# Two stage multiple change point detection in linear models. This function provides a two‐stage procedure for simultaneously detecting multiple change‐points in linear models. In the cutting stage, the change‐point problem is converted into a model selection problem so that a modern model selection method can be applied. In the refining stage, the change‐points obtained in the cutting stage are finalized via a refining method. The tuning parameter lambda is chosen by BIC. ```r tsmcplm(Y, X, method = c("lasso", "adapt", "mcp", "scad"), c) ``` ## Arguments - `Y`: an response vector. - `X`: the n-by-p design matrix. - `method`: the method to be used by lasso, adaptive lasso, mcp or scad. - `c`: ceiling(c*sqrt(length(Y))) is the length of each segments in spliting stage. ## Returns tsmcplm returns an object of class "tsmcplm". An object of class "tsmcplm" is a list containing the following components: - **change.points**: estimators of change points. ## Examples ```r ## example 1 : mean shift model ## true change point location: ## 100, 130, 150, 230, 250, 400, 440, 650, 760, 780, 810 Y <- rnorm(1000, 0, 0.5) + c(rep(0,100), rep(4,30),rep(-1,20), rep(2,80), rep(-2,20), rep(3,150), rep(-1, 40), rep(1,210), rep(5,110), rep(2,20), rep(7,30), rep(3,190)) ts.plot(Y) ##estimate change points tsmcplm(Y = Y, X = NULL, method = "adapt", c = 0.3) ## example 2: linear model: ## a periodic auto correlation series with period 122 and ## order of auto correlation 1 ### ## true change point location: ## 200, 350, 450, 550, 700, and 850 n=1000 y <- rnorm(n) for (t in 2:n) { y[t] <- cos(t*pi/61) + 3*sin(t*pi/61) + 0.5*y[t-1] + (2*sin(t*pi/61) + 0.1 * y[t-1])*(200 < t)+ (2* cos(t*pi/61) - 4 *sin(t*pi/61) - 0.6* y[t-1] )*(350 < t) + (2* sin(t*pi/61) + 0.7* y[t-1] )*(450 < t) + (-3* sin(t*pi/61) - 0.3* y[t-1] )*(550 < t) + (-3* cos(t*pi/61) + 5* sin(t*pi/61))* (700 < t) + (3* cos(t*pi/61) - 5* sin(t*pi/61) - 0.4*y[t-1] )* (850 < t) + rnorm(1) } ts.plot(y) x <- sapply(2:n, function(t){cbind(cos(t*pi/61), sin(t*pi/61), y[t-1])}, simplify = FALSE) x <- do.call(rbind, x) tsmcplm(Y = y[-1], X = x, method = "adapt", c = 2) ``` ## References Jin, B., Wu, Y., & Shi, X. (2016). Consistent two‐stage multiple change‐point detection in linear models. **Canadian Journal of Statistics**, 44(2), 161-179. ## See Also ncvreg lars

tsmcplm function