Major Research Subjects of Yajima, Y. (1998-2000) Professor

Further information is available at http://www.e.u-tokyo.ac.jp/~yajima/index.html

1. A generalization of cointegration analysis and its application to an economic data
   It is said that there exists a cointegration in a multivariate time series if each component series is nonstationary but a linear combination of these series is stationary. However stationary processes considered by usual cointegration analysis have been restricted to weakly dependent stationary processes in which the correlation between distant observations goes to zero very rapidly.
   We generalized the definition of cointegration so that it includes strongly dependent stationary processes in which the correlation between distant observations goes to zero slowly and is not negligible. And we applied it to real crude oil data in U.S., Europe and Asia and obtained an indication of cointegration which was not found by the previous cointegration analysis.
2. A nonparametric predictor of a strongly dependent stationary process
   We proved asymptotic properties of a nonparametric predictor for future values of a strongly dependent stationary process. These results can be applied to a signal extraction problem in a stationary process which is composed of both short-term and long-term time series.
3. A test statistic for a separable time series model
   The autocorrelation of a separable time series model is expressed by the product of the temporal correlation and the spatial correlation. The number of parameters is small and this model is useful if the sample size is not large. We constructed a nonparametric test statistic for this model and derived its limiting distribution. We applied it to real temperature data obtained at 13 Japanese major observatories and showed its usefulness.