Nothing
par.ci <- function(data=data, seed=123, CI="AD", B=1000, N=50, a=NULL,
p.arima=NULL, q.arima=NULL, p.max=3, q.max=3,
alpha=0.05, alpha2=0.05, num.lb=10, ic="BIC", Var.Cov.eps=NULL)
{
if (!is.matrix(data)) stop("data must be a matrix")
if (ncol(data) < 2) stop("data must have at least 2 columns")
if (!is.numeric(seed)) stop ("seed must be numeric")
set.seed(seed)
if ((CI != "AD") & (CI != "B") & (CI != "all")) stop("IC=AD or IC=B or IC=all is required")
if (is.null(B)) stop ("B must not be NULL")
if (length(B) !=1) stop ("B must be an only value")
if (!is.numeric(B)) stop ("B must be numeric")
if (B<1) stop ("B must be a positive value")
if (is.null(N)) stop ("N must not be NULL")
if (length(N) !=1) stop ("N must be an only value")
if (!is.numeric(N)) stop ("N must be numeric")
if (N<0) stop ("N must be a positive value")
if ((!is.null(p.arima)) && (length(p.arima) !=1)) stop ("p.arima must be an only value")
if ((!is.null(p.arima)) && (!is.numeric(p.arima))) stop ("p.arima must be numeric")
if ((!is.null(p.arima)) && (p.arima<0)) stop ("p.arima must be a positive value")
if ((!is.null(q.arima)) && (length(q.arima) !=1)) stop ("q.arima must be an only value")
if ((!is.null(q.arima)) && (!is.numeric(q.arima))) stop ("q.arima must be numeric")
if ((!is.null(q.arima)) && (q.arima<0)) stop ("q.arima must be a positive value")
if (is.null(p.max)) stop ("p.max must not be NULL")
if (length(p.max) !=1) stop ("p.max must be an only value")
if (!is.numeric(p.max)) stop ("p.max must be numeric")
if (p.max<0) stop ("p.max must be a positive value")
if (is.null(q.max)) stop ("q.max must not be NULL")
if (length(q.max) !=1) stop ("q.max must be an only value")
if (!is.numeric(q.max)) stop ("q.max must be numeric")
if (q.max<0) stop ("q.max must be a positive value")
if (is.null(alpha)) stop ("alpha must not be NULL")
if (length(alpha) !=1) stop ("alpha must be an only value")
if (!is.numeric(alpha)) stop ("alpha must be numeric")
if ( (alpha<0) | (alpha>1) ) stop ("alpha must be between 0 and 1")
if (is.null(alpha2)) stop ("alpha2 must not be NULL")
if (length(alpha2) !=1) stop ("alpha2 must be an only value")
if (!is.numeric(alpha2)) stop ("alpha2 must be numeric")
if ( (alpha2<0) | (alpha2>1) ) stop ("alpha2 must be between 0 and 1")
if (is.null(num.lb)) stop ("num.lb must not be NULL")
if (length(num.lb) !=1) stop ("num.lb must be an only value")
if (!is.numeric(num.lb)) stop ("num.lb must be numeric")
if (num.lb<=0) stop ("num.lb must be a positive value")
if ( (ic != "BIC") & (ic != "AIC") & (ic != "AICC") ) stop("ic=BIC or ic=AIC or ic=AICC is required")
if ( (!is.null(Var.Cov.eps)) && (sum(is.na(Var.Cov.eps)) != 0) ) stop("Var.Cov.eps must have numeric values")
if ( (!is.null(Var.Cov.eps)) && (!is.matrix(Var.Cov.eps)) ) stop("Var.Cov.eps must be a matrix")
if ( (!is.null(Var.Cov.eps)) && ( (ncol(Var.Cov.eps) != nrow(data)) | (nrow(Var.Cov.eps) != nrow(data)) ) ) stop("Var.Cov.eps must have dimension n x n")
if ( (!is.null(Var.Cov.eps)) && (any(t(Var.Cov.eps) != Var.Cov.eps) ) ) stop("Var.Cov.eps must be symmetric")
n <- nrow(data)
p <- ncol(data)-1
Y <- data[, 1]
X <- data[, -1]
if (!is.matrix(X)) X <- as.matrix(X)
if (is.null(a)) {
if (p==1) a <- c(1)
else a <- c(1,rep(0,p-1))
}
else if (!is.vector(a)) stop ("a must be a vector")
else if (!is.numeric(a)) stop ("a must be numeric")
else if (p!=length(a)) stop("vector a must have length: ncol(data)-1")
beta.est <- par.est(data)
eps <- Y - X%*%beta.est
if (is.null(p.arima) && is.null(q.arima)) {
p.q <- best.arima(x=eps, order.max=c(p.max,0,q.max), include.mean=FALSE)
p_opt <- p.q[1,1]
q_opt <- p.q[1,2]
}
else if (is.null(p.arima) && !(is.null(q.arima))) {p_opt <- 0; q_opt <- q.arima}
else if (is.null(q.arima) && !(is.null(p.arima))) {q_opt <- 0; p_opt <- p.arima}
else {p_opt <- p.arima; q_opt <- q.arima}
eps.arima <- arima(x=eps, order=c(p_opt,0,q_opt), include.mean=FALSE)
# Residual analysis #########################################
if (CI=="B") {
b.pv.t <- c(rep(NA,num.lb+1))
fitdf <- sum(eps.arima$arma[1:2])
for (i in 1:num.lb)
b.pv.t[i] <- Box.test(x=residuals(eps.arima), lag = fitdf+i, type = "Ljung-Box", fitdf = fitdf)$p.value
b.pv.t[i+1] <- t.test(residuals(eps.arima), mu=0)$p.value
if (min(b.pv.t)<alpha2)
cat("The fitted ARMA model could be not appropriate", "\n")
} # ###########################################################
if ((CI=="AD") | (CI=="all")) {
# ###########################################################
# Asymptotic distribution
if (is.null(Var.Cov.eps)) {
Var.Cov.eps <- matrix(NA, n, n)
Var.Cov.mat <- var.cov.matrix(x=eps, n=n, p.max=p.max, q.max=q.max, ic=ic, p.arima=p_opt, q.arima=q_opt, alpha=alpha2, num.lb=num.lb)
Var.Cov.eps <- Var.Cov.mat[[1]]
ad.pv.Box.test <- Var.Cov.mat[[2]]
ad.pv.t.test <- Var.Cov.mat[[3]]
}
X.X <- t(X)%*%X
X.X.1 <- solve(X.X)
A <- n*X.X.1%*%t(X)%*%Var.Cov.eps%*%X%*%X.X.1
Dt <- sqrt((t(a)%*%A%*%a)/n)
z.quantile <- qnorm(1-alpha/2)
ci_inf_ad <- t(a)%*%beta.est - z.quantile * Dt
ci_sup_ad <- t(a)%*%beta.est + z.quantile * Dt
} # ###########################################################
if ((CI=="B") | (CI=="all")) {
if (p_opt==0) ar.coef <- 0
else ar.coef <- as.numeric(eps.arima$coef[1:p_opt])
if (q_opt==0) ma.coef <- 0
else ma.coef <- as.numeric(eps.arima$coef[(p_opt+1):(p_opt+q_opt)])
white.noise <- eps.arima$residuals
white.noise <- white.noise[(p_opt+1):n]
white.noise <- white.noise-mean(white.noise)
beta.est.boots <- matrix(NA,B,p)
for (m in 1:B) {
white.noise.sample <- sample(white.noise, size=n+N, replace=TRUE)
fi <- c(rep(NA,N+1))
fi[1] <- 1
fi[-1] <- ARMAtoMA(ar=ar.coef, ma=ma.coef, lag.max=N)
fi <- rev(fi)
eps.boots <- c(rep(NA,n))
for (i in 1:n) {
eps.ij.boots <- white.noise.sample[i:(i+N)]
eps.boots[i] <- fi%*%eps.ij.boots
}
Y.boots <- X%*%beta.est + eps.boots
data.boots <- cbind(Y.boots,X)
beta.est.boots[m,] <- par.est(data.boots)
}
beta.est <- as.vector(beta.est)
dif.beta <- t(beta.est.boots)-beta.est
z <- sqrt(n)*t(a)%*%dif.beta
z.quantile1 <- quantile(z,1-alpha/2)
z.quantile2 <- quantile(z,alpha/2)
ci_inf_b <- a%*%beta.est - (1/sqrt(n))*z.quantile1
ci_sup_b <- a%*%beta.est - (1/sqrt(n))*z.quantile2
}
if (CI=="B") list(Bootstrap=data.frame(ci_inf=ci_inf_b, ci_sup=ci_sup_b, p_opt=p_opt, q_opt=q_opt), pv.Box.test=b.pv.t[-num.lb+1], pv.t.test=b.pv.t[num.lb+1])
else if (CI=="AD") list(AD=data.frame(ci_inf=ci_inf_ad, ci_sup=ci_sup_ad, p_opt=p_opt, q_opt=q_opt), pv.Box.test=ad.pv.Box.test, pv.t.test=ad.pv.t.test)
else if (CI=="all") list(Bootstrap=data.frame(ci_inf=ci_inf_b, ci_sup=ci_sup_b, p_opt=p_opt, q_opt=q_opt),AD=data.frame(ci_inf=ci_inf_ad, ci_sup=ci_sup_ad, p_opt=p_opt, q_opt=q_opt), pv.Box.test=ad.pv.Box.test, pv.t.test=ad.pv.t.test)
}
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