locate.outliers.loops {tsoutliers}

Stage I of the Procedure: Locate Outliers (Loop Around Functions)

Description

These functions implement the inner and outer loops based of the procedure to locate outliers following the approach described in Chen and Liu (1993) .

Usage

locate.outliers.oloop(y, fit, types = c("AO", "LS", "TC"), 
  cval = NULL, maxit.iloop = 4, maxit.oloop = 4, 
  delta = 0.7, logfile = NULL)
locate.outliers.iloop(resid, pars, cval = 3.5, 
  types = c("AO", "LS", "TC"), maxit = 4, delta = 0.7, logfile = NULL)

Arguments

y

a time series.

fit

an Arima object. The output from arima or auto.arima

.

resid

a time series. Residuals from a time series model fitted to the data.

pars

a list containing the parameters of the model fitted to the data. See details in locate.outliers.

cval

a numeric. The critical value to determine the significance of each type of outlier.

types

a character vector indicating the type of outlier to be considered by the detection procedure among the following: innovational outliers ("IO"), additive outliers ("AO"), level shifts ("LS"), temporary changes ("TC") and seasonal level shifts ("SLS").

maxit

a numeric. The maximum number of iterations in the inner loop.

maxit.iloop

a numeric. Same as argument as maxit to be passed to locate.outliers.iloop.

maxit.oloop

a numeric. The maximum number of iterations in the outer loop.

delta

a numeric. Parameter of the temporary change type of outlier.

logfile

a character or NULL. It is the path to the file where tracking information is printed. Ignored if NULL.

Details

See also the details section in locate.outliers.

The function locate.outliers.iloop iterates around the function locate.outliers until no additional outliers are found or the maximum number of iterations is reached. After each iteration, the effect of the outliers on the residuals of the fitted model is removed and the t-statistics are obtained again for the modified residuals. No model selection or refit of the model is conducted within this loop.

The function locate.outliers.oloop is the outer loop of the procedure to locate outliers. It iterates around the function locate.outliers.iloop. At the end of each iteration the detected outliers are removed from the original data. Then, the time series model is fitted (or selected) again for the adjusted series and a new search for outliers is executed. The outer loop stops when no additional outliers are detected.

In function locate.outliers.oloop, if no value is specified for argument cval a default value based on the sample size is used. Let n be the number of observations. If n \le 50 then cval is set equal to 3.0; If n \ge 450 then cval is set equal to 4.0; otherwise cval is set equal to 3 + 0.0025 * (n - 50).

Value

locate.outliers.iloop returns a data frame defining by rows each detected outlier. The data frame follows the same format as the output from locate.outliers.

locate.outliers.oloop returns a list containing the following elements: fit: information from the last fitted model that will be required by other functions in the automatic procedure (parameter estimates, residuals and number of observations); outliers: a data frame defining by rows the detected outliers; iter: the number of iterations employed by the outer loop.

Note

In locate.outliers.iloop the default critical value, cval, is set equal to 3.5 and, hence, it is not based on the sample size. locate.outliers.oloop uses a default critical value based on the sampel size as in tso.

References

Chen, C. and Liu, Lon-Mu (1993). ‘Joint Estimation of Model Parameters and Outlier Effects in Time Series’. Journal of the American Statistical Association, 88(421), pp. 284-297.

Gómez, V. and Maravall, A. (1996). Programs TRAMO and SEATS. Instructions for the user. Banco de España, Servicio de Estudios. Working paper number 9628. http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/96/Fich/dt9628e.pdf

Gómez, V. and Taguas, D. (1995). Detección y Corrección Automática de Outliers con TRAMO: Una Aplicación al IPC de Bienes Industriales no Energéticos. Ministerio de Economía y Hacienda. Document number D-95006. https://www.sepg.pap.hacienda.gob.es/sitios/sepg/es-ES/Presupuestos/DocumentacionEstadisticas/Documentacion/Documents/DOCUMENTOS%20DE%20TRABAJO/D95006.pdf

Kaiser, R., and Maravall, A. (1999). Seasonal Outliers in Time Series. Banco de España, Servicio de Estudios. Working paper number 9915.

See Also

outliers.tstatistics, tso.

Examples

# additional outliers may be detected in the inner or outlier loops
# in this case, the inner does not find further potential outliers 
# and stops in the first iteration, while the outer loop detects 
# a new outlier
data("hicp")
y <- log(hicp[["011600"]])
fit <- arima(y, order = c(1, 1, 0), seasonal = list(order = c(2, 0, 2)))
resid <- residuals(fit)
pars <- coefs2poly(fit)
otypes <- c("AO", "LS", "TC")
mo0 <- locate.outliers(resid, pars, types = otypes)
mo0
mo1 <- locate.outliers.iloop(resid, pars, types = otypes)
mo1
mo2 <- locate.outliers.oloop(y, fit, types = otypes)
mo2$iter
mo2$outliers