afmtools.pdf

Package afmtoolsNovember 30, 2011Type Package Version 0.1.4 Date 2011-04-25 Title Estimation, Diagnostic and Forecasting Functions for ARFIMA models Author Javier Contreras-Reyes, Georg M. Goerg, Wilfredo Palma Maintainer Javier Contreras-Reyes Depends R (>= 2.6.0), polynom, fracdiff, hypergeo, sandwich, longmemo Description A collection of estimation, forecasting and diagnostic tools for autoregressive fractionally integrated moving-average process (ARFIMA). License GPL (>= 2) LazyLoad yes Repository CRAN Date/Publication 2011-07-28 06:14:14

R topics documented:afmtools-package . . . . arma-methods . . . . . arma.whittle . . . . . . arma.whittle.loglik . . . check.parameters.arma gw.test . . . . . . . . . . MammothCreek . . . . . per.arma . . . . . . . . pi.j . . . . . . . . . . . . pred.arma . . . . . . . psi.j . . . . . . . . . . . rho.arma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 5 7 8 10 11 12 13 15 17 18

2 rho.sowell . . . smv.afm . . . . spectrum.arma spectrum.arma . TreeRing . . . var.afm . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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afmtools-package

Estimation, Diagnostic and Forecasting functions for ARFIMA models

Description A collection of estimation, forecasting and diagnostic tools for autoregressive fractionally integrated moving-average process (ARFIMA). Details Package: Type: Version: Date: License: LazyLoad: afmtools Package 0.1.4 2011-03-22 GPL >= 2 yes

Functions The package includes several functions. The following ones are those more relevant for practical use: summary, plot, print, residuals and tsdiag options associated to arfima class object and residuals diagnostic. arfima.whittle and arfima.whittle.loglik for Whittle estimation (produce an arfima class object) and the log-likelihood function. gw.test and pred.arfima are the forecasting tools. spectrum.arfima, rho.sowell and var.afm produce the spectrum density, autocovariance function and parameter variance for ARFIMA models, respectively. It is suggested that the user starts by reading the documentation of (some of) these functions. Requirements R >= 2.6.0 Packages fracdiff, polynom, longmemo, sandwich and hypergeo.

afmtools-package Licence

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This package and its documentation are usable under the terms of the "GNU General Public License", a copy of which is distributed with the package. While the software is freely usable, it would be appreciated if a reference is inserted in publications or other work which makes use of it.

Author(s) Javier Contreras-Reyes, Seismological Service, Department of Geophysics, Universidad de Chile. . Georg M. Goerg, Department of Statistics, Carnegie Mellon University. Wilfredo Palma, Department of Statistics, Faculty of Mathematics, Ponticia Universidad Cat\olica de Chile. Please send comments, error reports, etc. to the maintainer Javier Contreras-Reyes.

References Bondon P. and Palma W. (2007). A class of antipersitent processes. Journal of Time Series Analysis 28, 261-273. Brockwell, P. and Davis, R. (1991). Time Series: Theory and Methods. Springer. New York. Contreras J. & Palma W. (2011). Estimation, Diagnostic and Forecasting Tools for ARFIMA Models: The afmtools package. Preprint. Giacomini R. and White H. (2006). Tests of Conditional Predictive Ability. Econometrica 74, 6. Graybill D. A. (1990). Pinus longaeva tree ring data. Mammoth Creek, Utah, National Climatic Data Center. Kokoszka P. S. and Taqqu M. S. (1995). Fractional ARIMA with stable innovations. Stochastic Processes and Their Applications 60, 19-47. Ljung G. M. and Box G. E. P. (1978). On a measure of lack of t in time series models. Biometrika 65, 297-303. Palma W. (2007). Long Memory Time Series: Theory and Methods. Wiley Series in Probability and Statistics. New Jersey. Palma W. & Olea R. (2010). An efcient estimator for Gaussian locally stationary processes. The Annals of Statistics 38, 2958-2997. Shumway, R. and Stoffer, D. (2006). Time Series Analysis and Its Applications: With R Examples, Springer. http://www.stat.pitt.edu/stoffer/tsa2/index.html Sowell F. (1992). Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics 53, 165-188.

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arma-methods

arfima-methods

Methods for tted ARFIMA models

Description summary, print, residuals, tsdiag and plot methods for class arfima model. A equivalent function of summary is provided in afmtools package called summary.arfima. tsdiag its a generic diagnostic function which produces several plots of the residual from a tted ARFIMA model. Usage ## S3 method for class plot(x, ...) ## S3 method for class residuals(object, ...) ## S3 method for class summary(object, ...) ## S3 method for class print(x, ...) ## S3 method for class tsdiag(object, gof.lag Arguments object, x gof.lag ... Details plot produces 4 gure: 1) AR and MA roots of the model; 2) Sample ACF and theoretical ACF implied by the estimates; 3) Periodogram and theoretical spectrum implied by the estimates; 4) Sample ACF of Residuals summary (and basically the same for print) gives a summary output in the summary.lm style - i.e. parameter estimates, standard errors, signicance, etc. residuals gives the residuals from the estimated ARFIMA model. This is not implemented directly via the AR() represenation of an ARFIMA(p,d,q) process, but using a trick: rst the original series is differenced with d using diffseries in the package fracdiff. Consequently an ARMA(p,q) should remain. Now instead of estimating the parameters again, an ARMA(p,q) model where ALL parameters are xed to the Whittle estimates is estimated with arima and then the residuals are obtained. Value for residuals a vector of class ts; for summary and print the tted ARFIMA model object. For tsdiag , produce plots of standardized residuals, autocorrelation function of the residuals, and the p-values of a Portmanteau test for all lags up to gof.lag. object of class arfima; usually a result of a call to arfima.whittle the maximum number of lags for a Portmanteau goodness-of-t test further arguments passed to or from other methods. arfima arfima arfima arfima arfima = 1 , ...)

arma.whittle Author(s) Georg M. Goerg, Javier Contreras-Reyes References

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Palma W. (2007). Long Memory Time Series: Theory and Methods. Wiley Series in Probability and Statistics. New Jersey. Ljung G. M. & Box G. E. P. (1978). On a measure of lack of t in time series models. Biometrika 65, 297303. See Also Box.test Examplesdata(MammothCreek) y=MammothCreek-mean(MammothCreek) mod 1 is chosen, method able to select between a set of Matrix Covariance Estimation methods, such as HAC, NeweyWest, Andrews and LumleyHeagerty a character string specifying the alternative hypothesis, must be one of two.sided (default), greater or less

Value statistic alternative p.value method data.name Author(s) Javier Contreras-Reyes References Giacomini R. & White H. (2006). Tests of Conditional Predictive Ability. Econometrica 74, 6. the value of the GW statistic a character string describing the alternative hypothesis the p-value for the test a character string indicating what type of Matrix Covariance Estimation method was performed a character string giving the name(s) of the data

MammothCreek See Also pred.arfima, predict Examplesr = 1 s = 3 y = arima.sim(n = r, list(ar = c( .8, - .4), ma = c(- .2, y.real = y[(length(y)-s+1):length(y)] obs = y[1:(r-s)] mod.arma