R: Monitoring of Empirical Fluctuation Processes

mefp {strucchange} | R Documentation

## 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 class '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 class '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.
`h` | (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 `alpha`s. 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.

### See Also

`plot.mefp`, `boundary.mefp`

### Examples

    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)

[Package strucchange version 1.5-2 Index]