monitorCointegration {cointmonitoR}

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

x

[numeric | matrix | data.frame]
Data on which to apply the monitoring procedure (RHS).

y

[numeric | matrix | data.frame]
Data on which to apply the monitoring procedure (LHS). Has to be one-dimensional. If matrix, it may have only one row or column, if data.frame just one column.

m

[numeric(1)]
Length of calibration period as fraction of the data's length (between 0.1 and 0.9) or as number of observations (see Details).

model

[character(1)]
The model to be used for modified OLS calculations. Should be one of FM-OLS ("FM"), D-OLS ("D") or IM-OLS ("IM").

trend

[logical]
Should an intercept and a linear trend be included? If FALSE (default), only an intercept is included.

kernel

[character(1)]
The kernel function to use for calculating the long-run variance. Default is Bartlett kernel ("ba"), see Details for alternatives.

bandwidth

[character(1) | numeric(1)]
The bandwidth to use for calculating the long-run variance. Default is Andrews (1991) ("and"), an alternative is Newey West (1994) ("nw"). You can also set the bandwidth manually.

D.options

[list | NULL]
Options for the D-OLS calculations. A list with elements n.lead, n.lag, kmax and info.crit – or NULL (then default arguments are the same as in cointRegD. See that help page for further information.) Missing list elements will be replaced automatically.

signif.level

[numeric(1)]
Level of significance (between 0.01 and 0.1). Detection time will be calculated only if the estimated p-value is smaller than signif.level. Default is 0.05.

return.stats

[logical]
Whether to return all test statistics. Default is TRUE.

return.input

[logical]
Whether to return the input data, default is TRUE.

check

[logical]
Wheather to check (and if necessary convert) the arguments. See checkVars for further information.

...

Arguments passed to getBandwidthNW (inter, weights), if bandwidth = "nw".

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")