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Author: Vance Martin Publisher: Cambridge University Press ISBN: 0521139813 Category : Business & Economics Languages : en Pages : 925
Book Description
"Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.
Author: Vance Martin Publisher: Cambridge University Press ISBN: 0521139813 Category : Business & Economics Languages : en Pages : 925
Book Description
"Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn"-- publisher.
Author: Abi Adams Publisher: Oxford University Press ISBN: 0191069442 Category : Business & Economics Languages : en Pages : 256
Book Description
This book is a practical guide for theory-based empirical analysis in economics that guides the reader through the first steps when moving between economic theory and applied research. The book provides a hands-on introduction to some of the techniques that economists use for econometric estimation and shows how to convert a selection of standard and advanced estimators into MATLAB code. The book first provides a brief introduction to MATLAB and its syntax, before moving into microeconometric applications studied in undergraduate and graduate econometrics courses. Along with standard estimation methods such as, for example, Method of Moments, Maximum Likelihood, and constrained optimisation, the book also includes a series of chapters examining more advanced research methods. These include discrete choice, discrete games, dynamic models on a finite and infinite horizon, and semi- and nonparametric methods. In closing, it discusses more advanced features that can be used to optimise use of MATLAB, including parallel computing. Each chapter is structured around a number of worked examples, designed for the reader to tackle as they move through the book. Each chapter ends with a series of readings, questions, and extensions, designed to help the reader on their way to adapting the examples in the book to fit their own research questions.
Author: A. Smith Publisher: Createspace Independent Publishing Platform ISBN: 9781979622196 Category : Languages : en Pages : 282
Book Description
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.
Author: Paolo Brandimarte Publisher: John Wiley & Sons ISBN: 1118625579 Category : Mathematics Languages : en Pages : 501
Book Description
A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.
Author: Ernie Chan Publisher: John Wiley & Sons ISBN: 1118460146 Category : Business & Economics Languages : en Pages : 230
Book Description
Praise for Algorithmic TRADING “Algorithmic Trading is an insightful book on quantitative trading written by a seasoned practitioner. What sets this book apart from many others in the space is the emphasis on real examples as opposed to just theory. Concepts are not only described, they are brought to life with actual trading strategies, which give the reader insight into how and why each strategy was developed, how it was implemented, and even how it was coded. This book is a valuable resource for anyone looking to create their own systematic trading strategies and those involved in manager selection, where the knowledge contained in this book will lead to a more informed and nuanced conversation with managers.” —DAREN SMITH, CFA, CAIA, FSA, Managing Director, Manager Selection & Portfolio Construction, University of Toronto Asset Management “Using an excellent selection of mean reversion and momentum strategies, Ernie explains the rationale behind each one, shows how to test it, how to improve it, and discusses implementation issues. His book is a careful, detailed exposition of the scientific method applied to strategy development. For serious retail traders, I know of no other book that provides this range of examples and level of detail. His discussions of how regime changes affect strategies, and of risk management, are invaluable bonuses.” —ROGER HUNTER, Mathematician and Algorithmic Trader
Author: James LeSage Publisher: CRC Press ISBN: 1420064258 Category : Business & Economics Languages : en Pages : 362
Book Description
Although interest in spatial regression models has surged in recent years, a comprehensive, up-to-date text on these approaches does not exist. Filling this void, Introduction to Spatial Econometrics presents a variety of regression methods used to analyze spatial data samples that violate the traditional assumption of independence between observat
Author: Charles G. Renfro Publisher: IOS Press ISBN: 9781586034269 Category : Business & Economics Languages : en Pages : 420
Book Description
This publication contains a substantial amount of detail about the broad history of the development of econometric software based on the personal recollections of many people. For economists, the computer has increasingly become the primary applied research tool, and it is software that makes the computer work.
Author: A. Smith Publisher: ISBN: 9781979581332 Category : Languages : en Pages : 250
Book Description
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
Author: A. Smith Publisher: ISBN: 9781979591898 Category : Languages : en Pages : 324
Book Description
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.Time series regression models attempt to explain the current response using the response history (autoregressive dynamics) and the transfer of dynamics from relevant predictors (or otherwise). Theoretical frameworks for potential relationships among variables often permit different representations of the system.Use time series regression models to analyze time series data, which are measurements that you take at successive time points
Author: Vance Martin
Author: Vance Martin
Author: Abi Adams
Author: A. Smith
Author: Paolo Brandimarte
Author: Ernie Chan
Author: James LeSage
Author: Charles G. Renfro
Author: A. Smith
Author: Joshua Chan
Author: A. Smith