mefp: Monitoring of Empirical Fluctuation Processes

Description

Online monitoring of structural breaks in a linear regression model. A sequential fluctuation test based on parameter estimates or OLS residuals signals structural breaks.

Usage

mefp(obj, ...)
# S3 method for formula
mefp(formula, type = c("OLS-CUSUM", "OLS-MOSUM", "RE", "ME",
    "fluctuation"), data, h = 1, alpha = 0.05,
    functional = c("max", "range"), period = 10,
    tolerance = .Machine$double.eps^0.5, CritvalTable = NULL,
    rescale = NULL, border = NULL, ...)
# S3 method for efp
mefp(obj, alpha=0.05, functional = c("max", "range"),
    period = 10, tolerance = .Machine$double.eps^0.5,
    CritvalTable = NULL, rescale = NULL, border = NULL, ...)
monitor(obj, data = NULL, verbose = TRUE)

Arguments

formula

a symbolic description for the model to be tested.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which efp is called from.

type

specifies which type of fluctuation process will be computed.

(only used for MOSUM/ME processes). A numeric scalar from interval (0,1) specifying the size of the data window relative to the sample size.

obj

Object of class "efp" (for mefp) or "mefp" (for monitor).

alpha

Significance level of the test, i.e., probability of type I error.

functional

Determines if maximum or range of parameter differences is used as statistic.

period

(only used for MOSUM/ME processes). Maximum time (relative to the history period) that will be monitored. Default is 10 times the history period.

tolerance

Tolerance for numeric == comparisons.

CritvalTable

Table of critical values, this table is interpolated to get critical values for arbitrary alphas. The default depends on the type of fluctuation process (pre-computed tables are available for all types). This argument is under development.

rescale

If TRUE the estimates will be standardized by the regressor matrix of the corresponding subsample similar to Kuan & Chen (1994); if FALSE the historic regressor matrix will be used. The default is to rescale the monitoring processes of type "ME" but not of "RE".

border

An optional user-specified border function for the empirical process. This argument is under development.

verbose

If TRUE, signal breaks by text output.

...

Currently not used.

Details

mefp creates an object of class "mefp" either from a model formula or from an object of class "efp". In addition to the arguments of efp, the type of statistic and a significance level for the monitoring must be specified. The monitoring itself is performed by monitor, which can be called arbitrarily often on objects of class "mefp". If new data have arrived, then the empirical fluctuation process is computed for the new data. If the process crosses the boundaries corresponding to the significance level alpha, a structural break is detected (and signaled).

The typical usage is to initialize the monitoring by creation of an object of class "mefp" either using a formula or an "efp" object. Data available at this stage are considered the history sample, which is kept fixed during the complete monitoring process, and may not contain any structural changes.

Subsequent calls to monitor perform a sequential test of the null hypothesis of no structural change in new data against the general alternative of changes in one or more of the coefficients of the regression model.

The recursive estimates test is also called fluctuation test, therefore setting type to "fluctuation" was used to specify it in earlier versions of strucchange. It still can be used now, but will be forced to "RE"

References

Leisch F., Hornik K., Kuan C.-M. (2000), Monitoring Structural Changes with the Generalized Fluctuation Test, Econometric Theory, 16, 835--854.

Zeileis A., Leisch F., Kleiber C., Hornik K. (2005), Monitoring Structural Change in Dynamic Econometric Models, Journal of Applied Econometrics, 20, 99--121. doi:10.1002/jae.776.

Zeileis A. (2005), A Unified Approach to Structural Change Tests Based on ML Scores, F Statistics, and OLS Residuals. Econometric Reviews, 24, 445--466. doi:10.1080/07474930500406053.

Zeileis A., Shah A., Patnaik I. (2010), Testing, Monitoring, and Dating Structural Changes in Exchange Rate Regimes, Computational Statistics and Data Analysis, 54(6), 1696--1706. doi:10.1016/j.csda.2009.12.005.

Examples

Run this code

# NOT RUN {
df1 <- data.frame(y=rnorm(300))
df1[150:300,"y"] <- df1[150:300,"y"]+1

## use the first 50 observations as history period
e1 <- efp(y~1, data=df1[1:50,,drop=FALSE], type="ME", h=1)
me1 <- mefp(e1, alpha=0.05)

## the same in one function call
me1 <- mefp(y~1, data=df1[1:50,,drop=FALSE], type="ME", h=1,
              alpha=0.05)

## monitor the 50 next observations
me2 <- monitor(me1, data=df1[1:100,,drop=FALSE])
plot(me2)

# and now monitor on all data
me3 <- monitor(me2, data=df1)
plot(me3)


## Load dataset "USIncExp" with income and expenditure in the US
## and choose a suitable subset for the history period
data("USIncExp")
USIncExp3 <- window(USIncExp, start=c(1969,1), end=c(1971,12))
## initialize the monitoring with the formula interface
me.mefp <- mefp(expenditure~income, type="ME", rescale=TRUE,
                   data=USIncExp3, alpha=0.05)

## monitor the new observations for the year 1972
USIncExp3 <- window(USIncExp, start=c(1969,1), end=c(1972,12))
me.mefp <- monitor(me.mefp)

## monitor the new data for the years 1973-1976
USIncExp3 <- window(USIncExp, start=c(1969,1), end=c(1976,12))
me.mefp <- monitor(me.mefp)
plot(me.mefp, functional = NULL)
# }