What should I do with structural breaks at return time series?- R

Question

Let say I have the below time series data(It is a return data of a financial derivative):

x<-structure(c(-0.030727, -0.009815, -0.001215, 0.010281, -0.03471, 
            0.01946, -0.027811, -0.002559, -0.001176, 8.3e-05, 0.026288, 
            -0.015959, 0.010825, -0.022024, 0.008582, 0.023524, 0.00139, 
            -0.022638, -0.002818, 0.00118, -0.033008, -0.018363, -0.003505, 
            0.003468, -0.003918, 0.016427, 0.022444, 0.021874, -0.010313, 
            0.003757, 0.014585, -0.014774, 0.008629, 0.008678, 0.001803, 
            -0.007109, 0.028474, 0.002943, 0.00085, 0.002037, -0.001861, 
            -0.012703, 0.005483, -0.002618, 0.018344, 0.000381, -0.00456, 
            0.007437, 0.002311, 0.004317, 0.002753, 0.002656, -0.011011, 
            0.000973, -0.001407, 0.016608, 0.004667, 0.000115, 0.009135, 
            -0.004638, -0.009834, 0.015728, -0.014812, 0.000478, -0.003571, 
            0.007973, 0.015343, -0.000309, -0.001552, 0.004405, -0.003978, 
            0.001578, -0.000453, -0.008051, -0.00213, -0.001535, -0.005156, 
            -0.011967, -0.006248, 0.008804, -0.01135, -0.007921, -0.001811, 
            0.004035, 0.002962, 0.012483, -0.01028, -0.004919, -0.004157, 
            0.012173, -0.012587, 0.004948, -0.005627, 0.012029, -0.000793, 
            0.019795, 0.006935, 0.001405, 0.006452, 0.002945, 0.000848, 0.003851, 
            -0.005818, 0.005285, -0.001402, 0.002595, -0.003226, -0.013005, 
            -0.009465, -0.001009, -0.001781, 0.002064, -0.009244, 0.007651, 
            0.001353, -0.002158, 0.015749, -0.042023, -0.024412, 0.020984, 
            0.018452, 0.013183, 0.004101, -0.008192, 0.00749, 0.003626, 0.016261, 
            0.006411, 0.006828, -0.003408, 0.005644, -0.000888, 0.005194, 
            -0.003846, 0.010579, -0.003154, 0.005162, -0.000496, 0.002433, 
            0.005807, 0.002947, 0.001386, 0.004266, -0.009004, 0.004275, 
            0.001261, 0.010565, -0.00153, 0.002364, -0.004008, 0.004566, 
            0.000858, 0.005551, -0.006656, 0.000297, 0.002195, -0.000338, 
            0.001187, 0.002947, -0.008091, -0.001053, 0.001288, 0.002566, 
            -0.001787, -0.001872, 0.00268, 0.004331, 0.004942, 0.001519, 
            -0.004638, -0.025724, 0.016634, -0.010927, 0.003586, 0.014567, 
            -0.000976, -0.001821, 0.001207, 0.010218, 0.008339, -0.006345, 
            -0.009137, 0.00913, 0.002417, -0.009332, 0.008099, -0.002097, 
            -0.002117, 0.004971, -0.001726, -0.002727, 0.00683, -0.015485, 
            -0.001482, -0.004916, 0.000159, -0.002754, 0.00843, 0.00049, 
            -0.000873), tsp = c(1, 200, 1))

I want to determine whether there is stuctural change at the time series.

First, I determine the arima model using auto.arima procedure.

Then I apply the below ols-cusum procedure to determine the whether there is a structural break:

https://stats.stackexchange.com/questions/104324/strucchange-package-on-arima-model

The code is below:

z<-auto.arima(x, max.p = 3, max.q=3)
fit <- arima(z, order = c(1,0,0), include.mean = FALSE)
e <- residuals(fit)
sigma <- sqrt(fit$sigma2)
n <- length(x)
cs <- cumsum(e) / sigma
retval <- list()
retval$coefficients <- coef(fit)
retval$sigma <- sigma
retval$process <- cs
retval$type.name <- "OLS-based CUSUM test"
retval$lim.process <- "Brownian bridge"
retval$datatsp <- tsp(50)
class(retval) <- c("efp")
plot(retval)

The result is as below:

Plot shows that there are structural breaks at the data.

It seemd to me strange. I wonder how to fit an arima model to this data without structural breaks. How should I deal with this data?

Thanks a lot.

What should I do with structural breaks at return time series?- R

0 Answers0