# Simulates, fits, and predicts persistent and anti-persistent time series. arfima Simulates with arfima.sim, fits with arfima, and predicts with a method for the generic function. Plots predictions and the original time series. Has the capability to fit regressions with ARFIMA/ARIMA-FGN/ARIMA-PLA errors, as well as transfer functions/dynamic regression. package ## Details ||| |:--|:--| |Package:|arfima| |Type:|Package| |Version:|1.4-0| |Date:|2017-06-20| |License:|MIT| A list of functions: `arfima.sim` - Simulates an ARFIMA, ARIMA-FGN, or ARIMA-PLA (three classes of mixed ARIMA hyperbolic decay processes) process, with possible seasonal components. `arfima` - Fits an ARIMA-HD (default single-start) model to a series, with options for regression with ARIMA-HD errors and dynamic regression (transfer functions). Allows for fixed parameters as well as choices for the optimizer to be used. `arfima0` - Simplified version of `arfima` `weed` - Weeds out modes too close to each other in the same fit. The modes with the highest log-likelihoods are kept `print.arfima` - Prints the relevant output of an `arfima` fitted object, such as parameter estimates, standard errors, etc. `summary.arfima` - A much more detailed version of `print.arfima` `coef.arfima` - Extracts the coefficients from a `arfima` object `vcov.arfima` - Theoretical and observed covariance matrices of the coefficients `residuals.arfima` - Extracts the residuals or regression residuals from a `arfima` object `fitted.arfima` - Extracts the fitted values from a `arfima` object `tacvfARFIMA` - Computes the theoretical autocovariance function of a supplied model. The model is checked for stationarity and invertibility. `iARFIMA` - Computes the Fisher information matrix of all non-FGN components of the given model. Can be computed (almost) exactly or through a psi-weights approximation. The approximation takes more time. `IdentInvertQ` - Checks whether the model is identifiable, stationary, and invertible. Identifiability is checked through the information matrix of all non-FGN components, as well as whether both types of fractional noise are present, both seasonally and non-seasonally. `lARFIMA` and `lARFIMAwTF` - Computes the log-likelihood of a given model with a given series. The second admits transfer function data. `predict.arfima` - Predicts from an `arfima` object. Capable of exact minimum mean squared error predictions even with integer d > 0 and/or integer dseas > 0. Does not include transfer function/leading indicators as of yet. Returns a `predarfima` object, which is composed of: predictions, and standard errors (exact and, if possible, limiting). `print.predarfima` - Prints the relevant output from a `predarfima` object: the predictions and their standard deviations. `plot.predarfima` - Plots a `predarfima` object. This includes the original time series, the forecasts and as default the standard 95% prediction intervals (exact and, if available, limiting). `logLik.arfima`, `AIC.arfima`, `BIC.arfima` - Extracts the requested values from an `arfima` object `distance` - Calculates the distances between the modes `removeMode` - Removes a mode from a fit `tacvf` - Calculates the theoretical autocovariance functions (tacvfs) from a fitted `arfima` object `plot.tacvf` - Plots the tacvfs `print.tacvf` - Prints the tacvfs `tacfplot` - Plots the theoretical autocorrelation functions (tacfs) of different models on the same data `SeriesJ`, `tmpyr` - Two datasets included with the package ## Examples ```r set.seed(8564) sim <- arfima.sim(1000, model = list(phi = c(0.2, 0.1), dfrac = 0.4, theta = 0.9)) fit <- arfima(sim, order = c(2, 0, 1), back=TRUE) fit data(tmpyr) fit1 <- arfima(tmpyr, order = c(1, 0, 1), numeach = c(3, 3), dmean = FALSE) fit1 plot(tacvf(fit1), maxlag = 30, tacf = TRUE) fit2 <- arfima(tmpyr, order = c(1, 0, 0), numeach = c(3, 3), autoweed = FALSE, dmean = FALSE) fit2 fit2 <- weed(fit2) fit2 tacfplot(fits = list(fit1, fit2)) fit3 <- removeMode(fit2, 2) fit3 coef(fit2) vcov(fit2) fit1fgn <- arfima(tmpyr, order = c(1, 0, 1), numeach = c(3, 3), dmean = FALSE, lmodel = "g") fit1fgn fit1hd <- arfima(tmpyr, order = c(1, 0, 1), numeach = c(3, 3), dmean = FALSE, lmodel = "h") fit1hd data(SeriesJ) attach(SeriesJ) fitTF <- arfima(YJ, order= c(2, 0, 0), xreg = XJ, reglist = list(regpar = c(1, 2, 3)), lmodel = "n", dmean = FALSE) fitTF detach(SeriesJ) set.seed(4567) sim <- arfima.sim(1000, model = list(phi = 0.3, dfrac = 0.4, dint = 1), sigma2 = 9) X <- matrix(rnorm(2000), ncol = 2) simreg <- sim + crossprod(t(X), c(2, 3)) fitreg <- arfima(simreg, order = c(1, 1, 0), xreg = X) fitreg plot(sim) lines(residuals(fitreg, reg = TRUE)[[1]], col = "blue") ##pretty much a perfect match. ``` ## References Veenstra, J.Q. Persistence and Antipersistence: Theory and Software (PhD Thesis) ## Author(s) JQ (Justin) Veenstra, A. I. McLeod Maintainer: JQ (Justin) Veenstra

arfima-package