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Econometric Modeling with Matlab. State-Space Models

Econometric Modeling with Matlab. State-Space Models
Author: B. Noriega
Publisher: Independently Published
Total Pages: 196
Release: 2019-03-08
Genre: Mathematics
ISBN: 9781799064183

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Econometrics Toolbox provides functions for modeling economic data. You can select and estimate economic models for simulation and forecasting. For time series modeling and analysis, the toolbox includes univariate Bayesian linear regression, univariate ARIMAX/GARCH composite models with several GARCH variants, multivariate VARX models, and cointegration analysis. It also provides methods for modeling economic systems using state-space models and for estimating using the Kalman filte. You can use a variety of diagnostics for model selection, including hypothesis tests, unit root, stationarity, and structural change.The more important topics in this book are the next: -"State-Space Models?" -"Kalman Filter?" -"Explicitly Create State-Space Model Containing Known Parameter Values"-"Create State-Space Model with Unknown Parameters" -"Create State-Space Model Containing ARMA State" -"Implicitly Create State-Space Model Containing Regression Component"-"Implicitly Create Diffus State-Space Model Containing Regression Component"-"Implicitly Create Time-Varying State-Space Model" -"Implicitly Create Time-Varying Diffus 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 Diffus State-Space Model" -"Estimate State-Space Model Containing Regression Component"-"Filter States of State-Space Model" -"Filter Time-Varying State-Space Model" -"Filter Time-Varying Diffus 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 Diffus 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 Diffus State-Space Model" -"Compare Simulation Smoother to Smoothed States" -"Rolling-Window Analysis of Time-Series Models" -"Assess State-Space Model Stability Using Rolling Window Analysis" -"Choose State-Space Model Specificatio Using Backtesting"


State-Space Models

State-Space Models
Author: Yong Zeng
Publisher: Springer Science & Business Media
Total Pages: 358
Release: 2013-08-15
Genre: Business & Economics
ISBN: 1461477891

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State-space models as an important mathematical tool has been widely used in many different fields. This edited collection explores recent theoretical developments of the models and their applications in economics and finance. The book includes nonlinear and non-Gaussian time series models, regime-switching and hidden Markov models, continuous- or discrete-time state processes, and models of equally-spaced or irregularly-spaced (discrete or continuous) observations. The contributed chapters are divided into four parts. The first part is on Particle Filtering and Parameter Learning in Nonlinear State-Space Models. The second part focuses on the application of Linear State-Space Models in Macroeconomics and Finance. The third part deals with Hidden Markov Models, Regime Switching and Mathematical Finance and the fourth part is on Nonlinear State-Space Models for High Frequency Financial Data. The book will appeal to graduate students and researchers studying state-space modeling in economics, statistics, and mathematics, as well as to finance professionals.


Econometric With Matlab

Econometric With Matlab
Author: A. Smith
Publisher: Createspace Independent Publishing Platform
Total Pages: 282
Release: 2017-11-10
Genre:
ISBN: 9781979622196

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Econometrics Toolbox provides functions for modeling economic data. You can select and estimate economic models for simulation and forecasting. For time series modeling and analysis, the toolbox includes univariate Bayesian linear regression, univariate ARIMAX/GARCH composite models with several GARCH variants, multivariate VARX models, and cointegration analysis. It also provides methods for modeling economic systems using state-space models and for estimating using the Kalman filter. You can use a variety of diagnostics for model selection, including hypothesis tests, unit root, stationarity, and structural change. A state-space model is a discrete-time, stochastic model that contains two sets of equations: - One describing how a latent process transitions in time (the state equation) - Another describing how an observer measures the latent process at each period (the observation equation) A diffuse state-space model is a state-space model that can contain at least one state with an infinite initial variance, called a diffuse state. In addition to having an infinite initial variance, all diffuse states are uncorrelated with all other states in the model. In a time-invariant state-space model: - The coefficient matrices are equivalent for all periods. - The number of states, state disturbances, observations, and observation innovations are the same for all periods. In a time-varying state-space model: - The coefficient matrices might change from period to period. - The number of states, state disturbances, observations, and observation innovations might change from period to period. For example, this might happen if there is a regime shift or one of the states or observations cannot be measured during the sampling time frame. Also, you can model seasonality using time-varying models. To create a standard or diffuse state-space model, use ssm or dssm, respectively. For time-invariant models, explicitly specify the parametric form of your state-space model by supplying the coefficient matrices. For time-variant, complex models, or models that require constraints, supply a parameter-to-matrix mapping function. The software can infer the type of state (stationary, the constant one, or nonstationary), but it is best practice to supply the state type using, for example, the StateType name-value pair argument. To filter and smooth the states of a specified ssm or dssm model, the software uses the standard Kalman filter or the diffuse Kalman filter. In the state-space model framework, the Kalman filter estimates the values of a latent, linear, stochastic, dynamic process based on possibly mismeasured observations. Given distribution assumptions on the uncertainty, the Kalman filter also estimates time series model parameters via maximum likelihood. This book develops state-space models for work with time series.


Econometric Modeling with Matlab. Multivariate Time Series Models

Econometric Modeling with Matlab. Multivariate Time Series Models
Author: B. Noriega
Publisher: Independently Published
Total Pages: 278
Release: 2019-03-06
Genre: Mathematics
ISBN: 9781798968253

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Econometrics Toolbox provides functions for modeling economic data. You can select and estimate economic models for simulation and forecasting. For time series modeling and analysis, the toolbox includes univariate Bayesian linear regression, univariate ARIMAX/GARCH composite models with several GARCH variants, multivariate VARX models, and cointegration analysis. It also provides methods for modeling economic systems using state-space models and for estimating using the Kalman filte. You can use a variety of diagnostics for model selection, including hypothesis tests, unit root, stationarity, and structural change.The more important topics in this book are the next: -"Vector Autoregression (VAR) Models" -"Multivariate Time Series Data Structures" -"Multivariate Time Series Model Creation" -"VAR Model Estimation" -"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" -"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"-"Multivariate Time Series Models with Regression Terms" -"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" -"Cointegration and Error Correction Analysis" -"Determine Cointegration Rank of VEC Model" -"Identifying Single Cointegrating Relations"-"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"


Econometrics With Matlab

Econometrics With Matlab
Author: A. Smith
Publisher:
Total Pages: 250
Release: 2017-11-09
Genre:
ISBN: 9781979581332

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Econometrics Toolbox provides functions for modeling economic data. You can select and estimate economic models for simulation and forecasting. For time series modeling and analysis, the toolbox includes univariate Bayesian linear regression, univariate ARIMAX/GARCH composite models with several GARCH variants, multivariate VARX models, and cointegration analysis. It also provides methods for modeling economic systems using state-space models and for estimating using the Kalman filter. You can use a variety of diagnostics for model selection, including hypothesis tests, unit root,stationarity, and structural change.A probabilistic time series model is necessary for a wide variety of analysis goals ,including regression inference, forecasting, and Monte Carlo simulation. When selecting a model, aim to find the most parsimonious model that adequately describes your data. Asimple model is easier to estimate, forecast, and interpret*Specification tests help you identify one or more model families that could plausiblydescribe the data generating process.*Model comparisons help you compare the fit of competing models, with penalties for complexity.*Goodness-of-fit checks help you assess the in-sample adequacy of your model, verify that all model assumptions hold, and evaluate out-of-sample forecast performance.Model selection is an iterative process. When goodness-of-fit checks suggest model assumptions are not satisfied-or the predictive performance of the model is not satisfactory-consider making model adjustments. Additional specification tests, model comparisons, and goodness-of-fit checks help guide this process..The most important content is the following:* Econometrics Toolbox Product Description* Econometric Modeling* Econometrics Toolbox Model Objects, Properties, and Methods* Stochastic Process Characteristics* Data Transformations* Data Preprocessing* 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* Hodrick-Prescott Filter* Using the Hodrick-Prescott Filter to Reproduce Their* Original Result* Seasonal Filters* Seasonal Adjusment* Seasonal Adjustment Using a Stable Seasonal Filter* Seasonal Adjustment Using S(n,m) Seasonal Filters* Box-Jenkins Methodology* Box-Jenkins Model Selection* Autocorrelation and Partial Autocorrelation* Theoretical ACF and PACF* Sample ACF and PACF* Ljung-Box Q-Test* Detect Autocorrelation* Engle's ARCH Test* Detect ARCH Effects* Unit Root Nonstationarity* Unit Root Tests* Assess Stationarity of a Time Series* Information Criteria* Model Comparison Tests* Likelihood Ratio Test* Lagrange Multiplier Test* Wald Test* Covariance Matrix Estimation* Conduct a Lagrange Multiplier Test* Conduct a Wald Test* Compare GARCH Models Using Likelihood Ratio Test* Check Fit of Multiplicative ARIMA Model* Goodness of Fit* Residual Diagnostics* Check Residuals for Normality* Check Residuals for Autocorrelation* Check Residuals for Conditional Heteroscedasticity* Check Predictive Performance* 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


State Space Modeling of Time Series

State Space Modeling of Time Series
Author: Masanao Aoki
Publisher: Springer Science & Business Media
Total Pages: 339
Release: 2013-03-09
Genre: Business & Economics
ISBN: 3642758835

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In this book, the author adopts a state space approach to time series modeling to provide a new, computer-oriented method for building models for vector-valued time series. This second edition has been completely reorganized and rewritten. Background material leading up to the two types of estimators of the state space models is collected and presented coherently in four consecutive chapters. New, fuller descriptions are given of state space models for autoregressive models commonly used in the econometric and statistical literature. Backward innovation models are newly introduced in this edition in addition to the forward innovation models, and both are used to construct instrumental variable estimators for the model matrices. Further new items in this edition include statistical properties of the two types of estimators, more details on multiplier analysis and identification of structural models using estimated models, incorporation of exogenous signals and choice of model size. A whole new chapter is devoted to modeling of integrated, nearly integrated and co-integrated time series.


Linear Time Series with MATLAB and OCTAVE

Linear Time Series with MATLAB and OCTAVE
Author: Víctor Gómez
Publisher: Springer Nature
Total Pages: 355
Release: 2019-10-04
Genre: Computers
ISBN: 3030207900

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This book presents an introduction to linear univariate and multivariate time series analysis, providing brief theoretical insights into each topic, and from the beginning illustrating the theory with software examples. As such, it quickly introduces readers to the peculiarities of each subject from both theoretical and the practical points of view. It also includes numerous examples and real-world applications that demonstrate how to handle different types of time series data. The associated software package, SSMMATLAB, is written in MATLAB and also runs on the free OCTAVE platform. The book focuses on linear time series models using a state space approach, with the Kalman filter and smoother as the main tools for model estimation, prediction and signal extraction. A chapter on state space models describes these tools and provides examples of their use with general state space models. Other topics discussed in the book include ARIMA; and transfer function and structural models; as well as signal extraction using the canonical decomposition in the univariate case, and VAR, VARMA, cointegrated VARMA, VARX, VARMAX, and multivariate structural models in the multivariate case. It also addresses spectral analysis, the use of fixed filters in a model-based approach, and automatic model identification procedures for ARIMA and transfer function models in the presence of outliers, interventions, complex seasonal patterns and other effects like Easter, trading day, etc. This book is intended for both students and researchers in various fields dealing with time series. The software provides numerous automatic procedures to handle common practical situations, but at the same time, readers with programming skills can write their own programs to deal with specific problems. Although the theoretical introduction to each topic is kept to a minimum, readers can consult the companion book ‘Multivariate Time Series With Linear State Space Structure’, by the same author, if they require more details.


State-Space Methods for Time Series Analysis

State-Space Methods for Time Series Analysis
Author: Jose Casals
Publisher: CRC Press
Total Pages: 286
Release: 2018-09-03
Genre: Mathematics
ISBN: 131536025X

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The state-space approach provides a formal framework where any result or procedure developed for a basic model can be seamlessly applied to a standard formulation written in state-space form. Moreover, it can accommodate with a reasonable effort nonstandard situations, such as observation errors, aggregation constraints, or missing in-sample values. Exploring the advantages of this approach, State-Space Methods for Time Series Analysis: Theory, Applications and Software presents many computational procedures that can be applied to a previously specified linear model in state-space form. After discussing the formulation of the state-space model, the book illustrates the flexibility of the state-space representation and covers the main state estimation algorithms: filtering and smoothing. It then shows how to compute the Gaussian likelihood for unknown coefficients in the state-space matrices of a given model before introducing subspace methods and their application. It also discusses signal extraction, describes two algorithms to obtain the VARMAX matrices corresponding to any linear state-space model, and addresses several issues relating to the aggregation and disaggregation of time series. The book concludes with a cross-sectional extension to the classical state-space formulation in order to accommodate longitudinal or panel data. Missing data is a common occurrence here, and the book explains imputation procedures necessary to treat missingness in both exogenous and endogenous variables. Web Resource The authors’ E4 MATLAB® toolbox offers all the computational procedures, administrative and analytical functions, and related materials for time series analysis. This flexible, powerful, and free software tool enables readers to replicate the practical examples in the text and apply the procedures to their own work.


Univariate Time Series Analysis with MATLAB

Univariate Time Series Analysis with MATLAB
Author: Perez M.
Publisher: Createspace Independent Publishing Platform
Total Pages: 222
Release: 2016-06-26
Genre:
ISBN: 9781534867062

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Econometrics Toolbox(tm) provides functions for modeling economic data. You can select and calibrate economic models for simulation and forecasting. For time series modeling and analysis, the toolbox includes univariate ARMAX/GARCH composite models with several GARCH variants, multivariate VARMAX models, and cointegration analysis. It also provides methods for modeling economic systems using state-space models and for estimating using the Kalman filter. You can use a variety of diagnostic functions for model selection, including hypothesis, unit root, and stationarity tests. This book focuses on Univariate Time Series Analysis.


Time Series Analysis by State Space Methods

Time Series Analysis by State Space Methods
Author: James Durbin
Publisher: Oxford University Press
Total Pages: 280
Release: 2001-06-21
Genre: Business & Economics
ISBN: 9780198523543

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State space time series analysis emerged in the 1960s in engineering, but its applications have spread to other fields. Durbin (statistics, London School of Economics and Political Science) and Koopman (econometrics, Free U., Amsterdam) extol the virtues of such models over the main analytical system currently used for time series data, Box-Jenkins' ARIMA. What distinguishes state space time models is that they separately model components such as trend, seasonal, regression elements and disturbance terms. Part I focuses on traditional and new techniques based on the linear Gaussian model. Part II presents new material extending the state space model to non-Gaussian observations. c. Book News Inc.