Type: Package
Title: Complete Discrete Fourier Transform (DFT) and Periodogram
Version: 0.1.2
Date: 2020-06-29
Author: Junho Yang
Maintainer: Junho Yang <junhoyang@stat.tamu.edu>
Description: Calculate the predictive discrete Fourier transform, complete discrete Fourier transform, complete periodogram, and tapered complete periodogram. This algorithm is based on the preprint "Spectral methods for small sample time series: A complete periodogram approach" (2020) by Sourav Das, Suhasini Subba Rao, and Junho Yang.
License: GPL-2
NeedsCompilation: no
Packaged: 2020-06-29 14:39:12 UTC; junhoyang
Repository: CRAN
Date/Publication: 2020-06-29 15:30:17 UTC

Complete Periodogram

Description

Function to calculate the complete periodogram.

Usage

complete.pgram(x, freq = 2 * pi * (1:length(x))/length(x), thres=NULL, ...)

Arguments

x

time series vector.

freq

frequency vector.

thres

(optional) positive threshold value.

...

Arguments used in the predictiveDFT function.

Details

The default frequencies are 2*pi*(1:n)/n, where n is a length of a time series.

Value

Real part of the complete periodogram vector.

Author(s)

Junho Yang

References

S. Das, S. Subba Rao, and J. Yang. Spectral methods for small sample time series: A complete periodogram approach. Submitted, 2020.

See Also

predictiveDFT

Examples

set.seed(123)
x <- arima.sim(model=list(ar=0.7), n=100)
v <- complete.pgram(x)

Complete DFT

Description

Function to calculate the complete DFT.

Usage

completeDFT(x, freq = 2 * pi * (1:length(x))/length(x), ...)

Arguments

x

time series vector.

freq

frequency vector.

...

Arguments used in the predictiveDFT function.

Details

The default frequencies are 2*pi*(1:n)/n, where n is a length of a time series.

Value

Complex valued complete DFT vector.

Author(s)

Junho Yang

References

S. Das, S. Subba Rao, and J. Yang. Spectral methods for small sample time series: A complete periodogram approach. Submitted, 2020.

See Also

predictiveDFT

Examples

set.seed(123)
x <- arima.sim(model=list(ar=0.7), n=100)
v <- completeDFT(x)

A new DFT function

Description

Function to calculate the DFT of time series vector as in the reference.

Usage

fft2(x, freq = 2 * pi * (1:length(x))/length(x))

Arguments

x

time series vector.

freq

frequency vector.

Details

sqrt(n) standardized. The default frequencies are 2*pi*(1:n)/n, where n is a length of a time series.

Value

DFT vector.

Author(s)

Junho Yang

References

S. Das, S. Subba Rao, and J. Yang. Spectral methods for small sample time series: A complete periodogram approach. Submitted, 2020.

See Also

taperDFT

Examples

set.seed(123)
x <- arima.sim(model=list(ar=0.7), n=100)
v <- fft2(x)

Predictive DFT.

Description

Function to calculate the predictive DFT.

Usage

predictiveDFT(x, freq = 2 * pi * (1:length(x))/length(x), taper = FALSE, ar = NULL, ...)

Arguments

x

time series vector.

freq

frequency vector.

taper

logical vector. If TRUE, use the tapered time series to estimate an AR coefficients. Default is FALSE.

ar

predetermined AR coefficients to evaluate the predictive DFT. Default is NULL.

...

Arguments passing ar() function.

Details

If ar vector is predetermined, then we evaluate the predictive DFT using the this AR coefficient vector (see eq (2.2) of the reference). If ar is not specified (default), then we fit the best fitting AR(p) model using AIC and Yule-Walker estimator.

Value

The complex valued predictive DFT vector.

Author(s)

Junho Yang

References

S. Das, S. Subba Rao, and J. Yang. Spectral methods for small sample time series: A complete periodogram approach. Submitted, 2020.

See Also

complete.pgram, tapered.complete.pgram

Examples

set.seed(123)
x <- arima.sim(model=list(ar=0.7), n=100)

v1 <- predictiveDFT(x) #default
v2 <- predictiveDFT(x,ar=c(0.7)) #predictive DFT using AR(1) model with coefficient: 0.7.
v3 <- predictiveDFT(x,taper=TRUE) #Using tapered time series to fit the best AR model. 
v4 <- predictiveDFT(x, method="ols") #Using ols method to fit the best AR model.

Tapered DFT

Description

Function to calculate the tapered DFT.

Usage

taperDFT(x, freq = 2 * pi * (1:length(x))/length(x), regularization.type = "1", p = 0.1)

Arguments

x

time series vector.

freq

frequency vector.

regularization.type

character. if "1": sum of the taper equals to n, if "2": square sum of the taper equals to n. Default is "1".

p

proprotion of taper.

Details

Tapered DFT. The default taper is a Tukey's (or Cosine-bell) taper.

Value

Complex valued tapered DFT vector.

Author(s)

Junho Yang.

See Also

fft2

Examples

set.seed(123)
x <- arima.sim(model=list(ar=0.7), n=100)
v <- taperDFT(x)

Tapered Complete Periodogram

Description

Function to calculate the tapered complete periodogram.

Usage

tapered.complete.pgram(x, freq=2*pi*(1:length(x))/length(x), taperx=NULL, thres=NULL, ...)

Arguments

x

time series vector.

freq

frequency vector.

taperx

predetermined tapered DFT. If NULL, we use default settings of the taperedDFT function to calculate the tapered DFT.

thres

positive threshold value.

...

Arguments used in the predictiveDFT function.

Details

The default frequencies are 2*pi*(1:n)/n, where n is a length of a time series.

Value

Real part of the tapered complete periodogram vector.

Author(s)

Junho Yang

References

S. Das, S. Subba Rao, and J. Yang. Spectral methods for small sample time series: A complete periodogram approach. Submitted, 2020.

See Also

predictiveDFT, complete.pgram

Examples

set.seed(123)
x <- arima.sim(model=list(ar=0.7), n=100)
v <- tapered.complete.pgram(x)