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Lecture Notes for ECN 200E - Macro Theory with Salyer at UC Davis (UCD)

Notes Information

Material Type:Class Note
Professor:Salyer
Class:ECN 200E - Macro Theory
Subject:Economics
University:University of California - Davis
Term:--
Keywords:
  • Probabilities
  • Distribution
  • Definitions
  • Conditional
  • Markov Process
  • Characterization
  • No Correlation
  • Eigenvalues
  • Diagonal Elements
  • Eigenvector
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Sample Document Text

Professor Salyer, Economics 200E 1 A brief introduction to discrete state Markov processes Suppose the random variable x t can take on n possible values denoted xi n i , , , ,...,G01 123 . A Markov process for x t is defined by the property: G01G02G01G02 Pr | , , ,... Pr |xxxxxxxx xxxx tjtitkth tjtiG01G02G02 G01 G01G01 G01 G01 G01 G01G01 112 1 . That is, the current realization provides all the information needed for making forecasts. For expositional purposes, we will use primarily a two-state Markov process: Possible realizations for x t are: x x x where x x t G01G02 G03 G04 G05 1 2 12 . The transition probabilities are denoted G01G02 G01 ij t j t i xxxxG01G01G01 G01 Pr | 1 and are given in matrix notation: (1) G06 G01 G07 G08 G09 G0A G0B G0C G01G01 G01G01 11 12 21 22 (Bold print denotes either a vector or matrix.) Note that each row of the transition probability matrix is a conditional probability distribution, hence the elements ...

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