# Fitting ARMA-GARCH Processes Fail-safe componentwise fitting of univariate ARMA-GARCH processes. ```r fit_ARMA_GARCH(x, ugarchspec.list = ugarchspec(), solver = "hybrid", verbose = FALSE, ...) ``` ## Arguments - `x`: `matrix`-like data structure, possibly an `xts` object. - `ugarchspec.list`: object of class `uGARCHspec` (as returned by `ugarchspec()`) or a list of such. In case of a list, its length has to be equal to the number of columns of `x`. `ugarchspec.list` provides the ARMA-GARCH specifications for each of the time series (columns of `x`). - `solver`: string indicating the solver used; see `?ugarchfit`. - `verbose`: `logical` indicating whether verbose output is given. - ``...``: additional arguments passed to the underlying `ugarchfit()`. ## Returns If `x` consists of one column only (e.g. a vector), `ARMA_GARCH()` returns the fitted object; otherwise it returns a list of such. ## Author(s) Marius Hofert ## See Also `fit_GARCH_11()` for fast(er) and numerically more robust fitting of GARCH(1,1) processes. ## Examples ```r library(rugarch) library(copula) ## Read the data, build -log-returns data(SMI.12) # Swiss Market Index data stocks <- c("CSGN", "BAER", "UBSN", "SREN", "ZURN") # components we work with x <- SMI.12[, stocks] X <- -returns(x) n <- nrow(X) d <- ncol(X) ## Fit ARMA-GARCH models to the -log-returns ## Note: - Our choice here is purely for demonstration purposes. ## The models are not necessarily adequate ## - The sample size n is *too* small here for properly capturing GARCH effects. ## Again, this is only for demonstration purposes here. uspec <- c(rep(list(ugarchspec(distribution.model = "std")), d-2), # ARMA(1,1)-GARCH(1,1) list(ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(2,2)), distribution.model = "std")), list(ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(1,2), include.mean = TRUE), distribution.model = "std"))) system.time(fitAG <- fit_ARMA_GARCH(X, ugarchspec.list = uspec)) str(fitAG, max.level = 1) # list with components fit, warning, error ## Now access the list to check ## Not run: ## Pick out the standardized residuals, plot them and fit a t copula to them ## Note: ugarchsim() needs the residuals to be standardized; working with ## standardize = FALSE still requires to simulate them from the ## respective standardized marginal distribution functions. Z <- sapply(fitAG$fit, residuals, standardize = TRUE) U <- pobs(Z) pairs(U, gap = 0) system.time(fitC <- fitCopula(tCopula(dim = d, dispstr = "un"), data = U, method = "mpl")) ## Simulate (standardized) Z set.seed(271) U. <- rCopula(n, fitC@copula) # simulate from the fitted copula nu <- sapply(1:d, function(j) fitAG$fit[[j]]@fit$coef["shape"]) # extract (fitted) d.o.f. nu Z. <- sapply(1:d, function(j) sqrt((nu[j]-2)/nu[j]) * qt(U.[,j], df = nu[j])) # Z ## Simulate from fitted model X. <- sapply(1:d, function(j) fitted(ugarchsim(fitAG$fit[[j]], n.sim = n, m.sim = 1, startMethod = "sample", rseed = 271, custom.dist = list(name = "sample", distfit = Z.[,j, drop = FALSE])))) ## Plots original vs simulated -log-returns opar <- par(no.readonly = TRUE) layout(matrix(1:(2*d), ncol = d)) # layout ran <- range(X, X.) for(j in 1:d) { plot(X[,j], type = "l", ylim = ran, ylab = paste(stocks[j], "-log-returns")) plot(X.[,j], type = "l", ylim = ran, ylab = "Simulated -log-returns") } par(opar) ## End(Not run) ```

fit_ARMA_GARCH function