# Compose and Decompose MAR(1)S Process `compose.mar1s` composes MAR(1)S process realization by given vector of log-innovations. `decompose.mar1s` extracts MAR(1)S process components from time series. ```r compose.mar1s(object, loginnov, start.time = head(time(loginnov), 1), xreg.absdata = NULL, init.absdata = NULL) decompose.mar1s(object, absdata, start.time = head(time(absdata), 1), init.absdata = rep(NA, NCOL(absdata))) ``` ## Arguments - `object`: An object of class `"mar1s"` specifying the model parameters. - `loginnov`: A univariate time series containing the log-innovations. - `absdata`: A univariate or multivariate time series containing the process realization. - `start.time`: The sampling time for the first simulation step. - `xreg.absdata`: A matrix-like object with row count = `n.ahead`, specifying the values for the external regressors. If `NULL`, default values are used. - `init.absdata`: A vector specifying the initial values of the process. If `NULL`, default values are used. ## Details Multiplicative AR(1) with Seasonal (MAR(1)S) process is defined as $$ x_t = exp(s_t + y_t)%\code{x[t] = exp(s[t] + y[t])} $$ $$ y_{t, 1} = b_1 y_{t, 2} + \dots + b_k y_{t, k + 1} + z_t%\code{y[t, 1] = b[1]*y[t, 2] + \dots + b[k]*y[t, k + 1] + z[t]} $$ $$ z_t = a z_{t-1} + e_t%\code{z[t] = a*z[t-1] + e[t]} $$ where $s[t]$ is the log-seasonal component, $y[t]$ is the AR(1) (log-stochastic) component, $e[t]$ is the log-residuals (random component). ## Returns - **absdata**: Realization of the process (a univariate or multivariate time series object). - **logdata**: Logarithm of `absdata` (a univariate or multivariate time series object). - **logstoch**: Log-stochastic component (a univariate or multivariate time series object). - **logresid**: Random component (a univariate time series object). ## Note `decompose.mar1s` and `fit.mar1s` compute the random component in different ways: `decompose.mar1s` uses `filter` while `fit.mar1s` saves the residuals returned by `arima`. The results may be different in: - **the first value:**: `decompose.mar1s` uses specified `init.absdata` while `arima` always assumes zero initial values for the fitted process; - **non-finite values:**: `decompose.mar1s` handles non-finite values more accurately. ## See Also `compose.ar1` for the AR(1) with external regressors processes, `fit.mar1s` for fitting MAR(1)S process to data, `sim.mar1s` for MAR(1)S process simulation and prediction. ## Examples ```r data(forest.fire, package = "mar1s") data(nesterov.index, package = "mar1s") ## Simple mar1s <- fit.mar1s(window(forest.fire, 1969, 1989)) x <- ts(rnorm(365, sd = mar1s$logresid.sd), start = c(1989, 1)) plot(compose.mar1s(mar1s, x)$absdata) decomp <- decompose.mar1s(mar1s, mar1s$decomposed$absdata) delta <- abs(nan2na(mar1s$decomposed$logresid) - nan2na(decomp$logresid)) stopifnot(all(na.exclude(tail(delta, -1)) < 1E-6)) ## External regressors mar1s <- fit.mar1s(window(forest.fire, 1969, 1989), window(nesterov.index[, "mean"], 1969, 1989)) x <- rnorm(365, sd = mar1s$logresid.sd) xreg <- window(nesterov.index[, "mean"], 1989.001, 1990) plot(compose.mar1s(mar1s, x, c(1989, 1), xreg)$absdata) decomp <- decompose.mar1s(mar1s, mar1s$decomposed$absdata) delta <- abs(mar1s$decomposed$logstoch - decomp$logstoch) stopifnot(all(na.exclude(delta) < 1E-6)) delta <- abs(nan2na(mar1s$decomposed$logresid) - nan2na(decomp$logresid)) stopifnot(all(na.exclude(tail(delta, -1)) < 1E-6)) ```

compose.mar1s function