# Simulate from a univariate log-GARCH model Simulate the y series (typically a financial return or the error in a regression) from a log-GARCH model. Optionally, the conditional standard deviation, the standardised error (z) and their logarithmic transformations are also returned. ```r lgarchSim(n, constant = 0, arch = 0.05, garch = 0.9, xreg = NULL, backcast.values = list(lnsigma2 = NULL, lnz2 = NULL, xreg = NULL), check.stability = TRUE, innovations = NULL, verbose = FALSE, c.code=TRUE) ``` ## Arguments - `n`: integer, length of y (i.e. number of observations) - `constant`: the value of the intercept in the log-volatility specification - `arch`: numeric vector with the arch coefficients - `garch`: numeric vector with the garch coefficients - `xreg`: numeric vector (of length n) with the conditioning values - `backcast.values`: backcast values for the recursion (chosen automatically if NULL) - `check.stability`: logical. If TRUE (default), then the roots of arch+garch are checked for stability - `innovations`: Etiher NULL (default) or a vector of length n with the standardised errors (i.e. z). If NULL, then the innovations are normal with mean zero and unit variance - `verbose`: logical. If FALSE (default), then only the vector y is returned. If TRUE, then a matrix with all the output is returned - `c.code`: logical. If TRUE (default), then compiled C-code is used for the recursion (faster) ## Details Empty ## Returns A `zoo` vector of length n if verbose = FALSE (default), or a `zoo` matrix with n rows if verbose = TRUE. ## References Sucarrat, Gronneberg and Escribano (2013), 'Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown', MPRA Paper 49344: [http://mpra.ub.uni-muenchen.de/49344/](http://mpra.ub.uni-muenchen.de/49344/) ## Author(s) Genaro Sucarrat, [http://www.sucarrat.net/](http://www.sucarrat.net/) ## See Also `mlgarchSim`, `lgarch`, `mlgarch` and `zoo` ## Examples ```r ##simulate 500 observations w/default parameter values: set.seed(123) y <- lgarchSim(500) ##simulate the same series, but with more output: set.seed(123) y <- lgarchSim(500, verbose=TRUE) head(y) ##plot the simulated values: plot(y) ##simulate w/conditioning variable: x <- rnorm(500) y <- lgarchSim(500, xreg=0.05*x) ##simulate from a log-GARCH with a simple form of leverage: z <- rnorm(500) zneg <- as.numeric(z < 0) zneglagged <- glag(zneg, pad=TRUE, pad.value=0) y <- lgarchSim(500, xreg=0.05*zneglagged, innovations=z) ##simulate from a log-GARCH w/standardised t-innovations: set.seed(123) n <- 500 df <- 5 z <- rt(n, df=df)/sqrt(df/(df-2)) y <- lgarchSim(n, innovations=z) ```

lgarchSim function