The max log likellihood function is simply a function of the error covariance matrix + constant...

38

  • date post

    19-Dec-2015

  • Category

    Documents

  • view

    227

  • download

    1

TAGS:

Transcript of The max log likellihood function is simply a function of the error covariance matrix + constant...

Page 1: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 2: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 3: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

The max log likellihood function is simply a function of the error covariance matrix+ constant terms!

Page 4: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

The max of the log likelihood function:

Proof:

Page 5: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 6: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

The distribution of the ML estimates:

The covariance matrix

Page 7: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 8: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 9: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

The unrestricted VAR(2)

Page 10: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 11: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

ECM representations

Page 12: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Ecm with m=1

Page 13: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Interpreting the first row as a disequilibrium error:

from the long-run steady-state relation:

Page 14: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Ecm with m=2

Page 15: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Ecm in acceleration rates, changes and levels

Page 16: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Invariant and variant testsF-tests of ind. Regressors:

m=1

Acceler. Rates:

Log likelihood value identical in all cases!

m=2

VAR

Page 17: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

The relationship between the ECM parameters

Page 18: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 19: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Misspecification tests

Page 20: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 21: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 22: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 23: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 24: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 25: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Information criteria

Page 26: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Choice of lag length

Page 27: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 28: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Trace correlation

= 0.40

Page 29: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Tests of residual autocorrelation

Page 30: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Tests of residual heteroscedasticity

Page 31: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Normality

• Skewness and excess kurtosis

• Univariate normality tests (Jarque-Bera)

• Mulivariate normallity test (Doornik-Hansen)

Page 32: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Univariate Normality tests

Page 33: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Asymptotic normality tests

Univariate Jarque-Bera type of test:

Multivariate Jarque-Bera type of test:

Page 34: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Approximate normality tests

Page 35: The max log likellihood function is simply a function of the error covariance matrix + constant terms!
Page 36: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

Multivariate Bowman-Shenton normality test

Page 37: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

What about the other tests?

Page 38: The max log likellihood function is simply a function of the error covariance matrix + constant terms!

The univariate normality tests


Measuring Test Measurement Error: A General Approach et al Measuring... · measurement error is reflected in the covariance structure of observed test scores. In turn, we explain

Measuring Test Measurement Error: A General Approach et al Measuring... · measurement error is reflected in the covariance structure of observed test scores. In turn, we explain

Influence function of the error rate of generalized k-means - Joint ...€¦ · Influence function of the error rate of generalized k-means Ch. Ruwet Introduction Error rate Influence

Influence function of the error rate of generalized k-means - Joint ...€¦ · Influence function of the error rate of generalized k-means Ch. Ruwet Introduction Error rate Influence

Nonparametric Covariance Function Estimation for ...tcai/paper/Covariance-Function.pdfHilbert space framework. A regularization method is introduced through a careful characteriza-tion

Nonparametric Covariance Function Estimation for ...tcai/paper/Covariance-Function.pdfHilbert space framework. A regularization method is introduced through a careful characteriza-tion

Advanced data assimilation methods with evolving forecast error covariance

Advanced data assimilation methods with evolving forecast error covariance

Background Error Covariance Modeling

Background Error Covariance Modeling

Intrinsic Non-stationary Covariance Function for Climate ... · 2 Covariance functions used in climate modeling In this section, we provide relevant background about stationary and

Intrinsic Non-stationary Covariance Function for Climate ... · 2 Covariance functions used in climate modeling In this section, we provide relevant background about stationary and

Estimation of error covariance matrices in data assimilation · A comparison of adaptive kalman lters for a tropical paci c ocean model. ... Adaptive error covariances estimation

Estimation of error covariance matrices in data assimilation · A comparison of adaptive kalman lters for a tropical paci c ocean model. ... Adaptive error covariances estimation

Introduction - Stanford Universityadl.stanford.edu/aa222/Lecture_Notes_files/gpr.pdf · AA222: Introduction to Multidisciplinary Design Optimization 12. Covariance Function Covariance

Introduction - Stanford Universityadl.stanford.edu/aa222/Lecture_Notes_files/gpr.pdf · AA222: Introduction to Multidisciplinary Design Optimization 12. Covariance Function Covariance

Covariance function estimation in Gaussian process …statmath.wu.ac.at/research/talks/resources/Bachoc_WU_2015.pdf · Covariance function estimation in Gaussian process regression

Covariance function estimation in Gaussian process …statmath.wu.ac.at/research/talks/resources/Bachoc_WU_2015.pdf · Covariance function estimation in Gaussian process regression

ME 233 Review · Z-transform. 16 Cross-covariance function Proof: Define. 17 Auto-covariance function Z-transform Proof: Define. 18 ... Next Topic • Stable causal LTI systems driven

ME 233 Review · Z-transform. 16 Cross-covariance function Proof: Define. 17 Auto-covariance function Z-transform Proof: Define. 18 ... Next Topic • Stable causal LTI systems driven

Errors and uncertainty: instrumental noise: only present in first term of auto-covariance function → error propagation random error: ~ 1 / √ # independent.

Errors and uncertainty: instrumental noise: only present in first term of auto-covariance function → error propagation random error: ~ 1 / √ # independent.

A multi-objective optimization method based on Gaussian ... · q)=k(x p,x q), and the covariance function fully specify the GP. Note that the covariance function k(,) can be any function

A multi-objective optimization method based on Gaussian ... · q)=k(x p,x q), and the covariance function fully specify the GP. Note that the covariance function k(,) can be any function

The Radius of Univalence of the Error Function

The Radius of Univalence of the Error Function

Generalized background error covariance matrix model (GEN_BE ...

Generalized background error covariance matrix model (GEN_BE ...

FPGA-based Hyperspectral Covariance Coprocessor for … · FPGA-based Hyperspectral Covariance Coprocessor for Size, ... 4.3 Relative Error of Covariance Matrix ... This research

FPGA-based Hyperspectral Covariance Coprocessor for … · FPGA-based Hyperspectral Covariance Coprocessor for Size, ... 4.3 Relative Error of Covariance Matrix ... This research

ON THE EFFECT OF COVARIANCE FUNCTION ...ayoung/papers/CONT.pdfIn the geostatistical literature the variogram 2γ(t) = E(Z(x+ t) −Z(x))2 is used more often than the covariance function,

ON THE EFFECT OF COVARIANCE FUNCTION ...ayoung/papers/CONT.pdfIn the geostatistical literature the variogram 2γ(t) = E(Z(x+ t) −Z(x))2 is used more often than the covariance function,

Comparative study on the error covariance matrices for KF and EnKF using the barotropic S-model

Comparative study on the error covariance matrices for KF and EnKF using the barotropic S-model

An introduction to the GOCE error variance covariance ...

An introduction to the GOCE error variance covariance ...

Using SAS PROC CALIS to fit Level-1 error covariance ... · tal patterns. Correctly specifying the growth model might lead to a simple covariance structure (Grimm & Widaman, 2010).

Using SAS PROC CALIS to fit Level-1 error covariance ... · tal patterns. Correctly specifying the growth model might lead to a simple covariance structure (Grimm & Widaman, 2010).

Title stata.com anova — Analysis of variance and covariance · PDF fileanova— Analysis of variance and covariance 3 Adv. model bse(term) indicates the between-subjects error term

Title stata.com anova — Analysis of variance and covariance · PDF fileanova— Analysis of variance and covariance 3 Adv. model bse(term) indicates the between-subjects error term