This function is for calculating the optimal number of factors in an approximate factor model.

1 | ```
POETKhat(Y)
``` |

`Y` |
p by n matrix of raw data, where p is the dimensionality, n is the sample size. It is recommended that Y is de-meaned, i.e., each row has zero mean. |

This method was proposed by Bai & Ng (2002) and Hallin & Liska (2007). They propose two penalty functions and in turn minimize the corresponding information criteria. Notice that this method may underestimate K. POET is very robust to over-estimating K. But under-estimating K can result to VERY BAD performance. Therefore we strongly recommend choosing a relatively large K (normally less than 8) to avoid missing any important common factor.

`K1HL` |
estimated number of factors based on the first infomation criterion using Hallin & Liska method |

`K2HL` |
estimated number of factors based on the second information criterion using Hallin & Liska method |

`K1BN` |
estimated number of factors based on the first infomation criterion using Bai & Ng method |

`K2BN` |
estimated number of factors based on the second information criterion using Bai & Ng method |

Jianqing Fan, Yuan Liao, Martina Mincheva

Bai,Ng,2002.Determining the number of factors in approximate factor models. Econometrica 70,191-221.

Hallin,Liska,2007.Determining the number of factors in the general dynamic factor model.JASA 102,603-617.

Alessi,Barigozzi,Capasso,2010. Improved penalization for determining the number of factors in approximate factor models. Statistics and Probability Letters 80, 1806-1813.

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