[Paper Review] Segmentation procedure based on Fisher's exact test and its application to foreign exchange rates

Akihiro Sato, Hideki Takayasu|arXiv (Cornell University)|Sep 3, 2013

Control Systems and Identification21 references3 citations

TL;DR

This paper proposes a non-parametric segmentation method for univariate time series using Fisher’s exact test to detect change points by minimizing p-values. Applied to AUD/JPY exchange rate log-returns, the method identifies statistically significant segments, with results validated against shuffled data that yield higher p-values, confirming the method's sensitivity to true structural breaks.

ABSTRACT

This study proposes the segmentation procedure of univariate time series based on Fisher's exact test. We show that an adequate change point can be detected as the minimum value of p-value. It is shown that the proposed procedure can detect change points for an artificial time series. We apply the proposed method to find segments of the foreign exchange rates recursively. It is also applied to randomly shuffled time series. It concludes that the randomly shuffled data can be used as a level to determine the null hypothesis.

Motivation & Objective

• To develop a non-parametric segmentation procedure for univariate time series based on Fisher’s exact test.
• To detect statistically significant change points by minimizing p-values from 2×2 contingency tables of extreme values.
• To validate the method on artificial nonstationary time series and real-world foreign exchange rate log-returns.
• To use randomly shuffled time series as a null hypothesis benchmark for p-value significance.
• To characterize detected segments in terms of mean and standard deviation of log-returns.

Proposed method

• The method constructs a 2×2 contingency table for each candidate boundary τ and threshold x_th, counting observations above and below x_th in pre- and post-τ intervals.
• Fisher’s exact test computes a two-sided p-value for each (τ, x_th) pair using hypergeometric probabilities.
• The change point is identified as the τ and x_th that yield the minimum p-value, indicating the most statistically significant separation.
• The procedure is applied recursively to detect multiple change points in a time series.
• Randomly shuffled log-return data is generated to preserve mean and variance, serving as a null distribution for p-value comparison.
• Segment-specific fitting curves for exchange rates are modeled using exponential functions of the form R(t) = exp(μ(t−t_k−1)+ρ), with ρ estimated via least squares.

Experimental results

Research questions

• RQ1 Can Fisher’s exact test effectively detect change points in nonstationary time series by minimizing p-values?
• RQ2 How does the method perform on artificial nonstationary time series with known structural breaks?
• RQ3 Can the proposed segmentation procedure detect meaningful economic events in real foreign exchange rate data?
• RQ4 Is the p-value from the original time series significantly lower than that from shuffled data, supporting the existence of true change points?
• RQ5 How do segment means and standard deviations relate to the detected change points in foreign exchange rates?

Key findings

• The method successfully detected six distinct segments in the AUD/JPY exchange rate log-return series, with change points aligning with major economic events such as the 2008 Lehman shock.
• The first two segments showed positive mean returns and low volatility, indicating a period of global economic growth.
• The third segment exhibited negative mean returns and increased volatility, reflecting global economic instability.
• The fourth segment showed a steep decline in AUD/JPY exchange rates due to the 2008 financial crisis, with a mean return of -0.005385 and standard deviation of 0.042808.
• The fifth and sixth segments showed stabilization with lower volatility and positive mean returns, indicating market recovery.
• Randomly shuffled data produced p-values consistently above 10−2, confirming that the original data’s low p-values are statistically significant and not due to chance.