Nonstationary Time Series Change Direction Forecast Method Using Squeeze Theorem

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  • はさみうちの原理を用いた非定常時系列の変化方向予測法

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本論文は，はさみうちの原理を用いた非定常時系列の変化方向を予測する方法を示したものである．はさみうちの原理は，同じ極限値を持つ2つの数列に挟まれた第3の数列も同じ極限値を持つという定理である．本研究では，この原理を月次のドル/円為替レートと日経平均株価に適用した．最初に，原系列に指数平滑移動平均とゼロラグ指数移動平均をそれぞれ適用し，2つの時系列を算出した．次に，はさみうちの原理に基づき，各々の時系列のボリンジャーバンドを計算しバンド幅の絞り込みを行った．次に，改良型先行インディケータにより，原系列をサインカーブに変換し，時系列の変化方向の予測値を算出した．最後に，ボリンジャーバンドがトレンドと判断した区間以外の予測値を採用した．その結果，ドル/円為替レートでは3カ月後までの，日経平均株価では4カ月後までの変化方向を80%以上予測することを可能にした．

This paper presents a method for forecasting the change direction of nonstationary time series using squeeze theorem. The squeeze theorem is a theorem that states that a third number sequence sandwiched between two number sequences with the same limit value also has the same limit value. In this study, we applied this theorem to the monthly the dollar/yen exchange rate and Nikkei Stock Average. First, we applied an exponential smoothing moving average and a Zero Lag exponential moving average to the original series to calculate two time series. Next, we narrowed down the band width by calculating the Bollinger bands for each time series based on the squeeze theorem. Next, the original series was converted into a sine curve using an improved leading indicator, and the predicted value of direction of change in the time series was calculated. Finally, we adopted predicted values other than that of the interval where the Bollinger Bands were determined to be a trend. As a result, we were able to predict over 80% of the direction of change in the dollar/yen exchange rate 3 months from now and the Nikkei Stock Average up to 4 months from now.

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