# Bootstrap for stochcorr `stoch.bootstrap` returns the Bootstrap confidence interval for estimated rho from `stochcorr`. ```r stoch.bootstrap(est, S_1, S_2, boot_iter=500, p=0.05, seed = NULL) ``` ## Arguments - `est`: object of class `cbm` or `vmp` - `S_1`: historical price of the first asset - `S_2`: historical price of the second asset - `boot_iter`: number of bootstrap iteration (Default is 500) - `p`: 1-p% confidence interval (Default is 0.05) - `seed`: (optional) seed value ## Returns Returns a matrix for the bootstrap (1-p)% confidence interval for rho. The first row of the matrix is the lower bound and the second row is the upper bound. ## Details This function returns a p% confidence interval for estimated rho from `stochcorr` using parametric bootstrap. See section 4 of Majumdar and Laha (2024) [doi:10.48550/arXiv.2412.06343](doi:10.48550/arXiv.2412.06343). ## Examples ```r library(stochcorr) data("nse2020") ## using von Mises process as the correlation process a <- stochcorr(nse2020$`USD/INR`, nse2020$Nifty, 1 / 250, corr_process = "vmp") b <- stoch.bootstrap(a, nse2020$`USD/INR`, nse2020$Nifty, seed = 100) rho_data <- as.data.frame(cbind(a$rho, nse2020$Date)) rho_data[, 2] <- as.Date(rho_data[, 2], origin = "1970-01-01") colnames(rho_data) <- c("Correlation", "Time") if(requireNamespace("ggplot2")){ library(ggplot2) ggplot2::ggplot(rho_data, aes(x = Time, y = Correlation)) + theme_test() + theme( text = element_text(size = 15), axis.text.x = element_text(angle = 90, hjust = 1) ) + geom_line() + geom_ribbon(aes(ymin = b[1, ], ymax = b[2, ]), fill = "blue", alpha = 0.15) + scale_y_continuous(breaks = round(seq(-1, 1, by = 0.05), 1)) + scale_x_date(breaks = "1 month", date_labels = "%B %Y") } ## using Circular Brownian Motions as the correlation process a <- stochcorr(nse2020$`USD/INR`, nse2020$Nifty, 1 / 250, corr_process = "cbm") b <- stoch.bootstrap(a, nse2020$`USD/INR`, nse2020$Nifty, seed = 100) rho_data <- as.data.frame(cbind(a$rho, nse2020$Date)) rho_data[, 2] <- as.Date(rho_data[, 2], origin = "1970-01-01") colnames(rho_data) <- c("Correlation", "Time") if(requireNamespace("ggplot2")){ library(ggplot2) ggplot2::ggplot(rho_data, aes(x = Time, y = Correlation)) + theme_test() + theme( text = element_text(size = 15), axis.text.x = element_text(angle = 90, hjust = 1) ) + geom_line() + geom_ribbon(aes(ymin = b[1, ], ymax = b[2, ]), fill = "blue", alpha = 0.15) + scale_y_continuous(breaks = round(seq(-1, 1, by = 0.05), 1)) + scale_x_date(breaks = "1 month", date_labels = "%B %Y")} ``` ## See Also `stochcorr()`

stoch.bootstrap function