An Alternative Approach to Measure Co-Movement between Two Time Series
Abstract
:1. Introduction
2. Introducing the HP of Two Series
2.1. Hurst Exponent of a Time Series
2.2. HP
2.2.1. Correlated Series
2.2.2. Cointegrated Series
2.2.3. Uncorrelated Series
2.2.4. Nonlinear Relationship
2.2.5. Copula Relationship
3. Testing HP in Financial Series
3.1. Paris Trading: Strategy Definition and Application
- First, the prices are normalized as defined by Ramos-Requena et al. (2017) [62]. Therefore, for a pair of stocks A and B, for each dollar invested in A we will invest b dollars in B, where b is given by , and (resp. ) is the log-return of A (resp. B).The series of the pair is defined such that its increments are given by .
- Pairs selection:To select the pairs, the correlation method is chosen by using Pearson’s correlation method and through the HP method, as it was explained in Section 2.2. The duration of this phase will be 250 or 500 days, as we will indicate later.
- Trading strategy (see Ramos-Requena et al. (2017) [62] for a more detailed description):
- When the pair is sold. The position is closed when or .
- When the pair is bought. The position is closed when or .
where m is a moving average of the series of the pair and s is a moving standard deviation of m.
- HP: daily returns are used.
- HP1: 10 days (2 weeks) returns are chosen.
- HP2: 20 days (4 weeks) returns are chosen and the selection period is 500 days (around 2 years).
3.2. HP
3.3. HP1
3.4. HP2
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Method | N | AAV | Sharpe R | % Max Drawdonw | % Profit |
---|---|---|---|---|---|
Correlation | 2 | 0.50% | 0.12 | 12.30% | 6.20% |
HP | 2 | 0.30% | 0.05 | 13.40% | 1.20% |
Correlation | 5 | 0.30% | 0.70 | 18.30% | 1.27% |
HP | 5 | 1.00% | 0.28 | 9.40% | 16.30% |
Correlation | 10 | 0.00% | −0.01 | 9.80% | −4.41% |
HP | 10 | 0.20% | 0.07 | 10.90% | −0.04% |
Correlation | 15 | 0.00% | −0.01 | 10.90% | −4.25% |
HP | 15 | 0.60% | 0.22 | 6.80% | 6.80% |
Correlation | 20 | 0.00% | 0.02 | 7.40% | −2.93% |
HP | 20 | 0.20% | 0.08 | 7.00% | −0.52% |
Correlation | 25 | 0.60% | 0.27 | 5.30% | 6.86% |
HP | 25 | 0.30% | 0.12 | 6.70% | 1.00% |
Correlation | 30 | 0.40% | 0.18 | 5.60% | 2.75% |
HP | 30 | 0.00% | 0.00 | 6.80% | −3.70% |
Method | N | AAV | Sharpe R | % Max Drawdown | % Profit |
---|---|---|---|---|---|
Correlation | 2 | 0.50% | 0.12 | 12.30% | 6.20% |
HP1 | 2 | 0.80% | 0.12 | 20.80% | 11.32% |
Correlation | 5 | 0.30% | 0.07 | 18.30% | 1.27% |
HP1 | 5 | 0.30% | 0.07 | 18.30% | 1.84% |
Correlation | 10 | 0.00% | −0.01 | 9.80% | −4.41% |
HP1 | 10 | 0.50% | 0.14 | 11.50% | 5.22% |
Correlation | 15 | 0.00% | −0.01 | 10.90% | −4.25% |
HP1 | 15 | 0.70% | 0.25 | 10.60% | 10.20% |
Correlation | 20 | 0.00% | 0.02 | 7.40% | −2.93% |
HP1 | 20 | 0.40% | 0.16 | 9.80% | 4.08% |
Correlation | 25 | 0.60% | 0.27 | 5.30% | 6.86% |
HP1 | 25 | 0.30% | 0.11 | 9.90% | 1.01% |
Correlation | 30 | 0.40% | 0.18 | 5.60% | 2.75% |
HP1 | 30 | 0.20% | 0.09 | 8.90% | −0.20% |
Method | N | AAV | Sharpe R | % Max Drawdonw | % Profit |
---|---|---|---|---|---|
Correlation | 2 | −1.40% | −0.32 | 30.00% | −24.67% |
HP2 | 2 | 1.20% | 0.20 | 23.20% | 19.64% |
Correlation | 5 | 1.10% | −0.32 | 23.10% | −20.71% |
HP2 | 5 | 1.60% | 0.39 | 15.00% | 27.43% |
Correlation | 10 | −0.80% | −0.28 | 15.10% | −15.54% |
HP2 | 10 | 0.70% | 0.23 | 13.00% | 9.31% |
Correlation | 15 | −0.30% | −0.11 | 12.10% | −7.74% |
HP2 | 15 | 0.70% | 0.26 | 7.50% | 8.71% |
Correlation | 20 | −0.30% | −0.15 | 13.00% | −8.83% |
HP2 | 20 | 0.70% | 0.31 | 6.20% | 9.43% |
Correlation | 25 | −0.40% | −0.19 | 12.50% | −9.76% |
HP2 | 25 | 0.60% | 0.29 | 5.10% | 7.59% |
Correlation | 30 | 0.00% | 0.00 | 10.70% | −3.54% |
HP2 | 30 | 0.60% | 0.30 | 5.80% | 7.39% |
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Ramos-Requena, J.P.; Trinidad-Segovia, J.E.; Sánchez-Granero, M.Á. An Alternative Approach to Measure Co-Movement between Two Time Series. Mathematics 2020, 8, 261. https://doi.org/10.3390/math8020261
Ramos-Requena JP, Trinidad-Segovia JE, Sánchez-Granero MÁ. An Alternative Approach to Measure Co-Movement between Two Time Series. Mathematics. 2020; 8(2):261. https://doi.org/10.3390/math8020261
Chicago/Turabian StyleRamos-Requena, José Pedro, Juan Evangelista Trinidad-Segovia, and Miguel Ángel Sánchez-Granero. 2020. "An Alternative Approach to Measure Co-Movement between Two Time Series" Mathematics 8, no. 2: 261. https://doi.org/10.3390/math8020261
APA StyleRamos-Requena, J. P., Trinidad-Segovia, J. E., & Sánchez-Granero, M. Á. (2020). An Alternative Approach to Measure Co-Movement between Two Time Series. Mathematics, 8(2), 261. https://doi.org/10.3390/math8020261