# ecmnobj

Multivariate normal negative log-likelihood function

## Description

example

Objective = ecmnobj(Data,Mean,Covariance) evaluates the negative log-likelihood function for ecmnmle.

Use ecmnobj after estimating the mean and covariance of Data with ecmnmle.

example

Objective = ecmnobj(___,CholCovariance) adds an optional argument for CholCovariance.

## Examples

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This example shows how to compute the value of the observed negative log-likelihood function for five years of daily total return data for 12 computer technology stocks, with six hardware and six software companies

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 NaNs. 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 ecmnobj based on the current maximum likelihood parameter estimates.

Objective = ecmnobj(Data,ECMMean,ECMCovar)
Objective = -3.0898e+04

## Input Arguments

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Data, specified as an NUMSAMPLES-by-NUMSERIES matrix with NUMSAMPLES samples of a NUMSERIES-dimensional random vector. Missing values are indicated by NaNs.

Data Types: double

Maximum likelihood parameter estimates for the mean of the Data using the ECM algorithm, specified as a NUMSERIES-by-1 column vector.

Maximum likelihood parameter estimates for the covariance of the Data using the ECM algorithm, specified as a NUMSERIES-by-NUMSERIES matrix.

(Optional) Cholesky decomposition of covariance matrix, specified as a matrix using chol as:

chol(Covariance)

Data Types: double

## Output Arguments

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Value of the observed negative log-likelihood function over the Data, returned as a numeric value.

## Version History

Introduced before R2006a