Mixed Time Series, and Cross Section Analyses of Number of Mainland U.S. Visitors to Hawaii during Years 1993-2007
Larry A. Nelson
Statistics, North Carolina State University, Raleigh, NC, United States

A statistical study was conducted to determine the factors which affected the number of visitors to Hawaii from the individual mainland United States during the years 1993-2007. The author provided statistical services to the Hawaii Visitors Bureau during the first few years of the 1960s. At that time it became apparent that number of visitors by state was associated with population of a state, airfare to Hawaii and per capita income of the state. One of the factors leading to the present study was an observed decline in visitors during the years 2006-2007 (leading into the international economic crises in the following years). Results of this present study have been published in the first issue of the Tourism Management Journal for 2011. Both a mixed time series model fitting, and cross section analyses were conducted. This article was the first reporting of the use of the mixed time series model in relating numbers of visitors to both fixed and random variables. Fitting of the mixed time series model and the cross section models led to the conclusion that Log Gross State Product, Log Chained Airfare and Log Distance to Orlando, Florida were the most important predictor variables of Log Number of Visitors to Hawaii. For the mixed model which included data for all years, Log Chained Gross State Product and Log Chained Airfare, Indices for two recessions plus a variable to represent the September 11, 2001 effect in addition to other fixed effects and random state effects were used to predict Log Number of Visitors to Hawaii. The intercepts and slopes (time series) for each state in the mixed time series model were estimated and this led to the identification of certain mainland states which should be the objects of more marketing focus. Cross section airfare elasticities on an annual basis were high and growing over time, whereas those estimated from the mixed time series analysis were much lower. Hence, separate terms for the two elasticities should be used in the future (i. e. temporal elasticity and spatial elasticity). The airfare effect explains why most of the visitors to Hawaii are from California and other western U. S. states. Only those eastern states which have large populations and high per capita incomes perform well in the Hawaii tourism market. There is also the Caribbean competition. To counteract the distance effect, stopovers in existing mainland resort cities when en route to Hawaii and promotions to develop a stronger presence of a Hawaii image on the mainland were recommended.


Larry A. Nelson, David A. Dickey and Joy M. Smith (2011) Estimating time series and cross section tourism demand models: Mainland United States to Hawaii data. Tourism Management 32 (1) 28-38.

Keywords: Mixed time series models; Models for Hawaii tourism; Statistics in tourism research

Biography: Dr. Larry Nelson received his Ph. D. at North Carolina State University in 1961. He was then on the faculty of the University of Hawaii for three years before entering the faculty of the Statistics Department of North Carolina State University in 1964. He was involved in statistical applications in the tourism industry in Hawaii during 1962-64. He was Managing Editor of Biometrics and Treasurer of the International Biometric Society for a period of ten years. He was awarded the second Rob Kempton Award for statistical services in developing countries by the International Biometric Society.