ECM Procedure

names the input data table for PROC ECM to use. The default is the most recently created data table. libref.data-table is a two-level name, where

The DATA= data table specifies a copula sample on a uniform scale that is generated by using the OUTUNIFORM= option in the SIMULATE statement in the CCOPULA procedure.

Each observation in this data table is expected to contain the probability of the loss for each of the marginal variables. That probability is determined by accounting for the dependence structure among the marginal variables.

identifies the sample to use when the marginal data tables contain multiple samples of the marginal variable, where sample-identifier is an integer. A marginal data table can contain multiple samples when it is a result of the perturbation analysis that the CCDM procedure conducts. Each sample is identified by the value of the _DRAWID_ variable. If you specify a sample-identifier value of k, then PROC ECM uses the observations in the marginal data tables whose _DRAWID_=k.

The sample-identifier applies to all the marginal data tables that you specify in one or more MARGINAL statements. You can override the sample-identifier for a specific marginal table by specifying the DRAWID= option in the MARGINAL statement that you specify for the respective marginal variable.

If you omit this option or the DRAWID= option in the MARGINAL statement, then PROC ECM uses a default value of 0 for the marginal tables that contain the _DRAWID_ variable.

specifies the accuracy to be achieved when estimating the empirical distribution function (EDF) in the body region of the distribution, where the body region is defined as the region that contains values whose EDF estimate is less than the value that you specify in the TAILSTARTEDF= option. The number you specify represents the desired proportion of observations that each bin in the body region should contain. The number must be between 0 and 1.

PROC ECM uses number for estimating the EDF of each marginal variable. If you specify percentiles in the OUTSUM statement, PROC ECM also uses number when estimating the EDF of the total loss.

By default, EDFACCURACY=1.0E–5.

computes the empirical distribution function (EDF) by making an additional pass over the data to count the final set of bins when the data are sampled and shuffled by the binning algorithm. This results in better EDF estimates, but at the cost of an additional data pass.

If you omit this option, then the final bin counts are approximated by inflating the counts by the sampling fraction. When the sampling fraction is less than 1, this count approximation happens only for the bins in the body region of the distribution.

If you specify a value of 1 for the SAMPLEFRACTION= option or if you specify the NOSHUFFLE option, then this option is not relevant and PROC ECM ignores it.

specifies the maximum number of iterations for the equal-proportions binning algorithm.

By default, MAXITER=50.

suppresses all displayed output. If you specify this option, then PROC ECM ignores any value that you specify for the PRINT= option.

suppresses the use of shuffling in the EDF estimation process.

If you omit this option, then PROC ECM shuffles each marginal variable’s data to different worker nodes so that it can perform in parallel the binning for different ranges of the marginal data. However, this additional parallelism comes at the cost of moving data across workers. When the majority of the data are in the body region of the distribution, you can reduce the amount of data that are being moved by using the SAMPLEFRACTION= option. However, if a marginal variable’s data are very large or the SAMPLEFRACTION= option value is closer to 1, then the amount of data movement can make the algorithm slow.

If you specify this option, the binning algorithm does not shuffle the marginal data. Instead, it estimates the boundaries for a global set of bins in each of the regions (body and tail) of the distribution. This estimation increases the number of parameters that the algorithm needs to optimize while reducing the parallelism in the binning algorithm. Also, the algorithm needs to share the bin boundaries with all the worker nodes after every iteration; so if the values of the EDFACCURACY= and TAILEDFACCURACY= options are very small (resulting in a large number of bins), you might not save much in data movement cost. The cost of shuffling the data, which the algorithm incurs only once, might be lower than the cost of sharing the large number of bin boundaries with all worker nodes after each iteration.

If you specify this option, the SAMPLEFRACTION= and SEED= options are irrelevant and PROC ECM ignores them.

specifies the method of computing the percentiles. This option applies to the computation of percentiles of the total loss sample. It also applies to each marginal variable for which you do not specify a percentile method in the corresponding MARGINAL statement.

You can specify the following values:

For more information about each method, see the section Percentile Computation Methods. By default, PCTLDEF=5.

specifies the desired displayed output. If you specify more than one display-option, then separate them with spaces and enclose them in parentheses. For more information about the displayed output, see the section Displayed Output.

You can specify the following global-display-option:

You can specify the following display-options:

Not specifying the PRINT= option or the ONLY global-display-option is equivalent to specifying the PRINT=(SUMMARYSTATISTICS) option if you do not specify any percentiles in the OUTSUM statement, or is equivalent to specifying the PRINT=(PERCENTILES SUMMARYSTATISTICS) option if you specify percentiles in the OUTSUM statement.

specifies the fraction of observations to sample from the body region of the distribution during the EDF estimation process, where number must be between 0 and 1.

Sampling helps reduce the amount of data that need to be communicated across the worker nodes of the CAS server. It can reduce the accuracy of the EDF and percentile estimates, but if your marginal samples have large numbers of observations, then the loss in accuracy is not as significant as the reduction in communication cost that the sampling provides.

By default, SAMPLEFRACTION=0.5.

specifies an integer to use as the seed in generating the pseudorandom numbers that are used for sampling the body region of the distribution.

If you omit this option or if you specify a number that is negative or 0, then PROC ECM uses as the seed a number that depends on the time of day from the computer’s clock.

specifies the accuracy to be achieved when estimating the empirical distribution function (EDF) in the tail region of the distribution, where number (which must be between 0 and 1) is the desired fraction of observations that each bin in the tail region should contain. The tail region is defined as the region that contains values whose EDF estimate is larger than or equal to the value that you specify in the TAILSTARTEDF= option.

PROC ECM uses number when it estimates the EDF of each marginal variable. If you specify percentiles in the OUTSUM statement, PROC ECM also uses number when it estimates the EDF of the total loss.

By default, TAILEDFACCURACY=1.0E–6.

specifies the empirical distribution function (EDF) value that marks the beginning of the tail region of the distribution, where number must be between 0 and 1. The first stage of the EDF estimation algorithm finds an approximate value whose EDF is close to number. The part of the sample whose values are less than defines the body region of the distribution, and the remaining values define the tail region of the distribution.

By default, TAILSTARTEDF=0.8.

specifies the tolerance value that determines when the equal-proportion binning algorithm has converged, where must be a number between 0 and 1. The algorithm converges when the difference in the fractions of observations in the largest and smallest bins is less than or equal to , where is the accuracy of the body or tail region that is being analyzed.

By default, TOLERANCE=0.5.

specifies the divisor to use in calculating the variance, standard deviation, kurtosis, and skewness of the total loss sample. You can specify one of the following values for the divisor, where N is the sample size:

By default, VARDEF=DF.