BP_estim {memochange}

Breakpoint estimators for a change in persistence

Description

This function estimates the location where the investigated time series exhibits a break in persistence. It requires knowledge of the direction of the break, i.e. an increase or decrease in persistence. This needs to be determined beforehand using one of the various persistence change tests provided in this package.

Usage

BP_estim(x, trend = c("none", "linear"), tau = 0.2, type = c("BT",
  "LKT", "LKSN", "MR"), direction = c("01", "10"), d_estim = c("ELW",
  "GPH"), d_bw = 0.7, m = 0, serial = c(FALSE, TRUE))

Arguments

x

the univariate numeric vector to be investigated. Missing values are not allowed.

trend

whether the time series exhibits a trend, "none" implies no trend and "linear" implies a linear trend.

tau

the function searches in the interval [T*tau,T*(1-tau)] for a break in persistence with T being the length of the time series. It must hold that 0<tau<0.5, default is tau=0.2 as commonly used in the literature. Note that if type="BT" and T*tau<=2+ as.numeric(trend=="linear"), type="LT" and T*tau<=2+ as.numeric(trend=="linear") + (m>3)*(m-3), type="LKSN" and T*tau<=10, or type="MR" and T*tau<=2+(p>1)*pthe break point cannot be found.

type

which type of break point estimator should be used, "LKSN" for the estimator by Leybourne, Kim, Smith, and Newbold (2003), "BT" for the estimator by Busetti and Taylor (2004), "LKT" for the estimator by Leybourne, Kim, and Taylor (2006), and MR for the estimator by Martins and Rodrigues (2014). See details.

direction

direction of the change in persistence, "01" implies an increase in persistence over time and "10" a decrease. See details.

d_estim

which estimator should be used to determine the order of integration in the two regimes, "GPH" corresponds to the estimator by Geweke and Porter-Hudak (1983) and "ELW" corresponds to the exact local Whittle estimator by Shimotsu and Phillips (2005).

d_bw

bandwidth used for estimating the order of integration d. Default is d_bw=0.7. Note that the estimation of the memory parameter can only be performed for 0<d_bw<=1 and it is even recommended to choose 0.5<=d_bw<=0.8 as otherwise the estimators might be inconsistent.")

m

Number of covariances used for the estimation of the long run variance when considering the LKT estimator. Default is m=0.

serial

boolean, indicating whether to account for serial correlation of the errors when considering the MR estimator. Default is serial=FALSE implying no correction for serial correlation.

Details

The estimators BT and LKSN are only consistent for changes from I(0) to I(1) or vice versa, the LKT estimator is consistent for changes from stationary to nonstationary memory or vice versa (cf. also Sibbertsen and Kruse (2009)), and the MR estimator is consistent for changes in d in general.

Value

Returns a list that contains break point, estimate of the order of integration in the two regimes (the memory parameter d) and standard deviation of this estimate.

Author(s)

Janis Becker

References

Leybourne, S., Kim, T., Smith, V., and Newbold, P. (2003): Tests for a change in persistence against the null of difference-stationarity. Econometrics Journal, 6, pp. 291-311.

Busetti, F. and Taylor, R. (2004): Tests of stationarity against a change in persistence. Journal of Econometrics, 123, pp. 33-66.

Leybourne, S., Kim, T., and Taylor, R. (2007): Cusum of squares-based tests for a change in persistence. Journal of Time Series Analysis, 28, pp. 408-433.

Martins, L.. and Rodrigues, P. (2014): Testing for persistence change in fractionally integrated models: An application to world inflation rates Cusum of squares-based tests for a change in persistence. Computational Statistics and Data Analysis, 76, pp. 502-522.

See Also

cusum_test, LKSN_test, MR_test, ratio_test.

Examples

set.seed(410)

# generate dummy-data
series <- c(rnorm(200), cumsum(rnorm(200)))

# estimate the break point
BP_estim(series, trend="none", type="BT", direction="01", d_estim="ELW")