This functions tests for the significance of a given set of outliers
in a time series model that is fitted including the outliers as regressor variables.
a list. The output returned by locate.outliers.oloop.
y
a time series.
cval
a numeric. The critical value to determine the significance of each type of outlier.
method
a character. The method to remove outliers. See details.
delta
a numeric. Parameter of the temporary change type of outlier.
n.start
a numeric. The number of warming observations added to the
input passed to the Kalman filter. Only for tsmethod = "stsm".
tsmethod.call
an optional call object. The call to the function used to fit the time
series model.
fdiff
currently ignored.
logfile
a character or NULL. It is the path to the file where
tracking information is printed. Ignored if NULL.
Details
In the regressions involved in this function, the variables included as regressors
stand for the effects of the outliers on the data.
These variables are the output returned by outliers.effects
not by outliers.regressors, which returns the regressors used in the
auxiliar regression where outliers are located
(see second equation defined in locate.outliers).
The outliers are defined in input x. If there are regressor variables
in tsmethod.call$xreg they are considered as other regressor variables
that are included in the regression to test for the significance of outliers.
Given a set of potential outliers detected by locate.outliers and
locate.outliers.oloop, three methods are considered to remove those outliers that
are not significant after fitting again the time series model:
"en-masse": The complete set of outliers is included as regressor variables and the
model is fitted again. Those outliers that turn out to be not significant for the critical
value cval are removed. The procedure is iterated until all the outliers are significant
in the final set of outliers.
"bottom-up": First the, the outlier with larger t-statistic is included in the
model. If it is significant the presence of the outlier is confirmed. Otherwise it is removed.
Then, the next outlier with larger t-statistic is included along with the first outlier and
tested for significance.
If after including a new outlier, e.g. the i-th outlier, the outliers that have been
confirmed so far significant become not significant, then the i-th outlier is removed
regardless of the value of its t-statistic.
The "bottom-up" may be preferred to "bottom-up" when there are are several outliers
since it may be hard to fit an ARIMA model with many regressor variables.
Value
A list containing the following elements:
xreg, the variables used as regressors;
xregcoefs, the coefficients of the outlier regressors;
xregtstats, the t-statistics of the outlier regressors;;
iter, the number of iterations used by method "en-masse";
fit, the fitted model;
outliers, the set of outliers after removing those that were not significant.
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.
## Not run:
data("hicp")
y <- log(hicp[["011600"]])
fit <- arima(y, order = c(1, 1, 0), seasonal = list(order = c(2, 0, 2)))
# initial set of outliers
res <- locate.outliers.oloop(y, fit, types = c("AO", "LS", "TC"))
res$outliers
# given the model fitted above, the effect on the data of some of
# the outliers is not significant (method = "en-masse")
remove.outliers(res, y, method = "en-masse",
tsmethod.call = fit$call)$outliers
# in this case, using method = "bottom-up" the firt four
# outliers with higher t-statistic are kept
remove.outliers(res, y, method = "bottom-up",
tsmethod.call = fit$call)$outliers
## End(Not run)
providing 
.