Financial Toolbox™

convert2sur - Convert multivariate normal regression model to seemingly unrelated regression (SUR) model

Syntax

DesignSUR = convert2sur(Design, Group)

Arguments

Design

A matrix or a cell array that depends on the number of data series NUMSERIES.

If NUMSERIES = 1, convert2sur returns the Design matrix.
If NUMSERIES > 1, Design is a cell array with NUMSAMPLES cells, where each cell contains a NUMSERIES-by-NUMPARAMS matrix of known values.

Group

Contains information about how data series are to be grouped, with separate parameters for each group. Specify groups either by series or by groups:

To identify groups by series, construct an index vector that has NUMSERIES elements. Element i = 1, ..., NUMSERIES in the vector, and has the index j = 1, ..., NUMGROUPS of the group in which series i is a member.
To identify groups by groups, construct a cell array with NUMGROUPS elements. Each cell contains a vector with the indexes of the series that populate a given group.
In either case, the number of series is NUMSERIES and the number of groups is NUMGROUPS, with 1 ≤ NUMGROUPS ≤ NUMSERIES.

Description

DesignSUR = convert2sur(Design, Group) converts a multivariate normal regression model into a seemingly unrelated regression model with a specified grouping of the data series. DesignSUR is either a matrix or a cell array that depends on the value of NUMSERIES:

If NUMSERIES = 1, DesignSUR = Design, which is a NUMSAMPLES-by-NUMPARAMS matrix.
If NUMSERIES > 1 and NUMGROUPS groups are to be formed, Design is a cell array with NUMSAMPLES cells, where each cell contains a NUMSERIES-by-(NUMGROUPS * NUMPARAMS) matrix of known values.

The original collection of parameters that are common to all series are replicated to form collections of parameters for each group.

Examples

This example has ten series in three groups, and two model parameters. Suppose

Group 1 has series 1, 3, 4, 8.

Group 2 has series 2, 6, 10.

Group 3 has series 5, 7, 9.

Either:

Group = [ 1, 2, 1, 1, 3, 2, 3, 1, 3, 2];

Group = cell(3,1);
Group{1} = [1, 3, 4, 8];
Group{2} = [2, 6, 10];
Group{3} = [5, 7, 9];

A regression with DesignSUR would have 3 x 2 = 6 model parameters.

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