1d:T737,# Calculation of functional correlation between two simultaneously observed processes. ```r FCCor( x, y, Lt, bw = stop("bw missing"), kern = "epan", Tout = sort(unique(unlist(Lt))) ) ``` ## Arguments - `x`: A list of function values corresponding to the first process. - `y`: A list of function values corresponding to the second process. - `Lt`: A list of time points for both `x` and `y`. - `bw`: A numeric vector for bandwidth of length either 5 or 1, specifying the bandwidths for E(X), E(Y), var(X), var(Y), and cov(X, Y). If `bw` is a scalar then all five bandwidths are chosen to be the same. - `kern`: Smoothing kernel for mu and covariance; "rect", "gauss", "epan", "gausvar", "quar" (default: "gauss") - `Tout`: Output time points. Default to the sorted unique time points. ## Returns A list with the following components: - **corr**: A vector of the correlation corr(X(t), Y(t)) evaluated at `Tout`. - **Tout**: Same as the input Tout. - **bw**: The bandwidths used for E(X), E(Y), var(X), var(Y), and cov(X, Y). ## Details `FCCor` calculate only the concurrent correlation corr(X(t), Y(t)) (note that the time points t are the same). It assumes no measurement error in the observed values. ## Examples ```r set.seed(1) n <- 200 nGridIn <- 50 sparsity <- 1:5 # must have length > 1 bw <- 0.2 kern <- 'epan' T <- matrix(seq(0.5, 1, length.out=nGridIn)) ## Corr(X(t), Y(t)) = 1/2 A <- Wiener(n, T) B <- Wiener(n, T) C <- Wiener(n, T) + matrix((1:nGridIn) , n, nGridIn, byrow=TRUE) X <- A + B Y <- A + C indEach <- lapply(1:n, function(x) sort(sample(nGridIn, sample(sparsity, 1)))) tAll <- lapply(1:n, function(i) T[indEach[[i]]]) Xsp <- lapply(1:n, function(i) X[i, indEach[[i]]]) Ysp <- lapply(1:n, function(i) Y[i, indEach[[i]]]) plot(T, FCCor(Xsp, Ysp, tAll, bw)[['corr']], ylim=c(-1, 1)) abline(h=0.5) ```1e:T49a,M7.49933 0.25C3.49635 0.25 0.25 3.49593 0.25 7.50024C0.25 10.703 2.32715 13.4206 5.2081 14.3797C5.57084 14.446 5.70302 14.2222 5.70302 14.0299C5.70302 13.8576 5.69679 13.4019 5.69323 12

FCCor function