WaveLetLongMemory (version 0.1.2)

Wavelet: Estimating Long Memory using wavelets

Description

The function WVLM estimates the long memory prarameter using wavelets as well as using other two methods namely GPH and Semiparametric.

Usage

WVLM(Method,Xt,bandwidth,BetaLagParzen,typeWvtrans,filtertype)

Arguments

Method

GPH, SEMIPARAMETRIC, WAVELET

Xt

univariate time series

bandwidth

The bandwidth used in the regression equation

BetaLagParzen

exponent of the bandwidth used in the lag Parzen window

typeWvtrans

type of wavelet transform i.e. dwt or modwt

filtertype

Either a wt.filter object, a character string indicating which wavelet filter to use in the decomposition, or a numeric vector of wavelet coefficients

Value

Method

GPH, SEMIPARAMETRIC, WAVELET.

xt

univariate time series.

bandwidth

The bandwidth used in the regression equation.

WVLM

Out Approach.

GPH.Estimation

The GPH estimator is based on the regression equation using the periodogram function as an estimate of the spectral density.

SEM.Estimation

It is based on the regression equation using the smoothed periodogram function as an estimate of the spectral density..

Wavelet.Estimation

WAVELET method makes use Jensen (1994) estimator to estimate the memory parameter d in the ARFIMA(p,d,q) model based on wavelet technique.

References

Geweke, J. and Porter-Hudak, S. (1983) The estimation and application of long memory time series models. Journal of Time Series Analysis 4(4), 221 to 238.

Robinson, P. M. (1995). Gaussian Semiparametric Estimation of Long Range Dependence. The Annals of Statistics 23 (5), 1630 to 1661.

Jensen, M.J.(1999). Using wavelets to obtain a consistent ordinary least squares estimator of the long-memory parameter journal of forecasting, Journal of Forecasting 18, 17 to 32.

Paul, R. K., Samanta, S. and Gurung, B. (2015). Monte Carlo simulation for comparison of different estimators of long memory parameter: An application of ARFIMA model for forecasting commodity price. Model Assisted Statistics and Application, 10(2), 116 to 127.

Reisen, V. A. (1994) Estimation of the fractional difference parameter in the ARFIMA(p,d,q) model using the smoothed periodogram. Journal Time Series Analysis, 15(1), 335 to 350.

Examples

# NOT RUN {
## Simulating Long Memory Series
N <- 1000
PHI <- 0.2
THETA <- 0.1
SD <- 1
M <- 0
D <- 0.2
Seed <- 123

set.seed(Seed)
Sim.Series <- fracdiff::fracdiff.sim(n = N, ar = c(PHI), ma = c(THETA),
d = D, rand.gen = rnorm, sd = SD, mu = M)

Yt <- as.ts(Sim.Series$series)

## GPH Estimation
WVLM(Method="GPH",Xt=Yt,bandwidth = 0.5)

## SEMIPARAMETRIC Estimation
WVLM(Method="SEMIPARAMETRIC",Xt=Yt,bandwidth = 0.5,BetaLagParzen = 0.2)

## WAVELET Estimation using different filtertype
WVLM(Method="WAVELET",Xt=Yt,typeWvtrans = "modwt",filtertype = "haar")
WVLM(Method="WAVELET",Xt=Yt,typeWvtrans = "modwt",filtertype = "d6")
WVLM(Method="WAVELET",Xt=Yt,typeWvtrans = "modwt",filtertype = "s8")
# }