An alternative approach to estimating demand: neural network regression with conditional volatility for high frequency air passenger arrivals.

In this paper we provide an alternative approach to analyze the demand for international tourism in the Balearic Islands, Spain, by using a neural network model that incorporates time-varying conditional volatility. We consider daily air passenger arrivals to Palma de Mallorca, Ibiza and Mahon, which are located in the islands of Mallorca, Ibiza and Menorca, respectively, as a proxy for international tourism demand for the Balearic Islands. Spain is a world leader in terms of total international tourist arrivals and receipts, and Mallorca is one of the most popular destinations in Spain. For tourism management and marketing, it is essential to forecast high frequency international tourist demand accurately. As it is important to provide sensible international tourism demand forecast intervals, it is also necessary to model their variances accurately. Moreover, time-varying variances provide useful information regarding the risks associated with variations in international tourist arrivals.

[1]  Jeffrey S. Racine,et al.  Semiparametric ARX neural-network models with an application to forecasting inflation , 2001, IEEE Trans. Neural Networks.

[2]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .

[3]  Howell Tong,et al.  Threshold autoregression, limit cycles and cyclical data- with discussion , 1980 .

[4]  M. Medeiros,et al.  Building Neural Network Models for Time Series: A Statistical Approach , 2002 .

[5]  Joaquín Alegre,et al.  The length of stay in the demand for tourism. , 2006 .

[6]  Chi Hau Chen,et al.  Pattern recognition and signal processing , 1978 .

[7]  J. T. Hwang,et al.  Prediction Intervals for Artificial Neural Networks , 1997 .

[8]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[9]  J. Monahan.  Fully Bayesian analysis of ARMA time series models , 1983 .

[10]  W. Härdle,et al.  A Review of Nonparametric Time Series Analysis , 1997 .

[11]  Ulrich Anders,et al.  Model selection in neural networks , 1999, Neural Networks.

[12]  Halbert White,et al.  On learning the derivatives of an unknown mapping with multilayer feedforward networks , 1992, Neural Networks.

[13]  J. Alegre,et al.  Repeat Visitation in Mature Sun and Sand Holiday Destinations , 2006 .

[14]  J. Alegre,et al.  Determinants of the Price of German Tourist Packages on the Island of Mallorca , 2001 .

[15]  Kurt Hornik,et al.  Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks , 1990, Neural Networks.

[16]  Paul Waltman,et al.  A Threshold Model , 1974 .

[17]  Jaume Rosselló,et al.  The short-term price effect of a tourist tax through a dynamic demand model: The case of the Balearic Islands , 2005 .

[18]  J. Zakoian,et al.  Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes , 2004 .

[19]  H. Tong,et al.  ON ESTIMATING THRESHOLDS IN AUTOREGRESSIVE MODELS , 1986 .

[20]  C. Granger,et al.  Forecasting Volatility in Financial Markets: A Review , 2003 .

[21]  Halbert White,et al.  Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators , 1999, IEEE Trans. Inf. Theory.

[22]  Hong Zhang,et al.  Forecasting Volatility in Financial Markets , 2010 .

[23]  Xiaotong Shen,et al.  Sieve extremum estimates for weakly dependent data , 1998 .

[24]  Marcelo C. Medeiros,et al.  A flexible coefficient smooth transition time series model , 2005, IEEE Transactions on Neural Networks.

[25]  M. McAleer.  Automated Inference and Learning in Modelling Financial Volatility * , 2004 .

[26]  Halbert White,et al.  Artificial neural networks: an econometric perspective ∗ , 1994 .

[27]  Henri Theil,et al.  Theory and measurement of consumer demand , 1975 .

[28]  Timo Teräsvirta,et al.  Smooth transition autoregressive models - A survey of recent developments , 2000 .

[29]  Kurt Hornik,et al.  Degree of Approximation Results for Feedforward Networks Approximating Unknown Mappings and Their Derivatives , 1994, Neural Computation.

[30]  Michael McAleer,et al.  Modelling the uncertainty in monthly international tourist arrivals to the Maldives , 2007 .

[31]  David J. C. MacKay,et al.  Bayesian Interpolation , 1992, Neural Computation.

[32]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[33]  Daniel J. Slottje,et al.  The Sensitivity of the True Cost of Living to Price-Induced and Income-Induced Changes in Aggregate Consumers' Tastes , 1987 .

[34]  Simon L. Peyton Jones.  Haskell 98 Libraries: Input/Output , 2003, J. Funct. Program..

[35]  M. Loève.  On Almost Sure Convergence , 1951 .

[36]  Michael McAleer,et al.  Modelling international tourism and country risk spillovers for Cyprus and Malta. , 2007 .

[37]  M. Medeiros,et al.  Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination , 2005 .

[38]  Marcelo C. Medeiros,et al.  Local Global Neural Networks , 2004 .

[39]  J. R. Nadal,et al.  Modelling environmental attitudes toward tourism , 2007 .

[40]  Halbert White,et al.  Estimation, inference, and specification analysis , 1996 .

[41]  Kurt Hornik,et al.  Stationary and Integrated Autoregressive Neural Network Processes , 2000, Neural Computation.

[42]  Teresa Garín-Muñoz,et al.  Tourism in the Balearic Islands: A dynamic model for international demand using panel data , 2007 .

[43]  Marcelo C. Medeiros,et al.  A hybrid linear-neural model for time series forecasting , 2000, IEEE Trans. Neural Networks Learn. Syst..

[44]  Michael McAleer,et al.  Modelling multivariate international tourism demand and volatility , 2005 .

[45]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[46]  H. Akaike.  A new look at the statistical model identification , 1974 .

[47]  N. Wermuth,et al.  Nonlinear Time Series : Nonparametric and Parametric Methods , 2005 .

[48]  M. McAleer,et al.  Risk Management for International Tourist Arrivals: An Application to the Balearic Islands, Spain , 2009 .

[49]  C. Granger,et al.  Modelling Nonlinear Economic Relationships , 1995 .

[50]  P. Samuelson,et al.  Foundations of Economic Analysis. , 1948 .

[51]  David J. C. MacKay,et al.  A Practical Bayesian Framework for Backpropagation Networks , 1992, Neural Computation.

[52]  T. Teräsvirta.  Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models , 1994 .

[53]  W. Härdle.  Applied Nonparametric Regression , 1992 .

[54]  Timo Teräsvirta,et al.  Testing linearity against smooth transition autoregressive models , 1988 .

[55]  T. Knowles,et al.  The market viability of European mass tourist destinations. A post‐stagnation life‐cycle analysis , 1999 .