNPB, Disaster of Information Actual Monthly Edition June 2013, National Disater Relief Agency, p. 4, http://, accessed in April 18th, 2016, at hour 21.57.
A. Valadkhani and A. P. Layton, Quantifying the effect of the GST on inflation in Australia's capital cities: An intervention analysis, Australian Economic Review, 2 (2004), 125 - 138.
H. S. Van der Knoop and F. C. Hooijmans, A multivariate intervention model for the Dutch mint circulation: estimation and Monte Carlo simulation, Journal of Asian Economics, 2 (1989), 179-189.
W. W. S. Wei, Time Series Analysis: Univariate and Multivariate Methods, 2nd Edition, Addison-Wesley Publishing Company, Inc., New York, 2006.
R. E. Wimanda, Price variability and price convergence: evidence from Indonesia, Journal of Asian Economics, 20 (2009), 427 - 442.
R. A. Yaffee and M. McGee, Introduction to time series analysis and forecasting with applications of SAS and SPSS, Academic Press, Inc., San Diego, 2000.
F. Zhang, A. K. Wagner, S. B. Soumerai and D. R. Degnan, Methods for estimating confidence intervals in interrupted time series analysis of health interventions, Journal of Clinical Epidemiology, 62 (2009), 143 - 148.
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