1d:T7e2,# AR1 Transformer Function The transformer function takes a `bamlss.frame` object and transforms the response and the design matrices to account for lag 1 autocorrelation. The method is also known as Prais-Winsten estimation. ```r trans_AR1(rho = 0.1) AR1(rho = 0.1) ``` ## Arguments - `rho`: Specifies the correlation parameter at lag 1. ## Returns A transformer function which can be used in the `bamlss` call. ## References Johnston, John (1972). Econometric Methods (2nd ed.). New York: McGraw-Hill. pp. 259--265. ## See Also `bamlss.frame`, `bamlss`, `smooth2random`. ## Examples ```r ## Not run: ## Simulate AR1 data. set.seed(111) n <- 240 d <- data.frame("t" = 1:n) ## Nonlinear function. f <- function(x) { 2 + sin(x / n * 2 * pi - pi) } ## Correlated errors. rho <- 0.8 e <- rnorm(n, sd = 0.1) u <- c(e[1], rep(NA, n - 1)) for(i in 2:n){ u[i] <- rho * u[i - 1] + e[i] } ## Response. d$y <- f(d$t) + u ## Plot time-series data. plot(d, type = "l") ## Estimate models without and with AR1 transformation. b0 <- bamlss(y ~ s(t,k=20), data = d, criterion = "BIC") b1 <- bamlss(y ~ s(t,k=20), data = d, criterion = "BIC", transform = AR1(rho = 0.8)) ## Estimate full AR1 model. b2 <- bamlss(y ~ s(t,k=20), data = d, criterion = "BIC", family = "AR1") rho <- predict(b2, model = "rho", type = "parameter") print(range(rho)) ## Estimated standard deviations. sd0 <- predict(b0, model = "sigma", type = "parameter") sd1 <- predict(b1, model = "sigma", type = "parameter") sd2 <- predict(b2, model = "sigma", type = "parameter") print(round(c(sd0[1], sd1[1], sd2[1]), 2)) ## Plot fitted trends. p0 <- predict(b0, model = "mu") p1 <- predict(b1, model = "mu") p2 <- predict(b2, model = "mu") plot(d, type = "l") lines(f(d$t) ~ d$t, col = 2, lwd = 2) lines(p0 ~ d$t, col = 4, lwd = 2) lines(p1 ~ d$t, col = 3, lwd = 3) lines(p2 ~ d$t, col = 5, lwd = 3) legend("topleft", c("no trans", "with trans", "AR1 model", "truth"), lwd = 2, col = c(4, 3, 5, 2), bty = "n") ## End(Not run) ```

AR1_transform function