ICSS Procedure

@ICSS does the procedure for searching for breaks in variance using the algorithm described in Inclan and Tiao(1994). The underlying assumption is that the input data has a common mean, but possibly different variances within subsamples. Because this is doing a search for breaks, the test statistic has a non-standard distribution—the procedure takes the significance level (or critical value) as an input and searches for break points where the variance is significantly different before and after those points.

The original algorithm is based upon an assumption that the data are Normally distributed. Sanso, Arago and Carrion-i-Silvestre(2004) generalized this to allow for an estimated 4th moment (rather than using the implied 4th moment under the assumption of normality). You can get this variant by using the ROBUST option.

There have been proposals to combine ICSS analysis with GARCH models, using ICSS to identify "shift dummies". This is a bad idea. If the data are generated by a (fairly persistent) GARCH model, the ICSS procedure can "detect" several variance regimes. Or if the data are actually a set of episodes of different variances (what ICSS is actually designed to look for), then a GARCH "model" will often fit reasonably well, usually with fairly persistent GARCH coefficients. In short, ICSS and GARCH are substitutes, not complements.

@ICSS( options ) x start end

Parameters

x	series to analyze
start , end	range of x to use. By default, the defined range of x.

Options

SIGNIF=.01/[.05]/.10

CV=critical value for determining variance change [not used]

This determines the critical value used for determining whether a subsample split should be accepted. If CV isn't used, the SIGNIF option controls (with a default of .05), which uses the asymptotic critical values (1.358 for .05, 1.628 for .01 and 1.224 for .10). CV can be used for inputting a specific alternative value.

ROBUST/[NOROBUST]

If ROBUST, corrects the statistics for a non-Gaussian distribution (using sample estimates of the 4th moment).

BREAKS=(output) VECT[INT] of entries with breaks located [not used]

SUBSAMPLES=(output) RECT[INT] with subsamples [not used]

For the array created by SUBSAMPLES, ss(1,i) is the start entry of the ith subsample and ss(2,i) is the end entry. Note that there if there are K breaks, there will be K+1 subsamples. A breakpoint marks the end of a subsample.

[PRINT]/NOPRINT

TITLE=title for report ["ICSS Analysis of Series ..."

TRACE/[NOTRACE]

If TRACE, information is presented showing the decisions taken in coming up with sample breaks.

Example

INCLANTIAO.RPF is based upon the example from the original Inclan and Tiao paper. It identifies the variance breaks using the default .05 significance level.

set ldiff = log(ibm/ibm{1})

@ICSS(subsamples=ss) ldiff 2 369

The procedure identifies 2 breaks (output below) which means there will be three subsamples. The first is 2 to 236 (as is typical in change point analysis, the breakpoint is included at the end of a subsample), the second 237 to 280 and the last 281 to 369.

Sample Output

ICSS Analysis of Series LDIFF

Using significance level 0.05

Breakpoints found at entries

236

280