# Core change point detection algorithm (given known parameters) Implements the core step of the proposed change point detection (CPD) algorithm to estimate the locations of change points, given the inverse windowed covariance $\Sigma_{\mathrm{ALL}}^{*-1}$. The method computes detector statistics over a moving window using a projection-based quadratic form and identifies candidate change points via peak detection. ```r FluxPoint_raw(data, Sig_all_inv, w, D, needReproduce = FALSE) ``` ## Arguments - `data`: Numeric matrix of dimension $n \times p$, the multivariate time series. - `Sig_all_inv`: Numeric matrix of dimension $(p w) \times (p w)$, the inverse of the combined covariance $\Sigma_{\mathrm{ALL}}^*$ (accounts for random walk and VAR(1) effects within a window of size $w$). - `w`: Integer; window size used in the moving-window detection step. - `D`: Numeric; detection threshold used in the peak-finding step. - `needReproduce`: Logical; if `TRUE`, a fixed fold assignment is used in cross-validation to ensure reproducibility (default `FALSE`). ## Returns A list with: * `shiftIndices` — Binary matrix ($n \times p$) indicating selected components at each index. * `detectorStats` — Numeric vector of detector values over time. * `Projection_list` — Cache of projection matrices by active-set pattern. * `cps` — Indices of detected change points. ## Details For each center index $k$, a window of width $w$ is formed and contrast vectors are constructed to compare the first and second halves of the window. Before computing the detector statistic, a component-selection step is performed using an $\ell_1$-penalized regression (lasso, via `glmnet`) with weights $\Sigma_{\mathrm{ALL}}^{*-1}$ to identify variables that exhibit a shift. The resulting active set determines the projection used in the statistic. Sparse projection matrices indexed by the active-set pattern are cached and reused for computational efficiency. The detector statistic is defined as a weighted quadratic form measuring deviation from the baseline (no-change) projection, and locations at which the statistic exceeds the threshold `D` are declared as estimated change points. ## Examples ```r ## Minimal runnable example (fast) set.seed(123) p <- 1 mu0 <- rep(0, p) deltas <- list(c(3), c(4)) Sig_eta <- diag(0.01, p) Sig_nu <- random_Signu(p, 0) Phi <- random_Phi(p, 0) Sig_e1 <- get_Sig_e1_approx(Sig_nu, Phi) # Simulate data with two evenly spaced change points Y <- generate_data(mu0, deltas, Sig_eta, Sig_nu, Phi, Sig_e1, errortype = "n", number_cps = 2, lengthofeachpart = 100) # Windowed covariance and its inverse w <- 20 Sigs <- get_Sigs(w, p, Sig_eta, Sig_nu, Phi, Sig_e1) Sig_all_inv <- Sigs$Sig_all_inv # Run detector with a common threshold choice n <- nrow(Y) D <- min(4, log(exp(2) + p)) * log(n - w) res <- FluxPoint_raw(Y, Sig_all_inv, w, D) res$cps ## More realistic example (may take longer) set.seed(123) p <- 3 mu0 <- rep(0, p) deltas <- list(c(3, 0, -3), c(0, -2, 4)) Sig_eta <- diag(0.01, p) Sig_nu <- random_Signu(p, 0) Phi <- random_Phi(p, p) Sig_e1 <- get_Sig_e1_approx(Sig_nu, Phi) Y <- generate_data(mu0, deltas, Sig_eta, Sig_nu, Phi, Sig_e1, errortype = "n", number_cps = 2, lengthofeachpart = 100) w <- 20 Sigs <- get_Sigs(w, p, Sig_eta, Sig_nu, Phi, Sig_e1) Sig_all_inv <- Sigs$Sig_all_inv n <- nrow(Y) D <- min(4, log(exp(2) + p)) * log(n - w) res <- FluxPoint_raw(Y, Sig_all_inv, w, D) res$cps ```

FluxPoint_raw function