Econometrics Toolbox. User's Guide

Getting Started
	Econometrics Toolbox Product Description
	Econometric Modeling
		Model Selection
		Econometrics Toolbox Features
	Represent Time Series Models Using Econometrics Toolbox Objects
		Model Objects
		Model Properties
		Create Model Object
		Retrieve Model Properties
		Modify Model Properties
		Object Functions
	Stochastic Process Characteristics
		What Is a Stochastic Process?
		Stationary Processes
		Linear Time Series Model
		Unit Root Process
		Lag Operator Notation
		Characteristic Equation
	Bibliography
Data Preprocessing
	Data Transformations
		Why Transform?
		Common Data Transformations
	Trend-Stationary vs. Difference-Stationary Processes
		Nonstationary Processes
		Trend Stationary
		Difference Stationary
	Specify Lag Operator Polynomials
		Lag Operator Polynomial of Coefficients
		Difference Lag Operator Polynomials
	Nonseasonal Differencing
	Nonseasonal and Seasonal Differencing
	Time Series Decomposition
	Moving Average Filter
	Moving Average Trend Estimation
	Parametric Trend Estimation
	Use Hodrick-Prescott Filter to Reproduce Original Result
	Compare One-Sided and Two-Sided Hodrick-Prescott Filter Results
	Choose Time Series Filter for Business Cycle Analysis
	Seasonal Filters
		What Is a Seasonal Filter?
		Stable Seasonal Filter
		Sn × m seasonal filter
	Seasonal Adjustment
		What Is Seasonal Adjustment?
		Deseasonalized Series
		Seasonal Adjustment Process
	Seasonal Adjustment Using a Stable Seasonal Filter
	Seasonal Adjustment Using S(n,m) Seasonal Filters
Model Selection
	Select ARIMA Model for Time Series Using Box-Jenkins Methodology
	Autocorrelation and Partial Autocorrelation
		What Are Autocorrelation and Partial Autocorrelation?
		Theoretical ACF and PACF
		Sample ACF and PACF
		Compute Sample ACF and PACF in MATLAB®
	Ljung-Box Q-Test
	Detect Autocorrelation
		Compute Sample ACF and PACF
		Conduct the Ljung-Box Q-Test
	Engle’s ARCH Test
	Detect ARCH Effects
		Test Autocorrelation of Squared Residuals
		Conduct Engle's ARCH Test
	Unit Root Nonstationarity
		What Is a Unit Root Test?
		Modeling Unit Root Processes
		Available Tests
		Testing for Unit Roots
	Unit Root Tests
		Test Simulated Data for a Unit Root
		Test Time Series Data for Unit Root
		Test Stock Data for Random Walk
	Assess Stationarity of a Time Series
	Information Criteria for Model Selection
		Compute Information Criteria Using aicbic
	Model Comparison Tests
		Available Tests
		Likelihood Ratio Test
		Lagrange Multiplier Test
		Wald Test
		Covariance Matrix Estimation
	Conduct Lagrange Multiplier Test
	Conduct Wald Test
	Compare GARCH Models Using Likelihood Ratio Test
	Classical Model Misspecification Tests
	Check Fit of Multiplicative ARIMA Model
	Goodness of Fit
	Residual Diagnostics
		Check Residuals for Normality
		Check Residuals for Autocorrelation
		Check Residuals for Conditional Heteroscedasticity
	Assess Predictive Performance
	Nonspherical Models
		What Are Nonspherical Models?
	Plot a Confidence Band Using HAC Estimates
	Change the Bandwidth of a HAC Estimator
	Check Model Assumptions for Chow Test
	Power of the Chow Test
Econometric Modeler
	Analyze Time Series Data Using Econometric Modeler
		Prepare Data for Econometric Modeler App
		Import Time Series Variables
		Perform Exploratory Data Analysis
		Fitting Models to Data
		Conducting Goodness-of-Fit Checks
		Finding Model with Best In-Sample Fit
		Export Session Results
	Specifying Univariate Lag Operator Polynomials Interactively
		Specify Lag Structure Using Lag Order Tab
		Specify Lag Structure Using Lag Vector Tab
	Specifying Multivariate Lag Operator Polynomials and Coefficient Constraints Interactively
		Specify Lag Structure Using Lag Order Tab
		Specify Lag Structure Using Lag Vector Tab
		Specify Coefficient Matrix Equality Constraints for Estimation
	Prepare Time Series Data for Econometric Modeler App
		Prepare Table of Multivariate Data for Import
		Prepare Numeric Vector for Import
	Import Time Series Data into Econometric Modeler App
		Import Data from MATLAB Workspace
		Import Data from MAT-File
	Plot Time Series Data Using Econometric Modeler App
		Plot Univariate Time Series Data
		Plot Multivariate Time Series and Correlations
	Detect Serial Correlation Using Econometric Modeler App
		Plot ACF and PACF
		Conduct Ljung-Box Q-Test for Significant Autocorrelation
	Detect ARCH Effects Using Econometric Modeler App
		Inspect Correlograms of Squared Residuals for ARCH Effects
		Conduct Ljung-Box Q-Test on Squared Residuals
		Conduct Engle's ARCH Test
	Assess Stationarity of Time Series Using Econometric Modeler
		Test Assuming Unit Root Null Model
		Test Assuming Stationary Null Model
		Test Assuming Random Walk Null Model
	Assess Collinearity Among Multiple Series Using Econometric Modeler App
	Transform Time Series Using Econometric Modeler App
		Apply Log Transformation to Data
		Stabilize Time Series Using Nonseasonal Differencing
		Convert Prices to Returns
		Remove Seasonal Trend from Time Series Using Seasonal Difference
		Remove Deterministic Trend from Time Series
	Implement Box-Jenkins Model Selection and Estimation Using Econometric Modeler App
	Select ARCH Lags for GARCH Model Using Econometric Modeler App
	Estimate Multiplicative ARIMA Model Using Econometric Modeler App
	Perform ARIMA Model Residual Diagnostics Using Econometric Modeler App
	Specify t Innovation Distribution Using Econometric Modeler App
	Estimate Vector Autoregression Model Using Econometric Modeler
	Conduct Cointegration Test Using Econometric Modeler
	Estimate Vector Error-Correction Model Using Econometric Modeler
	Compare Predictive Performance After Creating Models Using Econometric Modeler
	Estimate ARIMAX Model Using Econometric Modeler App
	Estimate Regression Model with ARMA Errors Using Econometric Modeler App
	Compare Conditional Variance Model Fit Statistics Using Econometric Modeler App
	Perform GARCH Model Residual Diagnostics Using Econometric Modeler App
	Share Results of Econometric Modeler App Session
Time Series Regression Models
	Time Series Regression Models
	Regression Models with Time Series Errors
		What Are Regression Models with Time Series Errors?
		Conventions
	Create Regression Models with ARIMA Errors
		Default Regression Model with ARIMA Errors Specifications
		Specify regARIMA Models Using Name-Value Pair Arguments
		Specify Linear Regression Models Using Econometric Modeler App
	Specify the Default Regression Model with ARIMA Errors
	Modify regARIMA Model Properties
		Modify Properties Using Dot Notation
		Nonmodifiable Properties
	Create Regression Models with AR Errors
		Default Regression Model with AR Errors
		AR Error Model Without an Intercept
		AR Error Model with Nonconsecutive Lags
		Known Parameter Values for a Regression Model with AR Errors
		Regression Model with AR Errors and t Innovations
	Create Regression Models with MA Errors
		Default Regression Model with MA Errors
		MA Error Model Without an Intercept
		MA Error Model with Nonconsecutive Lags
		Known Parameter Values for a Regression Model with MA Errors
		Regression Model with MA Errors and t Innovations
	Create Regression Models with ARMA Errors
		Default Regression Model with ARMA Errors
		ARMA Error Model Without an Intercept
		ARMA Error Model with Nonconsecutive Lags
		Known Parameter Values for a Regression Model with ARMA Errors
		Regression Model with ARMA Errors and t Innovations
		Specify Regression Model with ARMA Errors Using Econometric Modeler App
	Create Regression Models with ARIMA Errors
		Default Regression Model with ARIMA Errors
		ARIMA Error Model Without an Intercept
		ARIMA Error Model with Nonconsecutive Lags
		Known Parameter Values for a Regression Model with ARIMA Errors
		Regression Model with ARIMA Errors and t Innovations
	Create Regression Models with SARIMA Errors
		SARMA Error Model Without an Intercept
		Known Parameter Values for a Regression Model with SARIMA Errors
		Regression Model with SARIMA Errors and t Innovations
	Specify Regression Model with SARIMA Errors
	Specify ARIMA Error Model Innovation Distribution
		About the Innovation Process
		Innovation Distribution Options
		Specify Innovation Distribution
	Impulse Response of Regression Models with ARIMA Errors
	Plot Impulse Response of Regression Model with ARIMA Errors
		Regression Model with AR Errors
		Regression Model with MA Errors
		Regression Model with ARMA Errors
		Regression Model with ARIMA Errors
	Maximum Likelihood Estimation of regARIMA Models
		Innovation Distribution
		Loglikelihood Functions
	regARIMA Model Estimation Using Equality Constraints
	Presample Values for regARIMA Model Estimation
	Initial Values for regARIMA Model Estimation
	Optimization Settings for regARIMA Model Estimation
		Optimization Options
		Constraints on Regression Models with ARIMA Errors
	Estimate Regression Model with ARIMA Errors
	Estimate a Regression Model with Multiplicative ARIMA Errors
	Select Regression Model with ARIMA Errors
	Choose Lags for ARMA Error Model
	Intercept Identifiability in Regression Models with ARIMA Errors
		Intercept Identifiability
		Intercept Identifiability Illustration
	Alternative ARIMA Model Representations
		Mathematical Development of regARIMA to ARIMAX Model Conversion
		Show Conversion in MATLAB®
	Simulate Regression Models with ARMA Errors
		Simulate an AR Error Model
		Simulate an MA Error Model
		Simulate an ARMA Error Model
	Simulate Regression Models with Nonstationary Errors
		Simulate a Regression Model with Nonstationary Errors
		Simulate a Regression Model with Nonstationary Exponential Errors
	Simulate Regression Models with Multiplicative Seasonal Errors
		Simulate a Regression Model with Stationary Multiplicative Seasonal Errors
		Untitled
	Monte Carlo Simulation of Regression Models with ARIMA Errors
		What Is Monte Carlo Simulation?
		Generate Monte Carlo Sample Paths
		Monte Carlo Error
	Presample Data for regARIMA Model Simulation
	Transient Effects in regARIMA Model Simulations
		What Are Transient Effects?
		Illustration of Transient Effects on Regression
	Forecast a Regression Model with ARIMA Errors
	Forecast a Regression Model with Multiplicative Seasonal ARIMA Errors
	Verify Predictive Ability Robustness of a regARIMA Model
	MMSE Forecasting Regression Models with ARIMA Errors
		What Are MMSE Forecasts?
		How forecast Generates MMSE Forecasts
		Forecast Error
	Monte Carlo Forecasting of regARIMA Models
		Monte Carlo Forecasts
		Advantage of Monte Carlo Forecasts
	Time Series Regression I: Linear Models
	Time Series Regression II: Collinearity and Estimator Variance
	Time Series Regression III: Influential Observations
	Time Series Regression IV: Spurious Regression
	Time Series Regression V: Predictor Selection
	Time Series Regression VI: Residual Diagnostics
	Time Series Regression VII: Forecasting
	Time Series Regression VIII: Lagged Variables and Estimator Bias
	Time Series Regression IX: Lag Order Selection
	Time Series Regression X: Generalized Least Squares and HAC Estimators
Bayesian Linear Regression
	Bayesian Linear Regression
		Classical Versus Bayesian Analyses
		Main Bayesian Analysis Components
		Posterior Estimation and Inference
	Implement Bayesian Linear Regression
		Workflow for Standard Bayesian Linear Regression Models
		Workflow for Bayesian Predictor Selection
	Specify Gradient for HMC Sampler
	Posterior Estimation and Simulation Diagnostics
		Diagnose MCMC Samples
		Perform Sensitivity Analysis
	Tune Slice Sampler for Posterior Estimation
	Compare Robust Regression Techniques
	Bayesian Lasso Regression
	Bayesian Stochastic Search Variable Selection
	Replacing Removed Syntaxes of estimate
		Replace Removed Syntax When Estimating Analytical Marginal Posterior
		Replace Removed Syntax When Estimating Numerical Marginal Posterior
		Replace Removed Syntax When Estimating Conditional Posterior
Conditional Mean Models
	Creating Univariate Conditional Mean Models
		Default ARIMA Model
		Specify Nonseasonal Models Using Name-Value Arguments
		Specify Multiplicative Models Using Name-Value Arguments
		Specify Conditional Mean Model Using Econometric Modeler App
		What Are Conditional Mean Models?
	Create Autoregressive Models
		Default AR Model
		AR Model with No Constant Term
		AR Model with Nonconsecutive Lags
		ARMA Model with Known Parameter Values
		AR Model with t Innovation Distribution
		Specify AR Model Using Econometric Modeler App
		What Are Autoregressive Models?
	Create Moving Average Models
		Default MA Model
		MA Model with No Constant Term
		MA Model with Nonconsecutive Lags
		MA Model with Known Parameter Values
		MA Model with t Innovation Distribution
		Specify MA Model Using Econometric Modeler App
		What Are Moving Average Models?
	Create Autoregressive Moving Average Models
		Default ARMA Model
		ARMA Model with No Constant Term
		ARMA Model with Known Parameter Values
		Specify ARMA Model Using Econometric Modeler App
		What Are Autoregressive Moving Average Models?
	Create Autoregressive Integrated Moving Average Models
		Default ARIMA Model
		ARIMA Model with Known Parameter Values
		Specify ARIMA Model Using Econometric Modeler App
		What Are ARIMA Models?
	Create Multiplicative ARIMA Models
		Seasonal ARIMA Model with No Constant Term
		Seasonal ARIMA Model with Known Parameter Values
		Specify Multiplicative ARIMA Model Using Econometric Modeler App
		What Are Multiplicative ARIMA Models?
	Create Multiplicative Seasonal ARIMA Model for Time Series Data
	Create ARIMA Models That Include Exogenous Covariates
		Create ARIMAX Model Using Longhand Syntax
		Specify ARMAX Model Using Dot Notation
		Specify ARIMAX or SARIMAX Model Using Econometric Modeler App
		What Are ARIMA Models That Include Exogenous Covariates?
	Modify Properties of Conditional Mean Model Objects
		Dot Notation
		Nonmodifiable Properties
	Specify Conditional Mean Model Innovation Distribution
		About the Innovation Process
		Choices for the Variance Model
		Choices for the Innovation Distribution
		Specify the Innovation Distribution
		Modify the Innovation Distribution
	Specify Conditional Mean and Variance Models
	Plot the Impulse Response Function of Conditional Mean Model
		IRF of Moving Average Model
		IRF of Autoregressive Model
		IRF of ARMA Model
		IRF of Seasonal AR Model
		More About the Impulse Response Function
	Time Base Partitions for ARIMA Model Estimation
		Partition Time Series Data for Estimation
	Box-Jenkins Differencing vs. ARIMA Estimation
	Maximum Likelihood Estimation for Conditional Mean Models
		Innovation Distribution
		Loglikelihood Functions
	Conditional Mean Model Estimation with Equality Constraints
	Presample Data for Conditional Mean Model Estimation
	Initial Values for Conditional Mean Model Estimation
	Optimization Settings for Conditional Mean Model Estimation
		Optimization Options
		Conditional Mean Model Constraints
	Estimate Multiplicative ARIMA Model
	Model Seasonal Lag Effects Using Indicator Variables
	Forecast IGD Rate from ARX Model
	Estimate Conditional Mean and Variance Model
	Choose ARMA Lags Using BIC
	Infer Residuals for Diagnostic Checking
	Monte Carlo Simulation of Conditional Mean Models
		What Is Monte Carlo Simulation?
		Generate Monte Carlo Sample Paths
		Monte Carlo Error
	Presample Data for Conditional Mean Model Simulation
	Transient Effects in Conditional Mean Model Simulations
	Simulate Stationary Processes
		Simulate AR Process
		Simulate MA Process
	Simulate Trend-Stationary and Difference-Stationary Processes
	Simulate Multiplicative ARIMA Models
	Simulate Conditional Mean and Variance Models
	Monte Carlo Forecasting of Conditional Mean Models
		Monte Carlo Forecasts
		Advantage of Monte Carlo Forecasting
	MMSE Forecasting of Conditional Mean Models
		What Are MMSE Forecasts?
		How forecast Generates MMSE Forecasts
		Forecast Error
	Convergence of AR Forecasts
	Forecast Multiplicative ARIMA Model
	Specify Presample and Forecast Period Data to Forecast ARIMAX Model
	Forecast Conditional Mean and Variance Model
	Model and Simulate Electricity Spot Prices Using the Skew-Normal Distribution
Conditional Variance Models
	Conditional Variance Models
		General Conditional Variance Model Definition
		GARCH Model
		EGARCH Model
		GJR Model
	Specify GARCH Models
		Default GARCH Model
		Specify Default GARCH Model
		Using Name-Value Arguments
		Specify GARCH Model Using Econometric Modeler App
		Specify GARCH Model with Mean Offset
		Specify GARCH Model with Known Parameter Values
		Specify GARCH Model with t Innovation Distribution
		Specify GARCH Model with Nonconsecutive Lags
	Specify EGARCH Models
		Default EGARCH Model
		Specify Default EGARCH Model
		Using Name-Value Arguments
		Specify EGARCH Model Using Econometric Modeler App
		Specify EGARCH Model with Mean Offset
		Specify EGARCH Model with Nonconsecutive Lags
		Specify EGARCH Model with Known Parameter Values
		Specify EGARCH Model with t Innovation Distribution
	Specify GJR Models
		Default GJR Model
		Specify Default GJR Model
		Using Name-Value Arguments
		Specify GJR Model Using Econometric Modeler App
		Specify GJR Model with Mean Offset
		Specify GJR Model with Nonconsecutive Lags
		Specify GJR Model with Known Parameter Values
		Specify GJR Model with t Innovation Distribution
	Modify Properties of Conditional Variance Models
		Dot Notation
		Nonmodifiable Properties
	Specify the Conditional Variance Model Innovation Distribution
	Specify Conditional Variance Model for Exchange Rates
	Maximum Likelihood Estimation for Conditional Variance Models
		Innovation Distribution
		Loglikelihood Functions
	Conditional Variance Model Estimation with Equality Constraints
	Presample Data for Conditional Variance Model Estimation
	Initial Values for Conditional Variance Model Estimation
	Optimization Settings for Conditional Variance Model Estimation
		Optimization Options
		Conditional Variance Model Constraints
	Infer Conditional Variances and Residuals
	Likelihood Ratio Test for Conditional Variance Models
	Compare Conditional Variance Models Using Information Criteria
	Monte Carlo Simulation of Conditional Variance Models
		What Is Monte Carlo Simulation?
		Generate Monte Carlo Sample Paths
		Monte Carlo Error
	Presample Data for Conditional Variance Model Simulation
	Simulate GARCH Models
	Assess EGARCH Forecast Bias Using Simulations
	Simulate Conditional Variance Model
	Monte Carlo Forecasting of Conditional Variance Models
		Monte Carlo Forecasts
		Advantage of Monte Carlo Forecasting
	MMSE Forecasting of Conditional Variance Models
		What Are MMSE Forecasts?
		EGARCH MMSE Forecasts
		How forecast Generates MMSE Forecasts
	Forecast GJR Models
	Forecast a Conditional Variance Model
	Converting from GARCH Functions to Model Objects
	Using Bootstrapping and Filtered Historical Simulation to Evaluate Market Risk
	Using Extreme Value Theory and Copulas to Evaluate Market Risk
Multivariate Time Series Models
	Vector Autoregression (VAR) Models
		Types of Stationary Multivariate Time Series Models
		Lag Operator Representation
		Stable and Invertible Models
		Models with Regression Component
		VAR Model Workflow
	Multivariate Time Series Data Formats
		Multivariate Time Series Data
		Load Multivariate Economic Data
		Multivariate Data Format
		Preprocess Data
		Time Base Partitions for Estimation
		Partition Multivariate Time Series Data for Estimation
	Vector Autoregression (VAR) Model Creation
		Create VAR Model
		Fully Specified Model Object
		Model Template for Unrestricted Estimation
		Partially Specified Model Object for Restricted Estimation
		Display and Change Model Objects
		Select Appropriate Lag Order
	Create and Adjust VAR Model Using Shorthand Syntax
	Create and Adjust VAR Model Using Longhand Syntax
	VAR Model Estimation
		Preparing VAR Models for Fitting
		Fitting Models to Data
		Examining the Stability of a Fitted Model
	Convert VARMA Model to VAR Model
	Fit VAR Model of CPI and Unemployment Rate
	Fit VAR Model to Simulated Data
	VAR Model Forecasting, Simulation, and Analysis
		VAR Model Forecasting
		Data Scaling
		Calculating Impulse Responses
	Generate VAR Model Impulse Responses
	Compare Generalized and Orthogonalized Impulse Response Functions
	Forecast VAR Model
	Forecast VAR Model Using Monte Carlo Simulation
	Forecast VAR Model Conditional Responses
	Implement Seemingly Unrelated Regression
	Estimate Capital Asset Pricing Model Using SUR
	Simulate Responses of Estimated VARX Model
	Simulate VAR Model Conditional Responses
	Simulate Responses Using filter
	VAR Model Case Study
	Convert from vgx Functions to Model Objects
	Cointegration and Error Correction Analysis
		Integration and Cointegration
		Cointegration and Error Correction
		The Role of Deterministic Terms
		Cointegration Modeling
	Determine Cointegration Rank of VEC Model
	Identifying Single Cointegrating Relations
		The Engle-Granger Test for Cointegration
		Limitations of the Engle-Granger Test
	Test for Cointegration Using the Engle-Granger Test
	Estimate VEC Model Parameters Using egcitest
	VEC Model Monte Carlo Forecasts
	Generate VEC Model Impulse Responses
	Identifying Multiple Cointegrating Relations
	Test for Cointegration Using the Johansen Test
	Estimate VEC Model Parameters Using jcitest
	Compare Approaches to Cointegration Analysis
	Testing Cointegrating Vectors and Adjustment Speeds
	Test Cointegrating Vectors
	Test Adjustment Speeds
	Model the United States Economy
	Incorporate Macroeconomic Scenario Projections in Loan Portfolio ECL Calculations
Structural Change Models
	Discrete-Time Markov Chains
		What Are Discrete-Time Markov Chains?
		Discrete-Time Markov Chain Theory
	Markov Chain Modeling
		Discrete-Time Markov Chain Object Framework Overview
		Markov Chain Analysis Workflow
	Create and Modify Markov Chain Model Objects
		Create Markov Chain from Stochastic Transition Matrix
		Create Markov Chain from Random Transition Matrix
		Specify Structure for Random Markov Chain
	Work with State Transitions
	Visualize Markov Chain Structure and Evolution
	Determine Asymptotic Behavior of Markov Chain
	Identify Classes in Markov Chain
	Compare Markov Chain Mixing Times
	Simulate Random Walks Through Markov Chain
	Compute State Distribution of Markov Chain at Each Time Step
	Create Threshold Transitions
	Visualize Threshold Transitions
	Evaluate Threshold Transitions
	Create Threshold-Switching Dynamic Regression Models
	Estimate Threshold-Switching Dynamic Regression Models
	Simulate Paths of Threshold-Switching Dynamic Regression Models
	Forecast Threshold-Switching Dynamic Regression Models
	Analyze US Unemployment Rate Using Threshold-Switching Model
	Creating Markov-Switching Dynamic Regression Models
		What Is a Markov-Switching Dynamic Regression Model?
		Markov-Switching Model Functionality of Econometrics Toolbox
		Represent Markov-Switching Model Using msVAR
	Create Univariate Markov-Switching Dynamic Regression Models
		Create Fully Specified Univariate Model
		Create Partially Specified Univariate Model for Estimation
		Create Partially Specified Univariate Model Containing Regression Components
	Modify msVAR Model Specifications
	Create Multivariate Markov-Switching Dynamic Regression Models
		Create Fully Specified Multivariate Model
		Create Fully Specified Multivariate Model Containing Regression Components
		Create Partially Specified Multivariate Model Containing Regression Components for Estimation
	Simulate Univariate Markov-Switching Dynamic Regression Model
	Simulate Multivariate Markov-Switching Dynamic Regression Model
	Monte Carlo Simulation of Markov-Switching Dynamic Regression Model Response Variables
	Analyze US Unemployment Rate Using Markov-Switching Model
State-Space Models
	What Are State-Space Models?
		Definitions
		State-Space Model Creation
	What Is the Kalman Filter?
		Standard Kalman Filter
		State Forecasts
		Filtered States
		Smoothed States
		Smoothed State Disturbances
		Forecasted Observations
		Smoothed Observation Innovations
		Kalman Gain
		Backward Recursion of the Kalman Filter
		Diffuse Kalman Filter
	Explicitly Create State-Space Model Containing Known Parameter Values
	Create State-Space Model with Unknown Parameters
		Explicitly Create State-Space Model Containing Unknown Parameters
		Implicitly Create Time-Invariant State-Space Model
	Create State-Space Model Containing ARMA State
	Implicitly Create State-Space Model Containing Regression Component
	Implicitly Create Diffuse State-Space Model Containing Regression Component
	Implicitly Create Time-Varying State-Space Model
	Implicitly Create Time-Varying Diffuse State-Space Model
	Create State-Space Model with Random State Coefficient
	Estimate Time-Invariant State-Space Model
	Estimate Time-Varying State-Space Model
	Estimate Time-Varying Diffuse State-Space Model
	Estimate State-Space Model Containing Regression Component
	Filter States of State-Space Model
	Filter Time-Varying State-Space Model
	Filter Data Through State-Space Model in Real Time
	Filter Time-Varying Diffuse State-Space Model
	Filter States of State-Space Model Containing Regression Component
	Smooth States of State-Space Model
	Smooth Time-Varying State-Space Model
	Smooth Time-Varying Diffuse State-Space Model
	Smooth States of State-Space Model Containing Regression Component
	Simulate States and Observations of Time-Invariant State-Space Model
	Simulate Time-Varying State-Space Model
	Simulate States of Time-Varying State-Space Model Using Simulation Smoother
	Estimate Random Parameter of State-Space Model
	Forecast State-Space Model Using Monte-Carlo Methods
	Forecast State-Space Model Observations
	Forecast Observations of State-Space Model Containing Regression Component
	Forecast Time-Varying State-Space Model
	Forecast State-Space Model Containing Regime Change in the Forecast Horizon
	Forecast Time-Varying Diffuse State-Space Model
	Compare Simulation Smoother to Smoothed States
	Rolling-Window Analysis of Time-Series Models
		Rolling-Window Analysis for Parameter Stability
		Rolling Window Analysis for Predictive Performance
	Assess State-Space Model Stability Using Rolling Window Analysis
		Assess Model Stability Using Rolling Window Analysis
		Assess Stability of Implicitly Created State-Space Model
	Choose State-Space Model Specification Using Backtesting
	Fit Bayesian Stochastic Volatility Model to S&P 500 Volatility
	Apply State-Space Methodology to Analyze Diebold-Li Yield Curve Model
	Analyze Linearized DSGE Models
	Perform Outlier Detection Using Bayesian Non-Gaussian State-Space Models
Functions
	addBusinessCalendar
	adftest
	aicbic
	archtest
	arima
	arima
	arma2ar
	arma2ma
	armafevd
	armairf
	asymptotics
	autocorr
	bayeslm
	bayesvarm
	bkfilter
	bssm
	chowtest
	cffilter
	classify
	collintest
	conjugateblm
	conjugatebvarm
	convert2daily
	convert2weekly
	convert2monthly
	convert2quarterly
	convert2semiannual
	convert2annual
	corr
	customblm
	cusumtest
	corrplot
	crosscorr
	diffuseblm
	diffusebvarm
	distplot
	dssm.disp
	ssm.disp
	dssm
	dtmc
	Econometric Modeler
	egarch
	egcitest
	eigplot
	empiricalblm
	empiricalbvarm
	estimate
	estimate
	estimate
	estimate
	estimate
	estimate
	dssm.estimate
	estimate
	regARIMA.estimate
	ssm.estimate
	estimate
	estimate
	estimate
	fevd
	fevd
	fevd
	fgls
	filter
	filter
	dssm.filter
	LagOp.filter
	filter
	filter
	ssm.filter
	filter
	filter
	forecast
	forecast
	forecast
	forecast
	dssm.forecast
	forecast
	regARIMA.forecast
	ssm.forecast
	forecast
	forecast
	forecast
	garch
	gctest
	gctest
	gjr
	graphplot
	hac
	hfilter
	hitprob
	hittime
	hpfilter
	i10test
	impulse
	impulse
	infer
	arima.infer
	regARIMA.infer
	infer
	infer
	irf
	irf
	irf
	irfplot
	LagOp.isEqLagOp
	isergodic
	LagOp.isNonZero
	isreducible
	LagOp.isStable
	jcitest
	jcontest
	kpsstest
	lagmatrix
	LagOp
	lassoblm
	lazy
	lbqtest
	lmctest
	lmtest
	lratiotest
	mcmix
	LagOp.minus
	mixconjugateblm
	mixsemiconjugateblm
	LagOp.mldivide
	LagOp.mrdivide
	msVAR
	LagOp.mtimes
	normalbvarm
	parcorr
	plot
	LagOp.plus
	pptest
	price2ret
	print
	print
	regARIMA.print
	recessionplot
	recreg
	redistribute
	dssm.refine
	ssm.refine
	regARIMA
	LagOp.reflect
	ret2price
	sampleroptions
	semiconjugateblm
	semiconjugatebvarm
	simplot
	ssm.simsmooth
	simsmooth
	simulate
	simulate
	simulate
	simulate
	simulate
	simulate
	simulate
	simulate
	ssm.simulate
	simulate
	simulate
	simulate
	dssm.smooth
	smooth
	ssm.smooth
	ssm
	ssm2bssm
	subchain
	summarize
	summarize
	summarize
	summarize
	regARIMA.summarize
	summarize
	summarize
	summarize
	summarize
	summarize
	threshold
	LagOp.toCellArray
	tsVAR
	ttdata
	ttplot
	ttstates
	tune
	update
	var2vec
	varm
	varm
	vec2var
	vecm
	vecm
	vratiotest
	waldtest
Appendices
	Data Sets and Examples