ecmnhess
Hessian of negative log-likelihood function
Description
computes an Hessian
= ecmnhess(Data
,Covariance
)NUMPARAMS
-by-NUMPARAMS
Hessian
matrix of the observed negative log-likelihood function based on current parameter
estimates.
Use ecmnhess
after estimating the mean and covariance of
Data
with ecmnmle
.
adds optional arguments for Hessian
= ecmnhess(___,InvCovar
,MatrixType
)InvCovar
and
MatrixType
.
Examples
Compute Hessian for Negative Log-Likelihood Function for Data
This example shows how to compute the Hessian for the negative log-likelihood function for five years of daily total return data for 12 computer technology stocks, with six hardware and six software companies
load ecmtechdemo.mat
The time period for this data extends from April 19, 2000 to April 18, 2005. The sixth stock in Assets is Google (GOOG), which started trading on August 19, 2004. So, all returns before August 20, 2004 are missing and represented as NaN
s. Also, Amazon (AMZN) had a few days with missing values scattered throughout the past five years.
[ECMMean, ECMCovar] = ecmnmle(Data)
ECMMean = 12×1
0.0008
0.0008
-0.0005
0.0002
0.0011
0.0038
-0.0003
-0.0000
-0.0003
-0.0000
⋮
ECMCovar = 12×12
0.0012 0.0005 0.0006 0.0005 0.0005 0.0003 0.0005 0.0003 0.0006 0.0003 0.0005 0.0006
0.0005 0.0024 0.0007 0.0006 0.0010 0.0004 0.0005 0.0003 0.0006 0.0004 0.0006 0.0012
0.0006 0.0007 0.0013 0.0007 0.0007 0.0003 0.0006 0.0004 0.0008 0.0005 0.0008 0.0008
0.0005 0.0006 0.0007 0.0009 0.0006 0.0002 0.0005 0.0003 0.0007 0.0004 0.0005 0.0007
0.0005 0.0010 0.0007 0.0006 0.0016 0.0006 0.0005 0.0003 0.0006 0.0004 0.0007 0.0011
0.0003 0.0004 0.0003 0.0002 0.0006 0.0022 0.0001 0.0002 0.0002 0.0001 0.0003 0.0016
0.0005 0.0005 0.0006 0.0005 0.0005 0.0001 0.0009 0.0003 0.0005 0.0004 0.0005 0.0006
0.0003 0.0003 0.0004 0.0003 0.0003 0.0002 0.0003 0.0005 0.0004 0.0003 0.0004 0.0004
0.0006 0.0006 0.0008 0.0007 0.0006 0.0002 0.0005 0.0004 0.0011 0.0005 0.0007 0.0007
0.0003 0.0004 0.0005 0.0004 0.0004 0.0001 0.0004 0.0003 0.0005 0.0006 0.0004 0.0005
⋮
To evaluate the negative log-likelihood function for ecmnmle
, use ecmnhess
based on the current maximum likelihood parameter estimates for ECMCovar
.
Hessian = ecmnhess(Data,ECMCovar)
Hessian = 90×90
107 ×
0.0001 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.0000 0.0001 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.0000 -0.0000 0.0002 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.0000 -0.0000 -0.0000 0.0003 -0.0000 0.0000 -0.0000 -0.0000 -0.0001 -0.0001 -0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.0000 -0.0000 -0.0000 -0.0000 0.0001 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0002 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0004 -0.0000 -0.0000 -0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.0000 -0.0000 -0.0000 -0.0001 0.0000 0.0000 -0.0000 -0.0000 0.0002 -0.0001 -0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.0000 -0.0000 -0.0000 -0.0001 -0.0000 0.0000 -0.0000 -0.0000 -0.0001 0.0004 -0.0000 -0.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
⋮
Input Arguments
Data
— Data
matrix
Data, specified as an
NUMSAMPLES
-by-NUMSERIES
matrix
with NUMSAMPLES
samples of a
NUMSERIES
-dimensional random vector. Missing values are
indicated by NaN
s.
Data Types: double
Covariance
— Maximum likelihood parameter estimates for covariance of Data
matrix
Maximum likelihood parameter estimates for the covariance of the
Data
using the ECM algorithm, specified as a
NUMSERIES
-by-NUMSERIES
matrix.
InvCovar
— Cholesky decomposition of covariance matrix
[ ]
(default) | matrix
(Optional) Inverse of covariance matrix, specified as a matrix using
inv
as:
inv(Covariance)
Data Types: double
MatrixType
— Matrix format
'full'
(default) | character vector
(Optional) Matrix format, specified as a character vector with a value of:
'full'
— Computes the full Hessian matrix.'meanonly'
— Computes only the components of the Hessian matrix associated with the mean.
Data Types: char
Output Arguments
Hessian
— Hessian matrix
matrix
Hessian matrix, returned as an
NUMPARAMS
NUMPARAMS
matrix of the
observed log-likelihood function based on current parameter estimates, where
NUMPARAMS = NUMSERIES * (NUMSERIES + 3)/2
if the
MatrixFormat
= 'full'
. If the
MatrixFormat
= 'meanonly'
, then
the NUMPARAMS = NUMSERIES
.
Version History
Introduced before R2006a
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