Abbreviation: PCA10

Category: Principal Components Analysis (PCA)

Input Parameters:

Name | Range | Default |

Time Series #1 | Close | |

Time Series #2 | Close | |

Time Series #3 | Close | |

Time Series #4 | Close | |

Time Series #5 | Close | |

Time Series #6 | Close | |

Time Series #7 | Close | |

Time Series #8 | Close | |

Time Series #9 | Close | |

Time Series #10 | Close | |

Window Size | Int >= 10 | 50 |

Vector Number | 1 <= Int <= 10 | 1 |

Calculation:

Performs the Principal Component Analysis of the last n points in the space of X1…X10, calculates the m^{th} eigenvector and projects the latest time point onto the direction of this eigenvector,

where

X1 = Time Series 1

X2 = Time Series 2

X3 = Time Series 3

X4 = Time Series 4

X5 = Time Series 5

X6 = Time Series 6

X7 = Time Series 7

X8 = Time Series 8

X9 = Time Series 9

X10 = Time Series 10

n = Window Size

m = Vector Number

Discussion:

Extracts the m^{th} principal component from the data. For more information on Principal Component Analysis refer to Principal Components Analysis (PCA) Discussion.

Note that the direction of the vector represents the direction that causes the m^{th} most variation, and thus may point in one of two directions. NeuroShell Trader performs this analysis so that the vector choosen is closest to the previous vector selected. Because of the way this is calculated, if the first data point is shifted (forward or backward in time), the sign of the entire series may be alternated. This may require your neural networks to be retrained or your Trading Strategies to be rebacktested.