ecmnobj

Multivariate normal negative log-likelihood function

Syntax

Objective = ecmnobj(Data,Mean,Covariance)

Objective = ecmnobj(___,CholCovariance)

Description

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.

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

Examples

Compute Value of the Observed Negative Log-Likelihood Function for Data

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

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 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

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 NaNs.

Data Types: double

Mean — Maximum likelihood parameter estimates for mean of Data

vector

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

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.

CholCovariance — Cholesky decomposition of covariance matrix

[ ] (default) | matrix

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

chol(Covariance)

Data Types: double

Output Arguments

Objective — Value of the observed negative log-likelihood function over Data

numeric

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