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functions.R
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functions.R
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# Rho estimation for AR1
rho_ar1 <- function(y) {
n <- length(y)
sum(y[2:n] * y[1:(n - 1)]) / sum(y[2:(n - 1)]^2)
}
# Rho estimation for AR2
rho_ar2 <- function(y) {
n <- length(y)
mat1 <- matrix(ncol = 2, nrow = 2)
mat1[1, 1] <- sum(y[2:(n - 1)]^2)
mat1[2, 1] <- mat1[1, 2] <- sum(y[3:(n - 1)] * y[2:(n - 2)])
mat1[2, 2] <- sum(y[3:(n - 2)]^2)
mat2 <- matrix(ncol = 1, nrow = 2)
mat2[1, 1] <- sum(y[2:n] * y[1:(n - 1)])
mat2[2, 1] <- sum(y[3:n] * y[1:(n - 2)])
solve(mat1) %*% mat2
}
restrict_parameters <- function(rho) {
for (i in seq_len(length(rho))) {
if (rho[i] > 1) {
rho[i] <- 1
}
if (rho[i] < -1) {
rho[i] <- -1
}
}
return(rho)
}
# Rho estimation for AR with order p
rho_arp <- function(y, order) {
n <- length(y)
mat1 <- matrix(ncol = order, nrow = order)
mat2 <- matrix(ncol = 1, nrow = order)
mat1[1, 1] <- sum(y[2:(n - 1)]^2)
for (i in 1:order) {
for (j in (i + 1):order) {
t1 <- (2 * order - 1)
t2 <- (2 * order)
if (i < order) {
mat1[i, i] <- sum(y[(t1 - order + 1):(n - order + 1)]^2)
mat1[i, j] <- mat1[j, i] <-
sum(y[(t2 - order + 1):(n - order + 1)] *
y[(t2 - order):(n - order)])
}else {
mat1[i, i] <- sum(y[t1:(n - order)]^2)
}
}
mat2[i, 1] <- sum(y[(i + 1):n] * y[1:(n - i)])
}
restrict_parameters((solve(mat1) %*% mat2))
}
pw_transform <- function(data, rho) {
rho <- unlist(rho)
data_t <- as.matrix(data)
order <- length(rho)
for (i in seq_len(order)) {
n <- nrow(data_t)
data_t <- data_t[(i + 1):n, ] - c(rho[i]) * data_t[1:(n - i), ]
}
as.data.frame(data_t)
}
get_bic <- function(model, order) {
df_ll <- order + length(model$coef) + 1
n <- length(model$residuals)
w <- rep(1, n)
res <- model$residuals
ll <- 0.5 * (sum(log(w)) - n *
(log(2 * pi) + 1 - log(n) +
log(sum(w * res^2))))
(-2 * ll + log(n) * df_ll)
}
prais_winsten <- function(formula, data,
response, predictors, order, tol = 1e-5) {
update <- TRUE
names <- 0
niter <- 1
while (update) {
if (niter > 1) {
data_t <- pw_transform(data, rho[niter, ])
} else {
data_t <- data
}
temp_mod <- lm(as.formula(formula), data = data_t)
if (niter > 1) {
temp_mod$coefficients[1] <- mean(response - c(temp_mod$coefficients[-1])*predictors)
}
res <- predict(temp_mod, as.data.frame(predictors)) - response
rho_est <- unlist(unname(ar(res, aic = FALSE, order.max = order)[2]))
rho_est <- data.frame(t(rho_est))
if (niter <= 1) { # initialize dataframe with rho values
rho <- data.frame(matrix(data = 0, ncol = length(rho_est)))
for (i in seq_len(ncol(rho))) {
names[i] <- paste("rho_", as.character(i), sep = "")
}
colnames(rho) <- names
}else { # check for convergence and update dataframe
for (i in seq_len(nrow(rho))) {
if (all(abs(rho_est - rho[i, ]) < tol)) {
update <- FALSE
}
}
}
colnames(rho_est) <- names
rho <- rbind(rho, rho_est)
niter <- niter + 1
}
bic <- get_bic(temp_mod, ncol(rho))
colnames(rho) <- names
list(rho = rho[-nrow(rho), ],
model = temp_mod,
BIC = bic)
}