Hierarchical Forecasting of the Zimbabwe International Tourist Arrivals
AbstractThe objectives of the paper is to: (1) adopt the hierarchical forecasting methods in modelling and forecasting international tourist arrivals in Zimbabwe; and (2) coming up with Zimbabwe international tourist arrivals Prediction Intervals (PIs) in Quantile Regression Averaging (QRA) to hierarchical tourism forecasts. Zimbabwe’s monthly international tourist arrivals data from January 2002 to December 2018 was used. The dataset used was before the COVID-19 period and were disaggregated according to the purpose of the visit (POV). Three hierarchical forecasting approaches, namely top-down, bottom-up and optimal combination approaches were applied to the data. The results showed the superiority of the bottom-up approach over both the top-down and optimal combination approaches. Forecasts indicate a general increase in aggregate series. The combined methods provide a new insight into modelling tourist arrivals. The approach is useful to the government, tourism stakeholders, and investors among others, for decision-making, resource mobilisation and allocation. The Zimbabwe Tourism Authority (ZTA) could adopt the forecasting techniques to produce informative and precise tourism forecasts. The data set used is before the COVID-19 pandemic and the models indicate what could happen outside the pandemic. During the pandemic the country was under lockdown with no tourist arrivals to report on. The models are useful for planning purposes beyond the COVID-19 pandemic.
World Bank,Ethiopia - Towards a strategy for pro-poor tourism development (English),
Washington, DC: World Bank, viewed 2 April 2019, 2006. http://documents.worldbank.org/curated/en/463631468256450819/Ethiopia-Towards-a-strategy-for-pro-poor-tourism-development.
G. Athanasopoulos, R.A. Ahmed, and R.J. Hyndman, Hierarchical forecasts for Australian domestic tourism, International Journal of Forecasting, vol. 25, no. 2, pp. 146–166, 2009. https://doi.org/10.1016/j.tourman.2007.04.009.
R.J. Hyndman, R.A. Ahmed, G. Athanasopoulos, and H.L. Shang, Optimal Combination Forecasts for Hierarchical Time Series, Computational Statistics and Data Analysis, vol. 55, no. 9, pp. 2579–2589, 2011. https://doi.org/10.1016/j.csda.2011.03.006.
H. Song, and S.F. Witt, Forecasting international tourist flows to Macau, Tourism management, vol. 27, no. 2, pp. 214–224, 2006.
S.B. Taieb, J.W. Taylor, and R.J. Hyndman, Hierarchical probabilistic forecasting of electricity demand with smart meter data, viewed 10 March 2019, 2017. http://www.souhaib-bentaieb.com/pdf/jasa probhts.pdf.
H. Booth, Demographic forecasting: 1980 to 2005 in review, International Journal of Forecasting, vol. 22, no. 3, pp. 547–581, 2006. https://doi.org/10.1016/j.ijforecast.2006.04.001.
J. Ndlovu, and E. Heath, Re-branding of Zimbabwe to enhance sustainable tourism development: Panacea or Villain, African Journal of Business Management, vol. 1, no. 12, pp. 947–955, 2013.
C. Chatfield, Time series Forecasting, Chapman & Hall/CRC, Boca Raton, Florida, 2000.
H.L. Shang, Mortality and life expectancy forecasting for a group of populations in developed countries: a multilevel functional data method, The Annals of Applied Statistics, vol. 10, no. 3, pp. 1639–1672, 2016. https://doi.org/10.1214/16-aoas953.
A. Khosravi, E. Mazloumi, S. Nahavandi, D. Creighton, and J.W.C. Van Lint, Prediction intervals to account for uncertainties in travel time prediction, IEEE Transactions on Intelligent Transportation Systems, vol. 12, no. 2, pp. 537–547, 2011. https://doi.org/10.1109/TITS.2011.2106209.
H. Constantino, J.P. Teixeira, and P.O. Fernandes, Tourism demand modelling and forecasting with artificial neural network models: The Mozambique case study, IV Congresso Internacional de Turismo da ESG/IPCA , Tourism for the 21stCentury, 3rdand 4thof December 2015.
M.A.M.A. Ibrahim, The determinants of international tourism demand for Egypt: Panel Data Evidence, European Journal of Economics, Finance and Administrative Sciences, vol. 3, pp. 50-58, 2011.
A. Muhammad, and D. Andrews, Determining tourist arrivals in Uganda: The impact of distance, trade and origin-specific factors, African Journal of Accounting, Economics, Finance and Banking Research, vol. 2, no. 2, pp. 51–62, 2008.
P.K. Chabari, Determinants of inbound tourism to Kenya,
newblock 2013. https://pdfs. semanticscholar.org/dd62/a31a707409934801d307b9dc50ff50b09a4d.pdf.
S. Hathroubi, Modelling and forecasting international tourism demand for Tunisia: A time varying parameter approach,
Interdisciplinary journal of contemporary research in business, vol. 3, no. 7, pp. 261–279, 2011.
H. Choyakh, A model of tourism demand for Tunisia: inclusion of the tourism investment variable, Tourism Economics, vol. 14, no. 4, pp. 819–838, 2008.
A.O. Akuno, M.O. Otieno, C.M. Mwangi, and L.A. Bichanga, Statistical models for forecasting tourists arrival in Kenya, Open Journal of Statistics, vol. 5, pp. 6065, 2015. http://dx.doi.org/10.4236/ojs.2015.51008.
A. Zakhary, N. El Gayar,and A.F. Atiya, A comparative study of the pickup method and its variations using a simulated hotel reservation data, ICGST International Journal on Artificial Intelligence and Machine Learning, vol. 8, pp. 15–21, 2009.
H. Song, and G. Li, Tourism demand modelling and forecasting. A review of recent research, Tourism Management, vol. 29, no. 2, pp. 203-220, 2008. https://doi.org/10.1016/j.tourman.2007.07.016.
D.C. Frechtling, Practical Tourism Forecasting, Oxford, UK: Butterworth-Heinemann, 1996.
S.F. Witt, and C.A. Witt, Forecasting tourism demand: a review of empirical research, International Journal of Forecasting, vol. 11, no. 3, pp. 447–475, 1992.
C. Petropoulos, K. Nikolopoulos, A. Patelis, and V. Assimakopoulos, A technical analysis approach to tourism demand forecasting, Applied Economics Letters, vol. 12, no. 6, pp. 327–333, 2005. doi:10.1080/13504850500065745.
C.N. Mutanga, E. Gandiwa, and N. Muboko, An analysis of tourist trends in northern Gonarezhou National Park, Zimbabwe, 1991- 2014, Cogent Social Sciences, vol. 3, no. 1, 1392921, 2017.
F. Kabote, B. Mashiri, and S. Vengesayi, Pricing and domestic tourism performance in Zimbabwe, African Journal of Hospitality, Tourism and Leisure, vol. 3, no. 2, pp. 1-12, 2014.
C. Mutsena, and F. Kabote, Zimbabwe policy environment and domestic tourism performance, International Journal of Safety and Security in Tourism and Hospitality, vol. 1, no. 13, pp. 1-14.
F. Choga, Comprehending determinants of demand: Zimbabwe tourism destination scenario, International Economics and Business, vol. 1, no. 1, pp. 17–23, 2015.
E. Muchapondwa, and O. Pimhidzai, Modelling International Tourism Demand for Zimbabwe, International Journal of Business and Social Science, vol. 2, no. 2, pp. 71–81, 2011.
T. Makoni, and D. Chikobvu, Hierarchical forecasting of tourist arrivals at the Victoria Rainforest, Zimbabwe, African Journal of Hospitality, Tourism and Leisure, vol. 7, no. 4, pp. 1–15, 2018.
T. Makoni, and D. Chikobvu, Modelling and Forecasting Zimbabwes Tourist Arrivals Using Time Series Method: A Case Study of Victoria Falls Rainforest, Southern African Business Review, vol. 22, pp. 1–22, 2018. https://doi.org/10.25159/1998-8125/3791.
L. Pascual, J. Romo, and E. Ruiz, Bootstrap prediction for returns and volatilities in GARCH models, Computational Statistics & Data Analysis, vol. 50, no. 9, pp. 2293–2312, 2006.
C. Choden, and S. Unhapipat, ARIMA model to forecast international tourist visit in Bumthang, Bhutan, Journal of Physics: Conference Series, vol. 1039, 8thInternational Conference on Applied Physics and Mathematics (ICAPM 2018) 27–29 January 2018, Phuket, Thailand. doi :10.1088/1742-6596/1039/1/012023.
B. Petrevska, Predicting tourism demand by A.R.I.M.A. models, Economic Research-Ekonomska Istraivanja, vol. 30, no. 1, pp. 939–950, 2017. doi:10.1080/1331677x.2017.1314822.
H.R.I. Peiris, A Seasonal ARIMA Model of Tourism Forecasting: The Case of Sri Lanka, Journal of Tourism, Hospitality and Sports, vol. 22, pp. 98–109, 2016.
Y.-W. Chang, and M.-Y. Liao, A Seasonal ARIMA Model of Tourism Forecasting: The Case of Taiwan, Asia Pacific Journal of Tourism Research, vol. 15, no. 2, pp. 215–221, 2010. doi:10.1080/10941661003630001.
A. Saayman, and M. Saayman, Forecasting tourist arrivals in South Africa, Acta Commercii, vol. 10, no. 1, pp. 281–293, 2010. https://doi.org/10.4102/ac.v10i1.141.
F.S. Witt, H. Song, and P. Louvieris, Statistical testing in forecasting model selection, Journal of Travel Research, vol. 42, no. 2, pp. 51–158, 2003.
V. Cho, A comparison of three different approaches to tourist arrival forecasting, Tourism Management, vol. 24, no. 3, pp. 323-330, 2003.
S.L. Wickramasuriya, G. Athanasopoulos, and R.J. Hyndman, Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization, Journal of the American Statistical Association, vol. 71, no. 353, pp. 68–71, 2018.
L. Morgan, Forecasting in Hierarchical Models, viewed 02 January 2019,2015. https://www.lancaster.ac.uk/ mor-
H. Widiarta, S. Viswanathan, and R. Piplani, Forecasting aggregate demand: an analytical evaluation of top-down versus bottom-up forecasting in a production planning framework, International Journal of Production Economics, vol. 118, no. 1, pp. 87–94, 2009. https://doi.org/10.1016/j.ijpe.2008.08.013.
G. Fliedner,An investigation of aggregate variable time series forecast strategies with specific subaggregate time series statistical correlation, Computers and Operations Research, vol. 26, no. 10-11, pp. 1133–1149, 1992. https://doi.org/10.1016/s0305- 0548(99)00017-9.
D.W. McLeavey, L. Seetharama, and S.L. Narasimhan, Production planning and inventory control, The Journal of the Operational Research Society, vol. 36, no. 6, pp. 536–545, 1995. https://doi.org/10.2307/2582831.
P. Wanke, and E. Saliby, Top-down or bottom-up forecasting?, Pesquisa Operacional, vol. 27, no. 3, pp. 591–605, 2007. https://doi.org/10.1590/s0101-74382007000300010.
B.J. Dangerfield, and J.S. Morris, Top-down or bottom-up: Aggregate versus disaggregate extrapolations, International Journal of Forecasting, vol. 8, no. 2, pp. 233–241, 1992. https://doi.org/10.1016/0169-2070(92)90121-o.
W.R. Kinney Jr., Predicting earnings: entity versus subentity data, Journal of Accounting Research, vol. 9, no. 1, pp. 127–136, 1971.
J. Nowotarski, and R. Weron, Computing electricity spot price prediction intervals using quantile regression and forecast averaging, Computational Statistics, vol. 30, pp. 791–803, 2015. https://doi.org/10.1007/s00180-014-0523-0.
E. Torsen, and L.I. Seknewna, Bootstrapping nonparametric prediction intervals for conditional value-at-risk with
heteroscedasticity, Journal of Probability and Statistics, vol. 2019, pp.1–6, 2019. https://doi.org/10.1155/2019/7691841.
G. Athanasopoulos, J.H. Rob, H. Song, and D. Wu, The tourism forecasting competition, International Journal of Forecasting, vol.27, no. 3, pp. 822–845, 2011. https://doi.org/10.1016/j.ijforecast.2010.04.009.
Z. Li, H. Yu, Y. Liu, and F. Liu, An improved adaptive exponential smoothing model for short-term travel time forecasting of urban arterial street, Acta automatica sinica, vol. 34, no. 11, pp. 1404–1409, 2008. https://doi.org/10.1016/s1874-1029(08)60062-2.
J.H. Kim, K. Wong, G. Athanasopoulos, and S. Liu, Beyond point forecasting: Evaluation of alternative prediction intervals for tourist arrivals, International Journal of Forecasting, vol. 27, no. 3, pp. 887–901, 2011. doi:10.1016/j.ijforecast.2010.02.014.
R.L. Winkler, A Decision-Theoretic Approach to Interval Estimation, Journal of the American Statistical Association, vol. 67, pp. 187–191, 1972.
R.J. Hyndman, A.J. Lee, and E. Wang, Fast computation of reconciled forecasts for hierarchical and grouped time series, Computational Statistics and Data Analysis, vol. 97, pp. 16–32, 2016. https://doi.org/10.1016/j.csda.2015.11.007.
R.J. Hyndman, and G. Athanasopoulos, Forecasting: principles and practice,
viewed 12 January 2019, 2014. https://robjhyndman.com/uwa les/fpp-notes.pdf.
R.J. Hyndman, and Y. Khandakar, Automatic Time Series Forecasting: The Forecast Package for R, Journal of Statistical Software, vol. 27, no. , pp. 1–22, 2007. https://doi.org/10.18637/jss.v027.i03.
G. Athanasopoulos, R.J. Hyndman, N. Kourentzes, and F. Petropoulos, Forecasting with temporal hierarchies, European Journal of Operational Research, vol. 262, no. 1, pp. 60–74, 2017. https://doi.org/10.1016/j.ejor.2017.02.046.
E. Ostertagova, and O. Ostertag, Forecasting using simple exponential smoothing method, Acta Electrotechnica et Informatica, vol. 12, no. 3, pp.62, 2012. https://doi.org/10.2478/v10198-012-0034-2.
S. Wang, Exponential smoothing for forecasting and Bayesian validation of computer models, viewed 5 May 2019, 2006. https://smartech.gatech.edu/handle/1853/19753.
M. Ruiter, Using Exponential Smoothing Methods for Modelling and Forecasting Short-Term Electricity Demand (Bachelor Thesis,ErasmusUniversityRotterdam,Rotterdam,Netherlands), viewed20March2019,2017.https://thesis.eur.nl/pub/38564/Ruiter-de.pdf.
S. Gelper, R. Fried, and C. Croux, Robust forecasting with exponential and Holt-Winters smoothing, Journal of forecasting, vol. 29, no. 3, pp. 285–300, 2010. https://doi.org/10.2139/ssrn.1089403.
B. Liu, J. Nowotarski, T. Hong, and R. Weron, Probabilistic load forecasting via Quantile Regression Averaging on sister forecasts, IEEE Transactions on Smart Grid, vol. 8, no. 2, pp. 730–737, 2017. https://doi.org/10.1109/tsg.2015.2437877.
S. Makridakis, R.M. Hogarth, and A. Gaba, Forecasting and uncertainty in the economic and business world, International Journal of Forecasting, vol. 25, no. 4, pp. 794–812, 2009. https://doi.org/10.1016/j.ijforecast.2009.05.012.
W.G.S. Konarasinghe, and N.R. Abeynayake, Modelling stock returns of individual companies of Colombo Stock Exchange, Conference Proceedings of the 1stInternational Forum for Mathematical Modelling, pp. 111–115, 2014.
G. Wahba, The approximate solution of linear operator equations when the data are noisy, SIAM Journal on Numerical Analysis, vol. 14, no. 4, pp. 651-667, 1977.
A. Zellner, J. Tobias, A note on aggregation, disaggregation and forecasting performance, Journal of Forecasting, vol. 19, no. 5, pp. 457–469, 2000. https://doi.org/10.1002/1099-131x(200009)19:5
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).