Aggregation, Heterogeneous Autoregression and Volatility of Daily International Tourist Arrivals and Exchange Rates

Tourism is a major source of service receipts for many countries, including Taiwan. The two leading tourism countries for Taiwan, comprising a high proportion of world tourist arrivals to Taiwan, are Japan and USA, which are sources of short and long haul tourism, respectively. As it is well known that a strong domestic currency can have adverse effects on international tourist arrivals, daily data from 1 January 1990 to 31 December 2008 are used to model the world price and US$ - New Taiwan $ and Yen - New Taiwan $ exchange rates, and tourist arrivals from the world, USA and Japan to Taiwan, as well as their associated volatility. The sample period includes the Asian economic and financial crises in 1997, and part of the global financial crisis of 2008-09. Inclusion of the exchange rate allows approximate daily price effects on world, US and Japanese tourist arrivals to Taiwan to be captured. The Heterogeneous Autoregressive (HAR) model does not reproduce the theoretical hyperbolic decay rates associated with fractionally integrated (or long memory) time series models, but it can nevertheless approximate quite accurately and parsimoniously the slowly decaying correlations associated with such models. The HAR model is used to approximate long memory properties in daily exchange rates and international tourist arrivals, to test whether alternative short and long run estimates of conditional volatility are sensitive to the approximate long memory in the conditional mean, to examine asymmetry and leverage in volatility, and to examine the effects of temporal and spatial aggregation. The empirical results show that the conditional volatility estimates are not sensitive to the approximate long memory nature of the conditional mean specifications. The QMLE for the GARCH(1,1), GJR(1,1) and EGARCH(1,1) models for world, US and Japanese tourist arrivals to Taiwan, and the world price and US$ / New Taiwan $ and Yen/ New Taiwan $ exchange rates, are statistically adequate and have sensible interpretations. Asymmetry (though not leverage) is found for several alternative HAR models for the world, US and Japanese tourist arrivals to Taiwan. For policy purposes, these empirical results suggest that an arbitrary choice of data frequency or spatial aggregation will not lead to robust findings as they are generally not independent of the level of aggregation used.