rdf: Regression in domain frequency
In descomponer: Seasonal Adjustment by Frequency Analysis

Description Usage Arguments Details Value References Examples

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

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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data(PIB)
data(celec)
rdf(celec,PIB)

Loading required package: taRifx
$datos
       Y         X        F        res
1  12458  65.72689 12438.74   19.26350
2  12822  67.48491 12909.66  -87.65586
3  13345  69.97484 13576.63 -231.63133
4  14288  72.98793 14383.75  -95.74524
5  15309  76.26133 15260.59   48.41183
6  16207  80.29488 16341.05 -134.05185
7  17290  83.50754 17201.62   88.37559
8  17805  85.91239 17845.81  -40.80958
9  19037  88.65090 18579.37  457.62803
10 19915  91.45826 19331.38  583.62284
11 20867  94.86328 20243.48  623.52297
12 21543  98.82299 21304.16  238.83875
13 21935 102.54758 22301.86 -366.86407
14 22253 103.69194 22608.40 -355.40283
15 21757  99.98619 21615.75  141.25334
16 22409 100.00000 21619.45  789.55406
17 20636  99.38237 21454.00 -818.00190
18 20663  97.30654 20897.95 -234.95105
19 19952  96.10971 20577.36 -625.35719

$Fregresores
    1           2
X1  1 88.15634053
X2  0 -5.68444051
X3  0 -9.44842574
X4  0 -2.21612456
X5  0 -2.62417102
X6  0 -0.79654010
X7  0 -2.39713050
X8  0 -1.53918705
X9  0 -1.43696347
X10 0 -1.18967332
X11 0 -0.69982435
X12 0 -0.92147295
X13 0 -0.82056751
X14 0 -1.14883279
X15 0 -0.66396550
X16 0 -1.26963280
X17 0 -0.21300734
X18 0 -1.09411248
X19 0 -0.01302282

$Tregresores
              1        2
 [1,] 0.2294157 15.07878
 [2,] 0.2294157 15.48210
 [3,] 0.2294157 16.05333
 [4,] 0.2294157 16.74458
 [5,] 0.2294157 17.49555
 [6,] 0.2294157 18.42091
 [7,] 0.2294157 19.15794
 [8,] 0.2294157 19.70965
 [9,] 0.2294157 20.33791
[10,] 0.2294157 20.98196
[11,] 0.2294157 21.76313
[12,] 0.2294157 22.67155
[13,] 0.2294157 23.52603
[14,] 0.2294157 23.78856
[15,] 0.2294157 22.93841
[16,] 0.2294157 22.94157
[17,] 0.2294157 22.79988
[18,] 0.2294157 22.32365
[19,] 0.2294157 22.04908

$Nregresores
[1] 2