For these 64 pairs individual sample 2-tail t-test is done for each trading signal to check the statistical significance of the obtained returns. The test result includes mean return for each signal, standard deviation of each signal set, and t statistics. The test result is shown below:

One-Sample Statistics | ||||

N | Mean | Std. Deviation | Std. Error Mean | |

0.7/0.5 | 64 | 3.685 | 10.481 | 1.310 |

0.7/0.4 | 64 | 4.136 | 11.074 | 1.384 |

0.6/0.4 | 64 | 2.860 | 2.805 | 0.351 |

0.6/0.3 | 64 | 2.736 | 2.225 | 0.278 |

0.5/0.3 | 64 | 7.251 | 31.051 | 3.881 |

0.5/0.2 | 64 | 2.823 | 4.132 | 0.517 |

0.4/0.2 | 64 | 2.032 | 1.991 | 0.249 |

0.4/0.1 | 64 | 2.802 | 7.050 | 0.881 |

0.3/0.1 | 64 | 1.971 | 2.632 | 0.329 |

Table 15: mean stat for bivariate pairs (correlation)

One-Sample Test | ||||||

Test Value = 0 | ||||||

t | df | Sig. (2-tailed) | MeanDifference | 95% Confidence Interval of the Difference | ||

Lower | Upper | |||||

0.7/0.5 | 2.813 | 63 | 0.007 | 3.685 | 1.067 | 6.303 |

0.7/0.4 | 2.988 | 63 | 0.004 | 4.136 | 1.370 | 6.902 |

0.6/0.4 | 8.156 | 63 | 0.000 | 2.860 | 2.159 | 3.561 |

0.6/0.3 | 9.836 | 63 | 0.000 | 2.736 | 2.180 | 3.292 |

0.5/0.3 | 1.868 | 63 | 0.066 | 7.251 | -0.505 | 15.007 |

0.5/0.2 | 5.466 | 63 | 0.000 | 2.823 | 1.791 | 3.856 |

0.4/0.2 | 8.164 | 63 | 0.000 | 2.032 | 1.535 | 2.530 |

0.4/0.1 | 3.179 | 63 | 0.002 | 2.802 | 1.041 | 4.563 |

0.3/0.1 | 5.991 | 63 | 0.000 | 1.971 | 1.314 | 2.628 |

**Table 16.**

For 63 degree of freedom t critical value (2 tailed) at 95% confidence level is 1.998. In the test result all the obtained t values are greater than the critical value, which suggests that the return series of every trade signal are statistically significant at 95% confidence level. In other words, it suggests that the average returns are feasible and reproducible in the future following the same trade signal.

This bivariate correlation weigh pair trading strategy return is statistically compared with the naive approach return. For the purpose the average of all signal return of every eligible pair is compared with the 1000 random simulation return from the NSE Index in the same time frame of the study. One way ANOVA testing has been done for mean comparison.

Mean of Bivariate equal weight pair strategy returns is = ^strategy = 337%

Mean of 1000 random return from NSE Nifty 50 index = ^Naive = 12.57%

ANOVA | |||||

artificial_pair correl bi simulation | |||||

Sum of Squares | df | MeanSquare | F | Sig. | |

Between Groups | 631.65 | 1 | 631.6518 | 464.45 | 9.618E-86 |

Within Groups | 1444.32 | 1062 | 1.360003 | ||

Total | 2075.98 | 1063 |

Table.17: ANOVA result for bivariate (correlation) pairs

Two series of variables are grouped and tested. Test result signifies that F value is very high compared to Critical F value. Hence the Null hypothesis is rejected at 99% confidence level. So, the means of Pair strategy return and Naive return are statistically different. Pair strategy return is much higher than the Naive return, and hence itâ€™s recommended to invest in bivariate correlation weigh pair.