descomponer {descomponer}

Time series decomposition

Description

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

Usage

descomponer(y,frequency,type)

Arguments

y

a Vector of the observed time-serie values

frequency

Number of times in each unit time interval

type

lineal (1), quadratic(2)

Details

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.

Value

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

References

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/)

Examples

data(ipi)
datos <- descomponer(ipi,12,2)
plot(ts(datos$datos,frequency=12))