F. Perez de Gracia

Testing for stock market bubbles using nonlinear models and fractional integration

In this article we test for bubbles in the S&P 500 stock market index using monthly data over the period 1871m1–2004m6. We use fractional integration techniques, allowing for structural breaks and a nonlinear adjustment process of prices to dividends. We find a significant structural break around 1932, a period in which the stock market began rising again after the market crash of 1929. Furthermore, we do not find evidence of asymmetric adjustment of prices to dividends when using both momentum-threshold autoregressive and threshold autoregressive models. Finally, we cannot reject the hypothesis of orders of integration equal to or higher than one and thus, we find support for the existence of bubbles in the S&P 500 stock market index.

Modelling Monthly Spanish Tourism: A Seasonal Fractionally Integrated Approach

The authors examine the monthly structure of Spanish tourism using fractionally integrated techniques. They propose the use of a procedure attributable to Robinson (1994) that permits the simultaneous testing of degrees of integration at both zero and seasonal frequencies. The tests have standard null and local limit distributions. However, finite-sample critical values are computed and the power properties of the tests in finite samples are also examined. The results, based on the numbers of foreigners and foreign guest nights in Spain, show that both frequencies are important, the order of integration at the long-run or zero frequency being much higher than that corresponding to the seasonal monthly structure.

Empirical evidence on real convergence in some OECD countries

The real convergence hypothesis in Australia, Canada, Japan and the UK is examined. For this purpose, the order of integration of the real GDP per capita series in these countries is examined as well as their differences with respect to the US which is used as a benchmark country. Both parametric and semiparametric methods are used and the results show that convergence is achieved in all countries, especially for the cases of Australia and Canada.

Persistence in international monthly arrivals in the Canary Islands.

This study analyses persistence in international monthly arrivals to the Canary Islands using a model based on fractional integration and seasonal autoregressions. Thus, the estimate of the fractional differencing parameter gives an indication of the long-run evolution of the series, while the AR coefficient refers to the short-run seasonal dynamics. The authors use both aggregate and disaggregate data by location of origin and island destination. The results show that the aggregate series corresponding to the total number of international arrivals in the Canary Islands is an I(d) process, with d slightly above 0.5, and the most persistent arrivals are those coming from Scandinavia and travelling to La Palma.