# Multiple change point detection and variable selection for nonstationary time series models. This function provides a novel and fast methodology for simultaneous multiple structural break estimation and variable selection for nonstationary time series models by using ASCAD or AMCP to estimate the chang-points proposed by Jin, Shi and Wu (2011). ```r cpvnts(Y, method = c("mcp", "scad"), p, lam.d) ``` ## Arguments - `Y`: an autoregressive time series. - `method`: the method to be used by mcp or scad. See `ncvreg` in R packages `ncvreg` for details. - `p`: an upper bound of autoregressive orders. - `lam.d`: an parameter of the refining procedure. Suggest lam.d=0.05 if the length of Y is smaller than 5000 and lam.d=0.01 otherwise. ## Returns cpvnts returns an object of class "cpvnts". An object of class "cpvnts" is a list containing the following components: - **variable.selection**: a matrix of variable selection. Element of the matrix is 1 if the variable is selected and 0 otherwise. - **change.points**: estimators of change points. ## Examples ```r ### Example 1: No change point with sample size 1000### n <- 1000 Y <- rnorm(n) cp1 <- c(3, 1000) a0 <- c(0.7) a1 <- c(1.3) a2 <- c(-0.8) for (j in 2:2) { for (i in (cp1[j - 1] + 1):cp1[j]) { Y[i] <- a0[j - 1] + a1[j - 1] * Y[i - 1] + a2[j - 1] * Y[i - 2] + rnorm(1) } } ts.plot(Y) # Y(t)=0.7+1.3Y(t-1)-0.8Y(t-2)+e(t) mcp.cp <- cpvnts(Y, "mcp", 4, 0.05) mcp.cp #result of AMCP scad.cp <- cpvnts(Y, "scad", 4, 0.05) scad.cp #result of ASCAD ### Example 2(Davis et al (2006)):Two change points with sample size ### 1024## n <- 1024 Y <- rnorm(n) cp1 <- c(3, 512, 769, 1024) a1 <- c(0.9, 1.69, 1.32) a2 <- c(0, -0.81, -0.81) for (j in 2:4) { for (i in (cp1[j - 1] + 1):cp1[j]) { Y[i] <- a1[j - 1] * Y[i - 1] + a2[j - 1] * Y[i - 2] + rnorm(1) } } ts.plot(Y) # Y(t)=0.9Y(t-1)+e(t),if t<512 Y(t)=1.69Y(t-1)-0.81Y(t-2)+e(t), if # 512

cpvnts function