The cointmonitoR package

Description

Consistent Monitoring of Stationarity and Cointegrating Relationships

Details

See the vignette:
vignette("cointmonitoR")

See the DESCRIPTION:
help(package = cointmonitoR)

See the README:
https://github.com/aschersleben/cointmonitoR/blob/master/README.md

Open the package documentation page:
package?cointmonitoR

Further information and bug reporting:
https://github.com/aschersleben/cointmonitoR

Functions

• monitorCointegration
  This procedure is able to monitor a cointegration model for level or trend cointegration and returns the corresponding break point, if available. It is based on parameter estimation on a pre-break "calibration" period at the beginning of the sample that is known or assumed to be free of structural change.

• monitorStationarity
  This procedure is a special case of monitorCointegration, since it's able to monitor a one-dimensional vector for level or trend stationarity.

• print
  Print clear results.

• plot
  Plot the test statitics and the values/residuals of a cointmonitoR model.

Dependencies

This package mainly depends on our cointReg package.

Procedure for Monitoring Level and Trend Cointegration

Description

This procedure is able to monitor a cointegration model for level or trend cointegration and returns the corresponding break point, if available. It is based on parameter estimation on a pre-break "calibration" period at the beginning of the sample that is known or assumed to be free of structural change and can be specified exactly via the m argument (see Details for further information).

Usage

monitorCointegration(x, y, m = 0.25, model = c("FM", "D", "IM"),
  trend = FALSE, kernel = c("ba", "pa", "qs", "tr"), bandwidth = c("and",
  "nw"), D.options = NULL, signif.level = 0.05, return.stats = TRUE,
  return.input = TRUE, check = TRUE, ...)

Arguments

Details

The calibration period can be set by setting the argument m to the number of the last observation, that should be inside this period. The corresponding fraction of the data's length will be calculated automatically. Alternatively you can set m directly to the fitting fraction value, but you should pay attention to the fact, that the calibration period may become smaller than intended: The last observation is calculated as floor(m * N) (with N the length of x).

The kernel that is used for calculating the long-run variance can be one of the following:

• "ba": Bartlett kernel

• "pa": Parzen kernel

• "qs": Quadratic Spectral kernel

• "tr": Truncated kernel

Value

[cointmonitoR] object with components:

Hsm [numeric(1)]

value of the test statistic

time [numeric(1)]

detected time of structural break

p.value [numeric(1)]

estimated p-value of the test (between 0.01 and 0.1)

cv [numeric(1)]

critical value of the test

sig [numeric(1)]

significance level used for the test

residuals [numeric]

residuals of the modified OLS model to be used for calculating the test statistics

model [character(1)]

cointOLS model ("FM", "D", or "IM")

trend [character(1)]

trend model ("level" or "trend")

name [character(1)]

name(s) of data

m [list(2)]

list with components:
$m.frac [numeric(1)]: calibration period (fraction)
$m.index [numeric(1)]: calibration period (length)

kernel [character(1)]

kernel function

bandwidth [list(2)]

$name [character(1)]: bandwidth function (name)
$number [numeric(1)]: bandwidth

statistics [numeric]

values of test statistics with the same length as data, but NA during calibration period (available if return.stats = TRUE)

input [numeric | matrix | data.frame]

copy of input data (available if return.stats = TRUE)

D.options [list]

information about further parameters (available if model = "D")

References

• Wagner, M. and D. Wied (2015): "Monitoring Stationarity and Cointegration," Discussion Paper, DOI:10.2139/ssrn.2624657.

See Also

Other cointmonitoR: monitorStationarity, plot.cointmonitoR, print.cointmonitoR

Examples

set.seed(42)
x = data.frame(x1 = cumsum(rnorm(200)), x2 = cumsum(rnorm(200)))
eps1 = rnorm(200, sd = 2)
eps2 = c(eps1[1:100], cumsum(eps1[101:200]))

y = x$x1 - x$x2 + 10 + eps1
monitorCointegration(x = x, y = y, m = 0.5, model = "FM")

y2 = y + seq(1, 30, length = 200)
monitorCointegration(x = x, y = y2, m = 0.5, model = "FM")
monitorCointegration(x = x, y = y2, m = 0.5, trend = TRUE, model = "FM")

y3 = x$x1 - x$x2 + 10 + eps2
monitorCointegration(x = x, y = y3, m = 0.5, model = "FM")
monitorCointegration(x = x, y = y3, m = 0.5, model = "D")
monitorCointegration(x = x, y = y3, m = 0.5, model = "IM")

Procedure for Monitoring Level and Trend Stationarity

Description

This procedure is able to monitor a one-dimensional vector for level or trend stationarity and returns the corresponding break point, if available. It is based on parameter estimation on a pre-break "calibration" period at the beginning of the sample that is known or assumed to be free of structural change and can be specified exactly via the m argument (see Details for further information).

Usage

monitorStationarity(x, m = 0.25, trend = FALSE, kernel = c("ba", "pa",
  "qs", "tr"), bandwidth = c("and", "nw"), signif.level = 0.05,
  return.stats = TRUE, return.input = TRUE, check = TRUE, ...)

Arguments

Details

The calibration period can be specified by setting the argument m to the number of its last observation. The corresponding fraction of the data's length will be calculated automatically. Alternatively you can set m directly to the fitting fraction value. Attention: The calibration period may become smaller than intended: The last observation is calculated as floor(m * N) (with N = length of x).

The kernel that is used for calculating the long-run variance can be one of the following:

• "ba": Bartlett kernel

• "pa": Parzen kernel

• "qs": Quadratic Spectral kernel

• "tr": Truncated kernel

Value

[cointmonitoR] object with components:

Hsm [numeric(1)]

value of the test statistic

time [numeric(1)]

detected time of structural break

p.value [numeric(1)]

estimated p-value of the test (between 0.01 and 0.1)

cv [numeric(1)]

critical value of the test

sig [numeric(1)]

significance level used for the test

trend [character(1)]

trend model ("level" or "trend")

name [character(1)]

name(s) of data

m [list(2)]

list with components:
$m.frac [numeric(1)]: calibration period (fraction)
$m.index [numeric(1)]: calibration period (length)

kernel [character(1)]

kernel function

bandwidth [list(2)]

$name [character(1)]: bandwidth function (name)
$number [numeric(1)]: bandwidth

statistics [numeric]

values of test statistics with the same length as data, but NA during calibration period (available if return.stats = TRUE)

input [numeric | matrix | data.frame]

copy of input data (available if return.stats = TRUE)

References

• Wagner, M. and D. Wied (2015): "Monitoring Stationarity and Cointegration," Discussion Paper, DOI:10.2139/ssrn.2624657.

See Also

Other cointmonitoR: monitorCointegration, plot.cointmonitoR, print.cointmonitoR

Examples

set.seed(1909)
x <- rnorm(200)
x2 <- c(x[1:100], cumsum(x[101:200]) / 2)

# Specify the calibration period
# as fraction of the total length of x:
monitorStationarity(x, m = 0.25)
monitorStationarity(x2, m = 0.465)

# Specify the calibration period
# by setting its last observation exactly:
monitorStationarity(x, m = 50)
monitorStationarity(x2, m = 93)

Plot Method for Monitoring Procedures.

Description

Plotting objects of class "cointmonitoR".

Usage

## S3 method for class 'cointmonitoR'
plot(x, what = "test", type, main, xlab, ylab,
  axes = TRUE, legend = TRUE, main.val, xlab.val, ylab.val, lines = TRUE,
  ...)

Arguments

See Also

Other cointmonitoR: monitorCointegration, monitorStationarity, print.cointmonitoR

Examples

### Monitoring stationarity (no break):
set.seed(1909)
x = rnorm(200)
test = monitorStationarity(x, m = 0.5)
plot(test)

oldpar = par(mfrow = c(2, 1), mar = c(4, 4, 1, 1))
plot(test, what = "both", legend = FALSE, main = "", main.val = "")
par(oldpar)


### Monitoring stationarity (break):
x = c(x[1:100], cumsum(rnorm(100, sd = 0.5)) + x[101:200])
test2 = monitorStationarity(x, m = 0.5)
plot(test2)

oldpar = par(mfrow = c(2, 1), mar = c(4, 4, 1, 1))
plot(test2, what = "both", legend = FALSE, main = "", main.val = "")
par(oldpar)


### Monitoring cointegration (no break):
set.seed(42)
x = data.frame(x1 = cumsum(rnorm(200)), x2 = cumsum(rnorm(200)))
eps1 = rnorm(200, sd = 2)
y = x$x1 - x$x2 + 10 + eps1
test3 = monitorCointegration(x = x, y = y, m = 0.5, model = "FM")
plot(test3)

oldpar = par(mfrow = c(2, 1), mar = c(4, 4, 1, 1))
plot(test3, what = "both", legend = FALSE, main = "", main.val = "")
par(oldpar)


### Monitoring cointegration (break):
eps2 = c(eps1[1:100], cumsum(eps1[101:200]))
y = x$x1 - x$x2 + 10 + eps2
test4 = monitorCointegration(x = x, y = y, m = 0.5, model = "FM")
plot(test4)

oldpar = par(mfrow = c(2, 1), mar = c(4, 4, 1, 1))
plot(test4, what = "both", legend = FALSE, main = "", main.val = "")
par(oldpar)

Print Method for Monitoring Procedures.

Description

Printing objects of class "cointmonitoR".

Usage

## S3 method for class 'cointmonitoR'
print(x, ..., digits = getOption("digits"))

Arguments

Value

The invisible x object.

See Also

Other cointmonitoR: monitorCointegration, monitorStationarity, plot.cointmonitoR

Examples

set.seed(42)
test = monitorStationarity(rnorm(100), m = 0.5)
print(test)

x = data.frame(x1 = cumsum(rnorm(200)), x2 = cumsum(rnorm(200)))
eps1 = rnorm(200, sd = 2)
eps2 = c(eps1[1:100], cumsum(eps1[101:200]))
y1 = x$x1 - x$x2 + 10 + eps1
y2 = x$x1 - x$x2 + 10 + eps2
test1 = monitorCointegration(x = x, y = y1, m = 0.5, model = "FM")
print(test1)
test2 = monitorCointegration(x = x, y = y2, m = 0.5, model = "FM")
print(test2)