Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models

Ezra Precious Ndidiamaka; Okonta Charles Arinze; Okoro Udu Ukpai

doi:doi:10.11648/j.pamj.20211004.12

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Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models

Ezra Precious Ndidiamaka, Okonta Charles Arinze, Okoro Udu Ukpai

Published in Pure and Applied Mathematics Journal (Volume 10, Issue 4)

Received: 27 July 2021 Accepted: 9 August 2021 Published: 19 August 2021

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Abstract

Tourism has become very important in international commerce and also represents one of the main sources of income for some developing countries in the world. It is the act of people travelling and staying in a place outside their usual environment for leisure, business or other purposes, and this may include sightseeing, camping, retreats, etc Tourism is one of the key economic growth contributors and has contributed towards complete growth and development of Australia by bringing numerous economic value and benefits to her, and also building her brand value, image and identity. This paper seeks to generate a periodic autoregressive PAR model that could be used to make reliable forecast for tourism in Australia. Periodic autoregressive models are for seasonally observed data, particularly quarterly and monthly. Its’ parameters take different values across the seasons. The data used in this work was extracted from the official website of the Australian Bureau of Statistics (ABS), (www.abs.gov.au). It consists of monthly historical data of the number of short term visitors in Australia from January 1998 to December 2017 and was analysed using R- statistical software. The result revealed the order of the PAR model, and also verified that there is periodic variation (periodicity) in the tourism data. It was also verified that there is existence of single unit root and periodic integration which led to the fitting of periodic integrated autoregressive (PIAR(2)) model as the suitable model for the Australian tourism data. Finally, the residual generated from the model was subjected to statistical test and it showed a white noise behavior. Based on these findings, it is concluded that periodic autoregressive time series model can be used to generate reliable forecast for Australian tourism data. Further research on the stochastic nature and seasonality of Australian tourism data was recommended.

Published in	Pure and Applied Mathematics Journal (Volume 10, Issue 4)
DOI	10.11648/j.pamj.20211004.12
Page(s)	96-103
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Periodicity, Periodic Autoregression, Residual, Tourism, Likelihood Ratio

References

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[4]	Boswijk, H. P., Frances, P. H., & Haldrup, N. (1997). Multiple Unit roots in Periodic Autoregression. Journal of Econometrics, 80, 167-193.
[5]	Box, G. E. P. & Jenkins, G. M. (1970). Time Series Analysis: forecasting and Control. Holden-Day, San Francisco.
[6]	Eugen, U. & Pereau, J. C. (2016). Application of periodic autoregressive process to the modeling of the Garonne river flows. Published in Stochastic Environmental Research and Risk Assessment, Springer Verlag (Germany), inPress, 30 (7), pp. 1785-1795. Doi: 10.1007/s00477-015-1193-3.
[7]	Eugen, U. & Pereau, J. C. (2017). Estimation and identification of periodic autoregressive models with one exogenous variable. Journal of Statistical Society. 46, 629-640.
[8]	Frances, P. H. & Paap, R. (1996). Periodic Integration: Further results on Model Selection and Forecasting. Statistical paper, 37, 33-52.
[9]	Franses, P. (1996), Periodicity and Stochastic Trends in Economic Time Series, Advanced Texts in Econometrics. Oxford University Press.
[10]	Franses, P. H. & Paap, R. (2004), Periodic Time Series Models, Advanced Texts in Econometrics. Oxford University Press.
[11]	Harvey, A. C. (1989). Forecasting Structural time series and Kalman Filter. Cambridge University Press, Cambridge.
[12]	Herwartz, H. (1997). Performance of Periodic Error Correction models in Forecasting Consumption Data. International Journal of Forecasting. 13, 421-431.
[13]	Hipel, K. W. and McLeod, A. I. (1994). Time Series Modelling of Water Resources and Environmental Systems. Vol. 45, pp iii-xxxvii, 1-1013 (1994), Elsevier Science Publishers.
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[17]	Lopez-de Lacalle, J. (2005), `Periodic autoregressive time series models in R: The partsm package', BILCODEC 2005 working paper, Universidad del Pas Vasco UPV/EHU - Departamento de Economa Aplicada III (Econometray Estadstica). URL: http://econpapers.repec.org/software/ehubilcod/200501. htm.
[18]	Novales, A. & Flores de Fruto, R. (1997). Forecasting with Periodic Models: A comparison with time Invariant Coefficient Models. International Journal of Forecasting. 13, 393-405.
[19]	Osborn, D. R. (1988). Seasonality and Habit Persistence in a Life Cycle Model of consumption. Journal of Applied Econometrics, 3, 255-266.
[20]	Osborn, D. R. & Smith, J. P. (1989). The Performance of Periodic Autoregressive Models in Forecasting Seasonal U. K. Consumption. Journal of Business & Economic Statistics, 7, 117-127.
[21]	R Development Core Team (2011), R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. URL: http://www.R-project.org.
[22]	Thomas, T. and William, B. (2006). Models for seasonal heteroskedastic time series estimation, testing and simulation evidence, Manuscript.
[23]	Tourism definition according to https://www.go2hr.ca
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APA Style

Ezra Precious Ndidiamaka, Okonta Charles Arinze, Okoro Udu Ukpai. (2021). Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models. Pure and Applied Mathematics Journal, 10(4), 96-103. https://doi.org/10.11648/j.pamj.20211004.12

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ACS Style

Ezra Precious Ndidiamaka; Okonta Charles Arinze; Okoro Udu Ukpai. Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models. Pure Appl. Math. J. 2021, 10(4), 96-103. doi: 10.11648/j.pamj.20211004.12

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AMA Style

Ezra Precious Ndidiamaka, Okonta Charles Arinze, Okoro Udu Ukpai. Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models. Pure Appl Math J. 2021;10(4):96-103. doi: 10.11648/j.pamj.20211004.12

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@article{10.11648/j.pamj.20211004.12,
  author = {Ezra Precious Ndidiamaka and Okonta Charles Arinze and Okoro Udu Ukpai},
  title = {Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {4},
  pages = {96-103},
  doi = {10.11648/j.pamj.20211004.12},
  url = {https://doi.org/10.11648/j.pamj.20211004.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211004.12},
  abstract = {Tourism has become very important in international commerce and also represents one of the main sources of income for some developing countries in the world. It is the act of people travelling and staying in a place outside their usual environment for leisure, business or other purposes, and this may include sightseeing, camping, retreats, etc Tourism is one of the key economic growth contributors and has contributed towards complete growth and development of Australia by bringing numerous economic value and benefits to her, and also building her brand value, image and identity. This paper seeks to generate a periodic autoregressive PAR model that could be used to make reliable forecast for tourism in Australia. Periodic autoregressive models are for seasonally observed data, particularly quarterly and monthly. Its’ parameters take different values across the seasons. The data used in this work was extracted from the official website of the Australian Bureau of Statistics (ABS), (www.abs.gov.au). It consists of monthly historical data of the number of short term visitors in Australia from January 1998 to December 2017 and was analysed using R- statistical software. The result revealed the order of the PAR model, and also verified that there is periodic variation (periodicity) in the tourism data. It was also verified that there is existence of single unit root and periodic integration which led to the fitting of periodic integrated autoregressive (PIAR(2)) model as the suitable model for the Australian tourism data. Finally, the residual generated from the model was subjected to statistical test and it showed a white noise behavior. Based on these findings, it is concluded that periodic autoregressive time series model can be used to generate reliable forecast for Australian tourism data. Further research on the stochastic nature and seasonality of Australian tourism data was recommended.},
 year = {2021}
}

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TY  - JOUR
T1  - Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models
AU  - Ezra Precious Ndidiamaka
AU  - Okonta Charles Arinze
AU  - Okoro Udu Ukpai
Y1  - 2021/08/19
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211004.12
DO  - 10.11648/j.pamj.20211004.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 96
EP  - 103
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211004.12
AB  - Tourism has become very important in international commerce and also represents one of the main sources of income for some developing countries in the world. It is the act of people travelling and staying in a place outside their usual environment for leisure, business or other purposes, and this may include sightseeing, camping, retreats, etc Tourism is one of the key economic growth contributors and has contributed towards complete growth and development of Australia by bringing numerous economic value and benefits to her, and also building her brand value, image and identity. This paper seeks to generate a periodic autoregressive PAR model that could be used to make reliable forecast for tourism in Australia. Periodic autoregressive models are for seasonally observed data, particularly quarterly and monthly. Its’ parameters take different values across the seasons. The data used in this work was extracted from the official website of the Australian Bureau of Statistics (ABS), (www.abs.gov.au). It consists of monthly historical data of the number of short term visitors in Australia from January 1998 to December 2017 and was analysed using R- statistical software. The result revealed the order of the PAR model, and also verified that there is periodic variation (periodicity) in the tourism data. It was also verified that there is existence of single unit root and periodic integration which led to the fitting of periodic integrated autoregressive (PIAR(2)) model as the suitable model for the Australian tourism data. Finally, the residual generated from the model was subjected to statistical test and it showed a white noise behavior. Based on these findings, it is concluded that periodic autoregressive time series model can be used to generate reliable forecast for Australian tourism data. Further research on the stochastic nature and seasonality of Australian tourism data was recommended.
VL  - 10
IS  - 4
ER  -

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Author Information

Ezra Precious Ndidiamaka

Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Nigeria
Okonta Charles Arinze

Department of Maths/Statistics, School of Science, Akanu Ibiam Federal Polytechnic, Unwana, Nigeria
Okoro Udu Ukpai

Department of Maths/Statistics, School of Science, Akanu Ibiam Federal Polytechnic, Unwana, Nigeria

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APA Style

Ezra Precious Ndidiamaka, Okonta Charles Arinze, Okoro Udu Ukpai. (2021). Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models. Pure and Applied Mathematics Journal, 10(4), 96-103. https://doi.org/10.11648/j.pamj.20211004.12

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ACS Style

Ezra Precious Ndidiamaka; Okonta Charles Arinze; Okoro Udu Ukpai. Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models. Pure Appl. Math. J. 2021, 10(4), 96-103. doi: 10.11648/j.pamj.20211004.12

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AMA Style

Ezra Precious Ndidiamaka, Okonta Charles Arinze, Okoro Udu Ukpai. Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models. Pure Appl Math J. 2021;10(4):96-103. doi: 10.11648/j.pamj.20211004.12

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@article{10.11648/j.pamj.20211004.12,
  author = {Ezra Precious Ndidiamaka and Okonta Charles Arinze and Okoro Udu Ukpai},
  title = {Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {4},
  pages = {96-103},
  doi = {10.11648/j.pamj.20211004.12},
  url = {https://doi.org/10.11648/j.pamj.20211004.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211004.12},
  abstract = {Tourism has become very important in international commerce and also represents one of the main sources of income for some developing countries in the world. It is the act of people travelling and staying in a place outside their usual environment for leisure, business or other purposes, and this may include sightseeing, camping, retreats, etc Tourism is one of the key economic growth contributors and has contributed towards complete growth and development of Australia by bringing numerous economic value and benefits to her, and also building her brand value, image and identity. This paper seeks to generate a periodic autoregressive PAR model that could be used to make reliable forecast for tourism in Australia. Periodic autoregressive models are for seasonally observed data, particularly quarterly and monthly. Its’ parameters take different values across the seasons. The data used in this work was extracted from the official website of the Australian Bureau of Statistics (ABS), (www.abs.gov.au). It consists of monthly historical data of the number of short term visitors in Australia from January 1998 to December 2017 and was analysed using R- statistical software. The result revealed the order of the PAR model, and also verified that there is periodic variation (periodicity) in the tourism data. It was also verified that there is existence of single unit root and periodic integration which led to the fitting of periodic integrated autoregressive (PIAR(2)) model as the suitable model for the Australian tourism data. Finally, the residual generated from the model was subjected to statistical test and it showed a white noise behavior. Based on these findings, it is concluded that periodic autoregressive time series model can be used to generate reliable forecast for Australian tourism data. Further research on the stochastic nature and seasonality of Australian tourism data was recommended.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Modelling Tourism in Australia Based on Periodic Autoregressive Time Series Models
AU  - Ezra Precious Ndidiamaka
AU  - Okonta Charles Arinze
AU  - Okoro Udu Ukpai
Y1  - 2021/08/19
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211004.12
DO  - 10.11648/j.pamj.20211004.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 96
EP  - 103
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211004.12
AB  - Tourism has become very important in international commerce and also represents one of the main sources of income for some developing countries in the world. It is the act of people travelling and staying in a place outside their usual environment for leisure, business or other purposes, and this may include sightseeing, camping, retreats, etc Tourism is one of the key economic growth contributors and has contributed towards complete growth and development of Australia by bringing numerous economic value and benefits to her, and also building her brand value, image and identity. This paper seeks to generate a periodic autoregressive PAR model that could be used to make reliable forecast for tourism in Australia. Periodic autoregressive models are for seasonally observed data, particularly quarterly and monthly. Its’ parameters take different values across the seasons. The data used in this work was extracted from the official website of the Australian Bureau of Statistics (ABS), (www.abs.gov.au). It consists of monthly historical data of the number of short term visitors in Australia from January 1998 to December 2017 and was analysed using R- statistical software. The result revealed the order of the PAR model, and also verified that there is periodic variation (periodicity) in the tourism data. It was also verified that there is existence of single unit root and periodic integration which led to the fitting of periodic integrated autoregressive (PIAR(2)) model as the suitable model for the Australian tourism data. Finally, the residual generated from the model was subjected to statistical test and it showed a white noise behavior. Based on these findings, it is concluded that periodic autoregressive time series model can be used to generate reliable forecast for Australian tourism data. Further research on the stochastic nature and seasonality of Australian tourism data was recommended.
VL  - 10
IS  - 4
ER  -

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