長期記憶時系列の記憶パラメーターのノンパラメトリック推定 : 円対ドル為替レートの長期持続性

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This paper gives a nonparamertic method of estimation of memory parameter d in the long memory time series by fractal dimension analysis. Two-segments curve in the mean length curve gives a characteristic time scale which separates between long and intermediate persistence. Memory parameter d is estimated by the power law index which is determined by the corresponding characteristic frequency. For original nondetrended series we find that d=0.45±0.13 for the part of long memeory process and d=-0.29±0.10 in the intermediate memory process. On the othe hand, for the linearly detrended series we also find d=0.41±0.18 in the part of long memory process and d=-0.33±0.55 in the part of intermediate memory process.
2001-01-25