1d:T7cf,# Estimate fluctuating mean segmentwise given detected change points Estimates the fluctuating mean sequence $\{\boldsymbol{\mu}_t\}_{t=1}^n$ segmentwise by applying the maximum likelihood estimation (MLE) procedure within each segment defined by detected change points. ```r estimate_musseg(data, cps, Sig_eta, Sig_nu, Phi, Sig_e1) ``` ## Arguments - `data`: Numeric matrix of dimension $n \times p$, representing the multivariate time series $\{\mathbf{y}_t\}_{t=1}^n$. - `cps`: Numeric vector of detected change point locations (sorted indices). - `Sig_eta`: Numeric $p \times p$ covariance matrix $\Sigma_{\boldsymbol{\eta}}$ of the random walk innovation. - `Sig_nu`: Numeric $p \times p$ covariance matrix $\Sigma_{\boldsymbol{\nu}}$ of the VAR(1) innovation. - `Phi`: Numeric $p \times p$ autoregressive coefficient matrix $\Phi$. - `Sig_e1`: Numeric $p \times p$ initial-state covariance matrix $\Gamma_{\boldsymbol{\epsilon}}(0)$. ## Returns A numeric matrix of dimension $n \times p$, containing the estimated fluctuating mean sequence across all segments. ## Details The time series is partitioned into contiguous segments defined by the specified change points. Within each segment, `estimate_mus` is applied to obtain the maximum likelihood estimate of the fluctuating mean sequence for that interval. The resulting segment-wise estimates are then concatenated to form a complete piecewise estimate of $\boldsymbol{\mu}_t$ over the entire time series. ## Examples ```r set.seed(123) p <- 3 mu0 <- rep(0, p) deltas <- list(c(3, 0, -3), c(-2, 4, 0)) 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) # Generate data and estimate mean segmentwise after known CPs Y <- generate_data(mu0, deltas, Sig_eta, Sig_nu, Phi, Sig_e1, errortype = "n", number_cps = 2, lengthofeachpart = 100) cps <- c(100, 200) mu_seg <- estimate_musseg(Y, cps, Sig_eta, Sig_nu, Phi, Sig_e1) dim(mu_seg) ```

estimate_musseg function