Description Usage Arguments Details Value References Examples

Decompose a time series into seasonal, trend and irregular components using the transform amplitude-frequency domain to time series.

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`y` |
a Vector of the observed time-serie values |

`frequency` |
Number of times in each unit time interval |

`type` |
lineal (1), quadratic(2) |

One could use a value of 7 for frequency when the data are sampled daily, and the natural time period is a week, or 4 and 12 when the data are sampled quarterly and monthly and the natural time period is a year.

Transforms the time series in amplitude-frequency domain, by a band spectrum regresion (Parra, F. ,2013) of the serie y_t and a OLS lineal trend, in which regression is carried out in the low and the sesaonal amplitude-frequency_t .The low frequency are the periodicity a n/2*frequency or (n-1)/2*frequency , if n is odd. The seasonal frequency are the periodicity: 2n/2*frequency,3n/2*frequency,4n/2*frequency,.. .

Use the "sort.data.frame" function, Kevin Wright (http://tolstoy.newcastle.edu.au/R/help/04/07/1076.html).

Slow computer in time series higher 1000 data.

The output is a data.frame object.

`y` |
The Vector of the observed time-serievalues |

`TDST` |
The trend and seasonal time serie of y |

`TD` |
The trend time serie of y |

`ST` |
The seasonal time serie of y |

`IR` |
The remainder time serie of y |

`regresoresTD` |
The regressors matrix use to the trend estimated |

`regresoresST` |
The regressors matrix use to the seasonal estimated |

`coeficientesTD` |
The coefficient vector use to the trend estimated |

`coeficientesSD` |
The coefficient vector use to the seasonal estimated |

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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