The paper considers a semiparametric estimation for a spectral density of a stationary process. The parametric component is prescribed by the parameter of fractional differencing, d (say). If d=0, the autocorrelation function of the process converges to zero very rapidly as the time span between observations goes to infinity. But if d>0, the spectral density diverges at the origin which means that the autocorrelation between distance observations is not negligible. This model is called a long-memory model. While the nonparametric component of the spectral density is a general continuous function. First the paper considered asymptotic properties of estimators of d. Next it considered some applications. The first one is the discrimination between a short memory model with a deterministic trend and a long-memory model. The second one is to construct a more efficient estimator than the least squares estimator for a regression model with long-memory errors. The third one is estimation of the nonparametric component. And finally an empirical analysis of actual foreign exchange rates is performed. [In Japanese.]
