Vector Autoregressions (cntd)

Slides:



Advertisements
Similar presentations
Financial Econometrics
Advertisements

Time Series Analysis Definition of a Time Series process
VAR Models Gloria González-Rivera University of California, Riverside
Vector Autoregressive Models
Econ 427 lecture 24 slides Forecast Evaluation Byron Gangnes.
Non-stationary data series
Unit Roots & Forecasting
Vector Error Correction and Vector Autoregressive Models
ANIMAL SPIRITS AND ECONOMIC FLUCTUATIONS SHI FANG Adviser: Prof. Peter Matthews ECON 700 Senior Research.
Econ Prof. Buckles1 Welcome to Econometrics What is Econometrics?
Econ 240C Lecture Part I. VAR Does the Federal Funds Rate Affect Capacity Utilization?
1 Ka-fu Wong University of Hong Kong Forecasting with Regression Models.
Econ 240C Lecture Part I. VAR Does the Federal Funds Rate Affect Capacity Utilization?
1 Econometrics 1 Lecture 6 Multiple Regression -tests.
Table of Contents Solving Linear Systems of Equations - Substitution Method Recall that to solve the linear system of equations in two variables... we.
Byron Gangnes Econ 427 lecture 14 slides Forecasting with MA Models.
Various topics Petter Mostad Overview Epidemiology Study types / data types Econometrics Time series data More about sampling –Estimation.
Byron Gangnes Econ 427 lecture 3 slides. Byron Gangnes A scatterplot.
Byron Gangnes Econ 427 lecture 11 slides Moving Average Models.
Byron Gangnes Econ 427 lecture 12 slides MA (part 2) and Autoregressive Models.
LECTURE 1 - SCOPE, OBJECTIVES AND METHODS OF DISCIPLINE "ECONOMETRICS"
Mathe III Lecture 3 Mathe III Lecture 3 Mathe III Lecture 3 Mathe III Lecture 3.
Time Series Basics (2) Fin250f: Lecture 3.2 Fall 2005 Reading: Taylor, chapter , 3.9(skip 3.6.1)
Byron Gangnes Econ 427 lecture 6 slides Selecting forecasting models— alternative criteria.
Byron Gangnes Econ 427 lecture 15 slides Forecasting with AR Models.
Byron Gangnes Econ 427 lecture 23 slides Intro to Cointegration and Error Correction Models.
An Introduction to Macroeconometrics: VEC and VAR Models Prepared by Vera Tabakova, East Carolina University.
Byron Gangnes Econ 427 lecture 18 slides Multivariate Modeling (cntd)
Financial Econometrics – 2014 – Dr. Kashif Saleem 1 Financial Econometrics Dr. Kashif Saleem Associate Professor (Finance) Lappeenranta School of Business.
Solving Systems by Substitution (isolated) Solving Systems by Substitution (not isolated)
Lecture 12 Time Series Model Estimation Materials for lecture 12 Read Chapter 15 pages 30 to 37 Lecture 12 Time Series.XLSX Lecture 12 Vector Autoregression.XLSX.
Dr. Thomas Kigabo RUSUHUZWA
Time Series Econometrics
Financial Econometrics Lecture Notes 4
Lecture 12 Time Series Model Estimation
Financial Econometrics Lecture Notes 2
An Introduction to Macroeconometrics: VEC and VAR Models
VAR models and cointegration
Ch8 Time Series Modeling
TIME SERIES ECONOMETRICS
Economics 5310 Lecture 26 Causality, VAR.
FORECASTING WITH A SYSTEM OF EQUATIONS: VECTOR AUTOREGRESSION
ECO 400-Time Series Econometrics VAR MODELS
Econ 427 lecture 13 slides ARMA Models Byron Gangnes.
CHAPTER 16 ECONOMIC FORECASTING Damodar Gujarati
Warm-Up Solve the system by substitution..
Title: Interest Rates and Economic Growth
Solve a system of linear equation in two variables
Forecasting with non-stationary data series
David Givens Sreekanth Venkataraman
Solving Systems of Equations using Substitution
Title: Interest Rates and Economic Growth
Solving Systems of Equations by Substitution
Analysis of Covariance ANCOVA
David Givens Sreekanth Venkataraman
Solving Systems of Equation by Substitution
Vector AutoRegression models (VARs)
VAR Models Gloria González-Rivera University of California, Riverside
Question How do you solve a system of simultaneous equations by substitution?
Solving Equations with Variables on Both Sides
Econ 427 lecture 7 slides Modeling Seasonals Byron Gangnes.
Solving Equations with Variables on Both Sides
АВЛИГАТАЙ ТЭМЦЭХ ҮНДЭСНИЙ ХӨТӨЛБӨР /танилцуулга/
Warm-Up Solve the system by graphing..
Multivariate Modeling (intro)
Chou, Mei-Ling Assistant Professor Nanya Institute of Technology
Econ 427 lecture 16 slides Stability Tests Byron Gangnes.
X ⦁ X = 64 ±8 ±14 X ⦁ X ⦁ X =
The student will be able to:
Happiness Presentation
Presentation transcript:

Vector Autoregressions (cntd) Econ 427 lecture 19 slides Vector Autoregressions (cntd) Byron Gangnes

Analyzing dependence in a VAR system We looked at Granger Causality tests last time. We can also use impulse-response functions to see how a shock to the variables affect each other. We want to know how an innovation in one of the variables will affect itself over time and the other variable(s). Byron Gangnes

Recall the VAR(1) model A VAR(1) for a system of N=2 variables runs 2 equations where in each case 1 lags of the own and other variables are included. where Byron Gangnes

Impulse-Response Functions We can write the VAR in moving average form: There are a couple difficulties here. First, we would like to “normalize” the size of a shock so that we can meaningfully compare size of shocks hitting the two variables and we would like to be able to shock one variable independently of the other and see how that affect both variables in the system. Byron Gangnes

Normalizing by the “Cholesky factors” Define: Note that by construction epsilon2-star is orthogonal to epsilon 1. How would you show that? Byron Gangnes

Proof of orthogonal errors Byron Gangnes

Normalizing by the “Cholesky factors” Substituting, this gives y1 and y2 as functions of shocks to epsilon1 and epsilon2*: Byron Gangnes

The model for Impulse-Response Analysis We also normalize both innovations so that they have a unit variance (not shown here—see discussion in book). The normalized model is: Note that it may make a difference which order you put the variables in. You can check that out empirically. Byron Gangnes

Forecasting with VARs Econometric models and interdependence of forecasts Byron Gangnes