Description Usage Arguments Details Value References Examples

Make a Band Spectrum Regression using the comun frequencies in cross-spectrum .

1 | ```
rdf(y,x)
``` |

`y` |
a Vector of the dependent variable |

`x` |
a Vector of the independent variable |

Transforms the time series in amplitude-frequency domain, order the fourier coefficient by the comun frequencies in cross-spectrum, make a band spectrum regresion (Parra, F. ,2013) of the serie y_t and x_t for every set of fourier coefficients, and select the model to pass the Durbin test in the significance chosen.

If not find significance for Band Spectrum Regression, make a OLS.

The generalized cross validation (gcv), is caluculated by: gcv=n*sse/((n-k)^2)

where "sse" is the residual sums of squares, "n" the observation, and k the coefficients used in the band spectrum regression.

Slow computer in time series higher 1000 data.

The output is a data.frame object.

`datos$Y` |
The Y time-serie |

`datos$X` |
The X time-serie |

`datos$F` |
The time - serie fitted |

`datos$reg` |
The error time-serie |

`Fregresores` |
The matrix of regressors choosen in frequency domain |

`Tregresores` |
The matrix of regressors choosen in time domain |

`Nregresores` |
The coefficient number of fourier chosen |

`sse` |
Residual sums of squares |

`gcv` |
Generalized Cross Validation |

DURBIN, J., "Tests for Serial Correlation in Regression Analysis based on the Periodogram ofLeast-Squares Residuals," Biometrika, 56, (No. 1, 1969), 1-15.

Engle, Robert F. (1974), Band Spectrum Regression,International Economic Review 15,1-11.

Harvey, A.C. (1978), Linear Regression in the Frequency Domain, International Economic Review, 19, 507-512.

Parra, F. (2014), Amplitude time-frequency regression, (http://econometria.wordpress.com/2013/08/21/estimation-of-time-varying-regression-coefficients/)

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