Approximate Conditional Mean Robust Smoother

DESCRIPTION:

Applies an approximate conditional mean type robust smoother to time series data to obtain smoothed data (component smo of the output) which is free of outliers.

USAGE:

acm.smo(x, gm, s0=<<see below>>, iter=1, a=2.5, b=5, psiovw=T, savesd=T) 

REQUIRED ARGUMENTS:

x
univariate time series or vector. Missing values are not allowed.
gm
list produced by function ar.gm from x; see acm.filt for details.

OPTIONAL ARGUMENTS:

s0
scale of the nominal Gaussian component of the additive noise, the default is the estimated innovations standard deviation (from gm) multiplied by 0.001. s0 must be greater than 0.
iter
number of iterations to be performed.
a
first break point for the Hampel two-part psi used in filtering.
b
second break point for the Hampel psi.
psiovw
logical flag: if TRUE, use psi(t)/t to calculate the weight function w(t); if FALSE, use psi'(t).
savesd
logical flag: if TRUE, calculate and save the estimated time varying scale of the smoothing error; if FALSE, omit these calculations.

VALUE:

a list containing the following components:
ar
vector of length order (= length(gm$ar)) containing the least squares estimate of the autoregression parameters calculated from the smoothed data.
chat
an order by order Toeplitz matrix containing the estimated autocovariance matrix of the smoothed data.
si
estimate of the innovations scale from the smoothed data.
smo
vector or time series containing the smoothed data.
st
vector or time series containing the estimated scale of the smoother error. This is only returned when savesd is TRUE.

REFERENCES:

Martin, R. D. (1982). Approximate conditional mean type smoothers and interpolators. In Smoothing Techniques for Curve Estimation. T. Gasser and M. Rosenblatt, eds. Springer Verlag, Berlin. pp. 117-143.

Martin, R. D. (1981). Robust methods for time series. In Applied Time Series Analysis II. D. F. Findley, ed. Academic Press, New York. pp. 683-759.

SEE ALSO:

, , .

EXAMPLES:

gm <- ar.gm(bicoal.tons,3) 
acm.smo(bicoal.tons,gm)