Section 3 is concerned with the basic tool for inference in state space models, that is the kalman. E0,e2,e3,e4,e50 abstract for a long while after the explosion of macroeconomics in the 1970s, the field looked like a battlefield. Chapter 1 develops a markov mixture model of macroeconomic fundamentals to analyze the shortrun dynamics of foreign exchange rates. National income determination business cycles and economic fluctuations, recession and expansion a business cycle is an irregular, seemingly random, and persistent fluctuation of real gdp around its trend growth rate. State space models play an important role in macroeconometric analysis and the bayesian approach has been shown to have many advantages. The book includes nonlinear and nongaussian time series models. Model uncertainty, state uncertainty, and statespace models. Appropriate data are then identified and aligned with their theoretical counterparts often by removing trends and isolating cycles. Statespace models have seen many other applications in economics. From this we will derive the frequency domain transfer function, and then move back to the time domain by considering the systems state space representation. Bonn summer school advances in empirical macroeconomics. Stability of the system eigenvalues of matrix a outside the. The code implements a class for handling linear state space models simulations, calculating moments, etc.
Young abstract statespace models have been increasingly used to study macroeconomic and. Notice also the vector x1, x2 etc in a linear system satisfies vector space definition. Research school of economics, australian national university may 20 abstract we introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. In our model, foreign exchange rates are simultaneously determined by. Essays on macroeconomics in mixed frequency estimations.
He formulates and calibrates a structural macro model with adjustment costs for pricing and only two shocks. Cowell sticerd and department of economics london school of economics december 2004. Robustness, model uncertainty, rational inattention, state uncertainty, signal. Over time however, largely because facts do not go away, a largely shared vision both of fluctuations and of methodology has. A state space forecasting model with fiscal and monetary. This paper outlines recent developments in state space modelling applied to macroeconomics using bayesian methods.
And thus the solution to the optimality conditions can be expressed in the following state space representation. Only issue is which set of states to use there are many choices. N 0,r wherext are the states and zt are the observables. Forecasting macroeconomic variables using a structural. Loglinearization of the model yields a statespace representation with parameters collected in the vector. Coupled with a distributional assumption regarding the disturbances included in the model, the statespace representation yields an associated likelihood function, which can be evaluated using the kalman lter. The state space representation and estimation of a time. Adaptive state space models with applications to the. State space models and filtering university of pennsylvania. The state space representation and estimation of a timevarying parameter var with stochastic volatility taeyoung doh and michael connolly. Hidden markov models, regimeswitching, and mathematical finance. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext.
Finally, the likelihood function associated with the statespace representation is evaluated using a filtering procedure. On applications of statespace modelling in macroeconomics. State space representation substituting the general 40 now in the above system can be written in statespace form. A general introduction to state space modeling in agentbased form is given in section 8. Section 5 discusses how to model expectations formation and more generally how statespace modelling can be used to address the. Assume we want to write the likelihood function of zt ztt t1. Linear state space models quantitative economics with python. A statespace representation consists of two equations, a measurement equation which. State space models, timevarying parameters, scoredriven models, business cycle, nancial stress. The combination of solution and estimation methods in a single chapter reflects our view of the central role of the tight integration of theory and data in macroeconomics. This edited collection explores recent theoretical developments of the models and their applications in economics and finance. We treat the federal deficit as a proxy for fiscal policy and the fed funds rate as a proxy for. Statespace models applications in economics and finance. This dissertation develops three new econometric models using bayesian state space representation model in order to apply to macroeconomics and international finance.
New keynesian macroeconomics and the term structure. We outline the directions of recent research, specically the problems being. Applications of state space models in finance this work is licensed under the creative commons license 2. Fractional state space analysis of economic systems mdpi. This feature makes the model interesting as distributional aspects of all kinds of government policies can be analyzed, but it also makes the state space very big. A crosssectional distribution as state variable requires new.
The working of the algorithm is demonstrated with two examples. In this lecture we consider statespace models, which often appear in macro. We start by characterizing equilibrium as a solution to a certain nonlinear system h u,z 0 1 where u represents the time path u0,u1. In particular, each step in the bayesian estimation procedure of a timevarying parameter var with stochastic volatility is explained.
A statespace representation consists of two equations, a measurement equation which links the observed variables to unobserved state vari. Minimal statespace realization in linear system theory. In a state space model, we have an potentially unobserved state variable. State space representation let the following system. Many dynamic time series models in economics and finance may be represented in state space form. As the authors themselves acknowledge, their classification differs slightly from some of those made by other scholars, but it. Agentbased state space models speci cally for economic study, referred to as agentbased computational economics ace models, are discussed in section 9. Section 3 provides empirical analysis of a timevarying parameter var with stochastic volatility using three u.
State space models and the kalman filter 1 introduction many timeseries models used in econometrics are special cases of the class of linear state space models developed by engineers to describe physical systems. This can be described for systems using matrix notation and we obtain the state space set of equations. Statespace models as an important mathematical tool has been widely used in many different fields. Model uncertainty, state uncertainty, and statespace models yulei luo, jun nie, eric r. The model can be characterized by a set of rst order conditions as, e t. Section 2 introduces state space models and provides the state space representation of some commonly applied linear processes, such as univariate and multivariate autoregressive moving average processes arma and dynamic factor models.
A statistical investigation of stock return decomposition based on the statespace framework jun ma and mark e. Bayesian inference for time series state space models. Using the sequencespace jacobian to solve and estimate. Second, our pricing kernelis consistentwiththeis equation, whereasinthesetwopapers, it isexogenously. The state variable for this economy turns out to be a crosssectional distribution of wealth across individuals. A practical guide to state space modeling jinlung lin institute of economics, academia sinica department of economics, national chengchi university march 2006 1.
Moving average stochastic volatility models with application to in. This article introduces the state space framework and explains the main ideas behind filtering, smoothing, and likelihood computation. While linear regression models use exogenous variables. Notation and statespace representation the model has a nonlinear statespace representation. With a truncation horizon of t, the linearized version of 1 is a system of nut equations in nut. Pdf forecasting macroeconomic variables using a structural state. This article provides a description of time series methods that emphasize modern macroeconomics and finance. Lecture notes for the course empirical macroeconomics.
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