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

长记忆时间序列；

• 批准号: 63530014
• 负责人: OKAMOTO Masanori
• 金额: $ 0.9万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63530014/
• 关键词: Long-memory Time Series; Exchange Rate Model; FGN; Fractional ARIMA; Power Function; Cointegration; Asymptotic Expansion; Ancillary Statistic; ペリオドグラム; R; S-分析; 直物為替レ-ト; 非線形回帰モデル; 長期記憶時系列モデル; 為替レート; Hurst係数; Cointegration; 非線型最小2乗推定量; 検定

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.

OKAMOTO在计算机上生成FGN和分数ARIMA（O，d，O）和ARIMA（l，d，O）来模拟长记忆时间序列。通过FGN加上一定的正弦分量，他得到了与真实的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（l，d，O）的影响。从周期图与频率的关系出发，估计了ARIMA分数阶差分的阶数d，并给出了附加1/2阶差分的ARIMA分数阶差分的阶数d。他提出了一个检验布朗运动与分数布朗运动的替代的零假设的统计量，并交换了它的幂函数。KIMURA & Okamoto从随机游走、利率平价、无偏预测和时间序列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同趋势。谷口研究了时间序列的渐近关联性。MAEKAWA给出了谱密度未知参数的样本分布的渐近展开式，直到三阶。他还报道了非线性回归模型中OLS估计的渐近展开。Fujikoshi对一些多元统计量的分布的渐近展开式的误差界作了一系列的研究。

项目成果

M.ODAKI: "On a statistical criterion for detecting cointegration and common trends in the vector time series." The Hiroshima Econmic Studies.10. 141-14 (1989)

M.ODAKI：“关于检测向量时间序列中的协整和共同趋势的统计标准。”

FUJIKOSHI, Yasurori: "Error bounds for asymptotic expansions of the maximum of the multivariate t- and F-variables with common denominatir." The Hiroshima Math.Journal. Vol.19, 1988, 319-327.

FUJIKOSHI、Yasurori：“具有共同分母的多元 t 变量和 F 变量最大值渐近展开的误差界限。”

K.MAEKAWA: "Asymptotic expansions and curvature measures in a nonlinear regression model." Reaearch Report 8907,Department of Economics,University of Western Ontario,Canada.19. (1989)

K.MAEKAWA：“非线性回归模型中的渐近展开和曲率测量。”

OKAMOTO, Masanori: "Long-range dependence of foreign exchange rate and estimation of parameter in fractionally differenced processes." The Hiroshima Economic Studies. Vol.11. (1990)

OKAMOTO，Masanori：“外汇汇率的长期依赖性和分数差分过程中参数的估计。”

TANIGUCHI, Masanobu: "Asymptotic ancillarity in time series analysis." Journal Japan Statist. Soc., Vol.18, 1988, 107-121.

TANIGUCHI, Masanobu：“时间序列分析中的渐近辅助性。”