Long-memory time series; its foundations and applications to economics.

OKAMOTO在计算机上生成了FGN和分数ARIMA（O,d，O）和ARIMA（1,d，O）来模拟长记忆时间序列。通过FGN加上一定的正弦分量，他得到了与实际汇率具有相同长记忆特性的模拟时间序列。他还研究了自回归部分对分数ARIMA的影响（1,d，O）。他从周期图与频率的关系中附加1/2的差值来估计ARIMA的分数阶差d度。他提出了一个检验布朗运动零假设与分数布朗运动备选方案的统计量，并对其幂函数进行了交换。KIMURA & Okamoto从随机游走、利率平价、无偏预测器和时间序列AR模型的角度研究了汇率模型，特别是不同模型的可预测性。ODAKI研究了常数项存在条件下的协整和共趋势。TANIGUCHI研究了时间序列的渐近辅助性。MAEKAWA给出了谱密度未知参数样本分布的渐近展开式，直至三阶。他还报道了非线性回归模型中OLS估计的渐近展开式。FUJIKOSHI对一些多元统计分布的渐近展开式的误差界进行了一系列的研究。

OKAMOTO generated FGN and fractional ARIMA(O,d,O) and ARIMA(l,d,O)on the computer to simulate long-memory time series. By FGN plus certain sinusoidal components,,he obtained the simulated time series having the same long-memory character as the real exchange rate. He also studied the effects of autoregressive part on fractional ARIMA(l,d,O). He estimate degree d of fractional differencing of ARIMA with additional 1/2 differencing from the relation of periodogram vs frequency. He presented a statistic testing the null hypothesis of Brownian motion vs the alternatives of fractional Brownian motion and commuted its power function. KIMURA & Okamoto studied about models of exchange rate from the point of view of random walk, interest parity, unbiased predictor and time series AR model, in particular about predictability of different models. ODAKI studied the cointegration and common trend under the condition of the existence of constant term. Asymptotic ancillarity in time series was studied by TANIGUCHI. MAEKAWA presented asymptotic expansion of the sample distribution of unknown parameter of spectral density up to the third order. He also reported asymptotic expansion of OLS estimate in nonlinear regression model. FUJIKOSHI made a series of studies on error bounds for asymptotic expansions of the distributions of some multivariate statistics.