ecmnfish
Fisher information matrix
Description
computes an Fisher
= ecmnfish(Data
,Covariance
)NUMPARAMS
-by-NUMPARAMS
Fisher information
matrix based on the current maximum likelihood parameter estimates.
Use ecmnfish
after estimating the mean and covariance of
Data
with ecmnmle
.
adds optional arguments for Fisher
= ecmnfish(___,InvCovar
,MatrixType
)InvCovar
and
MatrixType
.
Examples
This example shows how to compute the Fisher information matrix based on parameter estimates for Data
for five years of daily total returns 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
-0.0003
0.0004
⋮
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
0.0005 0.0006 0.0008 0.0005 0.0007 0.0003 0.0005 0.0004 0.0007 0.0004 0.0013 0.0007
0.0006 0.0012 0.0008 0.0007 0.0011 0.0016 0.0006 0.0004 0.0007 0.0005 0.0007 0.0020
⋮
To evaluate the negative log-likelihood function for ecmnmle
, use ecmnfish
based on the current maximum likelihood parameter estimates for ECMCovar
.
Fisher = ecmnfish(Data,ECMCovar)
Fisher = 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 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0001 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 0.0001 -0.0000 0.0000 -0.0000 0.0002 0.0000 -0.0000 0.0000 0.0001 0.0000 -0.0002 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 -0.0001 -0.0000 0.0000 -0.0000 -0.0001 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 -0.0001 0.0004 -0.0000 -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 0.0002 -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 0.0001 0.0000 -0.0001 -0.0001 0.0004 -0.0000 -0.0001 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 0.0001 -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 -0.0002 -0.0001 0.0000 -0.0000 -0.0001 -0.0000 0.0004 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 0 0 0 0 0 0 0 0 0 0 0 0.0756 0.0007 0.0000 -0.0036 -0.0000 0.0000 -0.0395 -0.0002 0.0009 0.0052 -0.0084 -0.0000 0.0002 0.0022 0.0002 -0.0030 -0.0000 0.0001 0.0008 0.0002 0.0000 -0.0194 -0.0001 0.0005 0.0051 0.0011 0.0004 0.0012 -0.0137 -0.0001 0.0003 0.0036 0.0008 0.0003 0.0018 0.0006 -0.0317 -0.0002
0 0 0 0 0 0 0 0 0 0 0 0 0.0007 0.0990 0.0005 -0.0122 -0.0024 0.0003 0.0045 -0.0258 0.0031 -0.0012 -0.0267 -0.0057 0.0013 0.0067 0.0015 0.0665 -0.0017 -0.0013 -0.0175 -0.0032 -0.0013 0.0069 -0.0127 0.0014 -0.0024 0.0030 -0.0087 -0.0009 0.0008 -0.0089 0.0011 -0.0006 0.0024 -0.0060 -0.0007 -0.0001 0.0015 -0.0208
0 0 0 0 0 0 0 0 0 0 0 0 0.0000 0.0005 0.0324 -0.0001 -0.0080 0.0005 0.0000 0.0031 -0.0004 0.0001 -0.0001 -0.0175 0.0021 -0.0008 0.0024 0.0003 0.0435 -0.0054 0.0021 -0.0117 0.0146 0.0000 0.0046 -0.0006 0.0002 -0.0012 0.0031 0.0002 0.0000 0.0005 -0.0001 0.0000 -0.0001 0.0004 0.0000 0.0000 0.0000 0.0011
⋮
Input Arguments
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
Maximum likelihood parameter estimates for the covariance of the
Data
using the ECM algorithm, specified as a
NUMSERIES
-by-NUMSERIES
matrix.
(Optional) Inverse of covariance matrix, specified as a matrix using inv
as:
inv(Covariance)
Data Types: double
(Optional) Matrix format, specified as a character vector with a value of:
'full'
— Computes the full Fisher information matrix.'meanonly'
— Computes only the components of the Fisher information matrix associated with the mean.
Data Types: char
Output Arguments
Fisher information matrix, returned as an
NUMPARAMS
NUMPARAMS
matrix based on current
parameter estimates, where NUMPARAMS = NUMSERIES * (NUMSERIES + 3)/2
if the MatrixFormat
= 'full'
. If the
MatrixFormat
= 'meanonly'
, then the
NUMPARAMS = NUMSERIES
.
More About
The Fisher information matrix is a key concept in statistics and information theory that measures the amount of information that an observable random variable carries about an unknown parameter upon which the probability of the random variable depends.
The Fisher information matrix is used to evaluate the efficiency of estimators and to derive confidence intervals.
Version History
Introduced before R2006a
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