Dynamic Regression Models (Lect 15)
|
|
- Laurence Gordon
- 5 years ago
- Views:
Transcription
1 Dynamic Regression Models (Lect 15) Ragnar Nymoen University of Oslo 21 March / 17
2 HGL: Ch 9; BN: Kap 10 The HGL Ch 9 is a long chapter, and the testing for autocorrelation part we have already covered. HGL starts the chapter with the Finite Distributed lag model (DL), for example Y t = β 0 + β 1 X t + β 2 X t 1 + ε t (1) and discuss estimation/testing with classical assumptions for ε t, and without But (1) is almost a usual static model, and because economic relationships are often more genuinely dynamic, it has low practical relevance. Therefore we focus the ARDL part of Ch 9, and starts with the simplest version of that model class 2 / 17
3 Autoregressive first order model AR(1) model I The simplest dynamic regression model. It has properties that carry over to more general models (ARDL below). Assume that we have t = 1, 2,..., T independent and identically distributed random variables ε t : Then, from ε t IID ( 0, σε 2 ), t = 1, 2,..., T Y t = β 0 + β 1 Y t 1 + ε t, β 1 < 1, ε t IID ( 0, σε 2 ), (2) we know something precise about the conditional distribution of Y t given Y t 1, and more generally the history of Y up to period t 1. 3 / 17
4 Autoregressive first order model AR(1) model II β 1 < 1 secures stationarity (HGL 9.1.3) for this model. We will refer to Y t as given by (2) as a 1st order autoregressive process, usually denoted AR(1). In direct parallel to the previous models we can write where Y t = E (Y t Y t 1 ) + ε t = β 0 + β 1 Y t 1 + ε t (3) E (ε t Y t 1 ) = 0 (4) by construction (in fact by assumption of β 1 < 1, but leave that for another course) (4) is necessary for pre-determinedness of Y t 1. But is E (ε t+j Y t 1 ) = 0 for j = 1, 2,... as well? And what about E (ε t 1 j Y t 1 ) for j = 1, 2? 4 / 17
5 Autoregressive first order model AR(1) model III To answer these questions: need to consider the solution of (2), which is a stochastic difference equation. 5 / 17
6 Solution I β 1 < 1 defines Y t as a causal-process: Stochastic shocks/impulses/news represented by ε come before (or in the same period) as the response in Y t. The backward-recursive solution of a causal-process is dynamically stable. We show in class that it is: t 1 Y t = β 0 β i 1 + β t t 1 1Y 0 + β i 1ε t i (5) i=0 i=0 where Y 0 is the initial condition. The conditional expectation is t 1 E (Y t Y 0 ) = β 0 β i 1 + β t 1Y 0 i=0 6 / 17
7 Solution II while the unconditional expectation of Y t is defined for the situation where t : E (Y t ) = β 0 1 β 1 (6) For simplicity, we regard Y 0 as a deterministic parameter. Then the variance is found as: t 1 Var(Y t ) = Var( i=0 β i 1ε t i ) = σ 2 ε t 1 ( ) β 2 i 1 i=0 = t σ 2 ε 1 β 2 1 (7) 7 / 17
8 Pre-determinedness of lagged Y I The solution for Y t 1 (make use of (5)!) shows that: and But also that: t 2 E (Y t 1 ε t ) = E ( i=0 β i 1ε t i 1 )ε t = 0 E (Y t 1 ε t+j ) = 0 for j = 1, 2,... E (Y t 1 ε t i ) = 0 for i = 1, 2, Y t 1 is a pre-determined explanatory variable. 8 / 17
9 Bias and consistency I To save notation: Consider the case of E (Y t ) = 0 = β 0 = 0. The OLS estimator β 1 is β 1 = T t=2 Y t Y t 1 T t=2 Y 2 t 1 = = ( ) T β1 Yt 1 2 t=2 T t=2 Yt T t=2 ( ) E ( β T t=2 Y t 1 ε t 1 β 1 = E T t=2 Yt 1 2 Cannot show that E of the bias term is zero ( ) ) Y t 1 ε t T t=2 Yt 1 2 (8) 9 / 17
10 Bias and consistency II Both the denominator and numerator are random variables, and they are not independent: For example will ε 2 be in the numerator and (because of Y 2 = ε 2 ) also in Y 2 Y 2 in the denominator. But, with reference to the Law of large numbers and Slutsky s theorem we have plim ( φ 1 φ 1 ) = plim 1 T T t=2 Y t 1 ε t plim 1 T T t=2 Y 2 t 1 = 0 σ 2 ε 1 β 2 1 = 0. since E (Y t 1 ε t ) = 0 (numerator) and β 1 < 1 (implies the existence of the variance). 10 / 17
11 Bias and consistency III The OLS estimator β 1 in the AR(1) is consistent, and it can be shown to be asymptotically normal: T ( β 1 β 1 ) d N ( 0, ( 1 β 2 )) 1 which entails that t-ratios can be compared with critical values from the normal distribution. Therefore: the large sample inference theory for the regression model extends to the AR(1) model. (9) 11 / 17
12 Analysis of finite sample bias in AR(1) In (2), the finite sample bias can be shown to be approximately ) E ( β 1 β 1 2β 1 T, We can make this more concrete with a Monte-Carlo analysis. In the experiment, the DGP is Y t = 0.5Y t 1 + ε Yt, ε Yt NIID (0, 1), and T = 10, 11,..., 99, 100. We use 1000 replications for each T and estimate the bias: ) Ê ( β 1(T ) β 1 = ) ( β 1(T )i β 1. i=1 12 / 17
13 Bias in the AR(1) model 0.01 Ê ( β 1(10) 0.5) = > = 0.1 Ê ( β 1(100) 0.5) = > = / 17
14 Monte Carlo analysis of AR(1) with exogenous regressor Y t = β 0 + β 1 Y t 1 + β 2 X t + ε t, β 1 < 1, ε t IID ( 0, σε 2 ). (10) which we will also refer to as an AutoRegressive Distributed Lag model, ARDL. We assume that X t is stricty exogenous Monte Carlo DGP: Y t = 0.5Y t X t + ε Yt, ε Yt NIID (0, 1), X t = 0.5X t 1 + ε Xt, ε Xt NIID (0, 2), ( ( There are now two biases, Ê ˆβ 1(T ) 0.5) and Ê ˆβ 2(T ) 1) 14 / 17
15 Biases in the ADL model ( Ê ˆβ 1(T ) 0.5) ( Ê ˆβ 2(T ) 1) / 17
16 Conclusions The OLS biases are small, and the speeds of convergence to zero are high OLS estimation, and the use t ratios and F -statistics for testing extend to dynamic models, given that the model is correctly specified, disturbances that have the usual classical assumptions conditional on Y t 1 and X t. In particular: Avoid residual autocorrelation because it will destroy pre-determinedness of Y t 1! The tests we have covered for Non-Normality, Heteroskedasticity and Autocorrelation in (Lect 13 and 14) are valid mis-specification tests also for ARDL models! 16 / 17
17 Dynamic response to shocks One purpose of estimating an ARDL model: Y t = β 0 + β 1 Y t 1 + β 2 X t + β 3 X t 1 + ε t (11) with classical assumptions for ε t conditional on Y t 1, X t and X t 1 is to estimate the dynamic response of Y to a permanent or temporary change in X. When we consider changes in the X, the key concept is dynamic multiplier. Can also study a temporary shock to ε (for example of magnitude one standard deviation σ) These dynamic effects are often called impulse-responses. In class: Derive dynamic multipliers (short), and show examples of estimated dynamic multipliers. Use of model in forecasting: Lecture / 17
ECON 3150/4150, Spring term Lecture 6
ECON 3150/4150, Spring term 2013. Lecture 6 Review of theoretical statistics for econometric modelling (II) Ragnar Nymoen University of Oslo 31 January 2013 1 / 25 References to Lecture 3 and 6 Lecture
More informationE 4160 Autumn term Lecture 9: Deterministic trends vs integrated series; Spurious regression; Dickey-Fuller distribution and test
E 4160 Autumn term 2016. Lecture 9: Deterministic trends vs integrated series; Spurious regression; Dickey-Fuller distribution and test Ragnar Nymoen Department of Economics, University of Oslo 24 October
More informationReliability of inference (1 of 2 lectures)
Reliability of inference (1 of 2 lectures) Ragnar Nymoen University of Oslo 5 March 2013 1 / 19 This lecture (#13 and 14): I The optimality of the OLS estimators and tests depend on the assumptions of
More informationE 4101/5101 Lecture 9: Non-stationarity
E 4101/5101 Lecture 9: Non-stationarity Ragnar Nymoen 30 March 2011 Introduction I Main references: Hamilton Ch 15,16 and 17. Davidson and MacKinnon Ch 14.3 and 14.4 Also read Ch 2.4 and Ch 2.5 in Davidson
More informationForecasting. Simultaneous equations bias (Lect 16)
Forecasting. Simultaneous equations bias (Lect 16) Ragnar Nymoen University of Oslo 11 April 2013 1 / 20 References Same as to Lecture 15 (as a background to the forecasting part) HGL, Ch 9.7.2 (forecasting
More informationThe regression model with one stochastic regressor (part II)
The regression model with one stochastic regressor (part II) 3150/4150 Lecture 7 Ragnar Nymoen 6 Feb 2012 We will finish Lecture topic 4: The regression model with stochastic regressor We will first look
More informationE 31501/4150 Properties of OLS estimators (Monte Carlo Analysis)
E 31501/4150 Properties of OLS estimators (Monte Carlo Analysis) Ragnar Nymoen 10 February 2011 Repeated sampling Section 2.4.3 of the HGL book is called Repeated sampling The point is that by drawing
More informationThe regression model with one stochastic regressor.
The regression model with one stochastic regressor. 3150/4150 Lecture 6 Ragnar Nymoen 30 January 2012 We are now on Lecture topic 4 The main goal in this lecture is to extend the results of the regression
More informationLecture 6: Dynamic panel models 1
Lecture 6: Dynamic panel models 1 Ragnar Nymoen Department of Economics, UiO 16 February 2010 Main issues and references Pre-determinedness and endogeneity of lagged regressors in FE model, and RE model
More informationECON 4160, Lecture 11 and 12
ECON 4160, 2016. Lecture 11 and 12 Co-integration Ragnar Nymoen Department of Economics 9 November 2017 1 / 43 Introduction I So far we have considered: Stationary VAR ( no unit roots ) Standard inference
More informationECON 4160, Spring term Lecture 12
ECON 4160, Spring term 2013. Lecture 12 Non-stationarity and co-integration 2/2 Ragnar Nymoen Department of Economics 13 Nov 2013 1 / 53 Introduction I So far we have considered: Stationary VAR, with deterministic
More informationECON 3150/4150, Spring term Lecture 7
ECON 3150/4150, Spring term 2014. Lecture 7 The multivariate regression model (I) Ragnar Nymoen University of Oslo 4 February 2014 1 / 23 References to Lecture 7 and 8 SW Ch. 6 BN Kap 7.1-7.8 2 / 23 Omitted
More informationThe regression model with one fixed regressor cont d
The regression model with one fixed regressor cont d 3150/4150 Lecture 4 Ragnar Nymoen 27 January 2012 The model with transformed variables Regression with transformed variables I References HGL Ch 2.8
More informationECON 4160: Econometrics-Modelling and Systems Estimation Lecture 7: Single equation models
ECON 4160: Econometrics-Modelling and Systems Estimation Lecture 7: Single equation models Ragnar Nymoen Department of Economics University of Oslo 25 September 2018 The reference to this lecture is: Chapter
More informationThe multiple regression model; Indicator variables as regressors
The multiple regression model; Indicator variables as regressors Ragnar Nymoen University of Oslo 28 February 2013 1 / 21 This lecture (#12): Based on the econometric model specification from Lecture 9
More informationLecture 7: Dynamic panel models 2
Lecture 7: Dynamic panel models 2 Ragnar Nymoen Department of Economics, UiO 25 February 2010 Main issues and references The Arellano and Bond method for GMM estimation of dynamic panel data models A stepwise
More informationEconometrics 2, Class 1
Econometrics 2, Class Problem Set #2 September 9, 25 Remember! Send an email to let me know that you are following these classes: paul.sharp@econ.ku.dk That way I can contact you e.g. if I need to cancel
More informationThe linear regression model: functional form and structural breaks
The linear regression model: functional form and structural breaks Ragnar Nymoen Department of Economics, UiO 16 January 2009 Overview Dynamic models A little bit more about dynamics Extending inference
More informationEconomics 308: Econometrics Professor Moody
Economics 308: Econometrics Professor Moody References on reserve: Text Moody, Basic Econometrics with Stata (BES) Pindyck and Rubinfeld, Econometric Models and Economic Forecasts (PR) Wooldridge, Jeffrey
More informationEconometrics of Panel Data
Econometrics of Panel Data Jakub Mućk Meeting # 6 Jakub Mućk Econometrics of Panel Data Meeting # 6 1 / 36 Outline 1 The First-Difference (FD) estimator 2 Dynamic panel data models 3 The Anderson and Hsiao
More informationECON 4160, Spring term 2015 Lecture 7
ECON 4160, Spring term 2015 Lecture 7 Identification and estimation of SEMs (Part 1) Ragnar Nymoen Department of Economics 8 Oct 2015 1 / 55 HN Ch 15 References to Davidson and MacKinnon, Ch 8.1-8.5 Ch
More informationSimultaneous Equation Models Learning Objectives Introduction Introduction (2) Introduction (3) Solving the Model structural equations
Simultaneous Equation Models. Introduction: basic definitions 2. Consequences of ignoring simultaneity 3. The identification problem 4. Estimation of simultaneous equation models 5. Example: IS LM model
More informationECON 4160: Econometrics-Modelling and Systems Estimation Lecture 9: Multiple equation models II
ECON 4160: Econometrics-Modelling and Systems Estimation Lecture 9: Multiple equation models II Ragnar Nymoen Department of Economics University of Oslo 9 October 2018 The reference to this lecture is:
More informationLinear Regression with Time Series Data
u n i v e r s i t y o f c o p e n h a g e n d e p a r t m e n t o f e c o n o m i c s Econometrics II Linear Regression with Time Series Data Morten Nyboe Tabor u n i v e r s i t y o f c o p e n h a g
More informationSlides to Lecture 3 of Introductory Dynamic Macroeconomics. Linear Dynamic Models (Ch 2 of IDM)
Partial recap of lecture 2 1. We used the ADL model to make precise the concept of dynamic multiplier. Slides to Lecture 3 of Introductory Dynamic Macroeconomics. Linear Dynamic Models (Ch 2 of IDM) Ragnar
More informationMA Advanced Econometrics: Applying Least Squares to Time Series
MA Advanced Econometrics: Applying Least Squares to Time Series Karl Whelan School of Economics, UCD February 15, 2011 Karl Whelan (UCD) Time Series February 15, 2011 1 / 24 Part I Time Series: Standard
More informationLinear Regression with Time Series Data
u n i v e r s i t y o f c o p e n h a g e n d e p a r t m e n t o f e c o n o m i c s Econometrics II Linear Regression with Time Series Data Morten Nyboe Tabor u n i v e r s i t y o f c o p e n h a g
More informationStatistics 910, #5 1. Regression Methods
Statistics 910, #5 1 Overview Regression Methods 1. Idea: effects of dependence 2. Examples of estimation (in R) 3. Review of regression 4. Comparisons and relative efficiencies Idea Decomposition Well-known
More informationECON 4160, Autumn term 2017 Lecture 9
ECON 4160, Autumn term 2017 Lecture 9 Structural VAR (SVAR) Ragnar Nymoen Department of Economics 26 Oct 2017 1 / 14 Parameter of interest: impulse responses I Consider again a partial market equilibrium
More informationEcon 4120 Applied Forecasting Methods L10: Forecasting with Regression Models. Sung Y. Park CUHK
Econ 4120 Applied Forecasting Methods L10: Forecasting with Regression Models Sung Y. Park CUHK Conditional forecasting model Forecast a variable conditional on assumptions about other variables. (scenario
More information11. Further Issues in Using OLS with TS Data
11. Further Issues in Using OLS with TS Data With TS, including lags of the dependent variable often allow us to fit much better the variation in y Exact distribution theory is rarely available in TS applications,
More informationNon-Stationary Time Series, Cointegration, and Spurious Regression
Econometrics II Non-Stationary Time Series, Cointegration, and Spurious Regression Econometrics II Course Outline: Non-Stationary Time Series, Cointegration and Spurious Regression 1 Regression with Non-Stationarity
More informationChristopher Dougherty London School of Economics and Political Science
Introduction to Econometrics FIFTH EDITION Christopher Dougherty London School of Economics and Political Science OXFORD UNIVERSITY PRESS Contents INTRODU CTION 1 Why study econometrics? 1 Aim of this
More informationF9 F10: Autocorrelation
F9 F10: Autocorrelation Feng Li Department of Statistics, Stockholm University Introduction In the classic regression model we assume cov(u i, u j x i, x k ) = E(u i, u j ) = 0 What if we break the assumption?
More informationTime Series Analysis. James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY
Time Series Analysis James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY & Contents PREFACE xiii 1 1.1. 1.2. Difference Equations First-Order Difference Equations 1 /?th-order Difference
More informationRegression with time series
Regression with time series Class Notes Manuel Arellano February 22, 2018 1 Classical regression model with time series Model and assumptions The basic assumption is E y t x 1,, x T = E y t x t = x tβ
More informationEksamen på Økonomistudiet 2006-II Econometrics 2 June 9, 2006
Eksamen på Økonomistudiet 2006-II Econometrics 2 June 9, 2006 This is a four hours closed-book exam (uden hjælpemidler). Please answer all questions. As a guiding principle the questions 1 to 4 have equal
More informationEconomics 536 Lecture 7. Introduction to Specification Testing in Dynamic Econometric Models
University of Illinois Fall 2016 Department of Economics Roger Koenker Economics 536 Lecture 7 Introduction to Specification Testing in Dynamic Econometric Models In this lecture I want to briefly describe
More informationBootstrapping Heteroskedasticity Consistent Covariance Matrix Estimator
Bootstrapping Heteroskedasticity Consistent Covariance Matrix Estimator by Emmanuel Flachaire Eurequa, University Paris I Panthéon-Sorbonne December 2001 Abstract Recent results of Cribari-Neto and Zarkos
More informationG. S. Maddala Kajal Lahiri. WILEY A John Wiley and Sons, Ltd., Publication
G. S. Maddala Kajal Lahiri WILEY A John Wiley and Sons, Ltd., Publication TEMT Foreword Preface to the Fourth Edition xvii xix Part I Introduction and the Linear Regression Model 1 CHAPTER 1 What is Econometrics?
More informationLecture 5: Unit Roots, Cointegration and Error Correction Models The Spurious Regression Problem
Lecture 5: Unit Roots, Cointegration and Error Correction Models The Spurious Regression Problem Prof. Massimo Guidolin 20192 Financial Econometrics Winter/Spring 2018 Overview Stochastic vs. deterministic
More informationTime Series Analysis. James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY
Time Series Analysis James D. Hamilton PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY PREFACE xiii 1 Difference Equations 1.1. First-Order Difference Equations 1 1.2. pth-order Difference Equations 7
More informationUsing all observations when forecasting under structural breaks
Using all observations when forecasting under structural breaks Stanislav Anatolyev New Economic School Victor Kitov Moscow State University December 2007 Abstract We extend the idea of the trade-off window
More information10) Time series econometrics
30C00200 Econometrics 10) Time series econometrics Timo Kuosmanen Professor, Ph.D. 1 Topics today Static vs. dynamic time series model Suprious regression Stationary and nonstationary time series Unit
More informationNon-Stationary Time Series and Unit Root Testing
Econometrics II Non-Stationary Time Series and Unit Root Testing Morten Nyboe Tabor Course Outline: Non-Stationary Time Series and Unit Root Testing 1 Stationarity and Deviation from Stationarity Trend-Stationarity
More informationEconometría 2: Análisis de series de Tiempo
Econometría 2: Análisis de series de Tiempo Karoll GOMEZ kgomezp@unal.edu.co http://karollgomez.wordpress.com Segundo semestre 2016 IX. Vector Time Series Models VARMA Models A. 1. Motivation: The vector
More informationEcon 623 Econometrics II Topic 2: Stationary Time Series
1 Introduction Econ 623 Econometrics II Topic 2: Stationary Time Series In the regression model we can model the error term as an autoregression AR(1) process. That is, we can use the past value of the
More informationA better way to bootstrap pairs
A better way to bootstrap pairs Emmanuel Flachaire GREQAM - Université de la Méditerranée CORE - Université Catholique de Louvain April 999 Abstract In this paper we are interested in heteroskedastic regression
More information7 Introduction to Time Series
Econ 495 - Econometric Review 1 7 Introduction to Time Series 7.1 Time Series vs. Cross-Sectional Data Time series data has a temporal ordering, unlike cross-section data, we will need to changes some
More informationChapter 2: Unit Roots
Chapter 2: Unit Roots 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and undeconometrics II. Unit Roots... 3 II.1 Integration Level... 3 II.2 Nonstationarity
More informationBCT Lecture 3. Lukas Vacha.
BCT Lecture 3 Lukas Vacha vachal@utia.cas.cz Stationarity and Unit Root Testing Why do we need to test for Non-Stationarity? The stationarity or otherwise of a series can strongly influence its behaviour
More informationLECTURE 11. Introduction to Econometrics. Autocorrelation
LECTURE 11 Introduction to Econometrics Autocorrelation November 29, 2016 1 / 24 ON PREVIOUS LECTURES We discussed the specification of a regression equation Specification consists of choosing: 1. correct
More informationLecture 6: Dynamic Models
Lecture 6: Dynamic Models R.G. Pierse 1 Introduction Up until now we have maintained the assumption that X values are fixed in repeated sampling (A4) In this lecture we look at dynamic models, where the
More informationTAKEHOME FINAL EXAM e iω e 2iω e iω e 2iω
ECO 513 Spring 2015 TAKEHOME FINAL EXAM (1) Suppose the univariate stochastic process y is ARMA(2,2) of the following form: y t = 1.6974y t 1.9604y t 2 + ε t 1.6628ε t 1 +.9216ε t 2, (1) where ε is i.i.d.
More informationDiscussion of Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions, by Li Pan and Dimitris Politis
Discussion of Bootstrap prediction intervals for linear, nonlinear, and nonparametric autoregressions, by Li Pan and Dimitris Politis Sílvia Gonçalves and Benoit Perron Département de sciences économiques,
More informationA Modified Fractionally Co-integrated VAR for Predicting Returns
A Modified Fractionally Co-integrated VAR for Predicting Returns Xingzhi Yao Marwan Izzeldin Department of Economics, Lancaster University 13 December 215 Yao & Izzeldin (Lancaster University) CFE (215)
More informationA Course on Advanced Econometrics
A Course on Advanced Econometrics Yongmiao Hong The Ernest S. Liu Professor of Economics & International Studies Cornell University Course Introduction: Modern economies are full of uncertainties and risk.
More informationIntroduction to Econometrics
Introduction to Econometrics T H I R D E D I T I O N Global Edition James H. Stock Harvard University Mark W. Watson Princeton University Boston Columbus Indianapolis New York San Francisco Upper Saddle
More information1 Estimation of Persistent Dynamic Panel Data. Motivation
1 Estimation of Persistent Dynamic Panel Data. Motivation Consider the following Dynamic Panel Data (DPD) model y it = y it 1 ρ + x it β + µ i + v it (1.1) with i = {1, 2,..., N} denoting the individual
More informationLecture 19 - Decomposing a Time Series into its Trend and Cyclical Components
Lecture 19 - Decomposing a Time Series into its Trend and Cyclical Components It is often assumed that many macroeconomic time series are subject to two sorts of forces: those that influence the long-run
More informationUNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Exam: ECON3150/ECON4150 Introductory Econometrics Date of exam: Wednesday, May 15, 013 Grades are given: June 6, 013 Time for exam: :30 p.m. 5:30 p.m. The problem
More informationBlock Bootstrap Prediction Intervals for Vector Autoregression
Department of Economics Working Paper Block Bootstrap Prediction Intervals for Vector Autoregression Jing Li Miami University 2013 Working Paper # - 2013-04 Block Bootstrap Prediction Intervals for Vector
More informationECON 3150/4150 spring term 2014: Exercise set for the first seminar and DIY exercises for the first few weeks of the course
ECON 3150/4150 spring term 2014: Exercise set for the first seminar and DIY exercises for the first few weeks of the course Ragnar Nymoen 13 January 2014. Exercise set to seminar 1 (week 6, 3-7 Feb) This
More informationAutoregressive models with distributed lags (ADL)
Autoregressive models with distributed lags (ADL) It often happens than including the lagged dependent variable in the model results in model which is better fitted and needs less parameters. It can be
More informationLECTURE 10: MORE ON RANDOM PROCESSES
LECTURE 10: MORE ON RANDOM PROCESSES AND SERIAL CORRELATION 2 Classification of random processes (cont d) stationary vs. non-stationary processes stationary = distribution does not change over time more
More informationEconometrics. Week 4. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague
Econometrics Week 4 Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Fall 2012 1 / 23 Recommended Reading For the today Serial correlation and heteroskedasticity in
More informationVector Autoregressive Model. Vector Autoregressions II. Estimation of Vector Autoregressions II. Estimation of Vector Autoregressions I.
Vector Autoregressive Model Vector Autoregressions II Empirical Macroeconomics - Lect 2 Dr. Ana Beatriz Galvao Queen Mary University of London January 2012 A VAR(p) model of the m 1 vector of time series
More information7 Introduction to Time Series Time Series vs. Cross-Sectional Data Detrending Time Series... 15
Econ 495 - Econometric Review 1 Contents 7 Introduction to Time Series 3 7.1 Time Series vs. Cross-Sectional Data............ 3 7.2 Detrending Time Series................... 15 7.3 Types of Stochastic
More informationEcon 423 Lecture Notes: Additional Topics in Time Series 1
Econ 423 Lecture Notes: Additional Topics in Time Series 1 John C. Chao April 25, 2017 1 These notes are based in large part on Chapter 16 of Stock and Watson (2011). They are for instructional purposes
More information1 Introduction to Generalized Least Squares
ECONOMICS 7344, Spring 2017 Bent E. Sørensen April 12, 2017 1 Introduction to Generalized Least Squares Consider the model Y = Xβ + ɛ, where the N K matrix of regressors X is fixed, independent of the
More informationBootstrap Testing in Econometrics
Presented May 29, 1999 at the CEA Annual Meeting Bootstrap Testing in Econometrics James G MacKinnon Queen s University at Kingston Introduction: Economists routinely compute test statistics of which the
More informationIntroductory Econometrics
Based on the textbook by Wooldridge: : A Modern Approach Robert M. Kunst robert.kunst@univie.ac.at University of Vienna and Institute for Advanced Studies Vienna December 17, 2012 Outline Heteroskedasticity
More informationMultivariate Time Series
Multivariate Time Series Fall 2008 Environmental Econometrics (GR03) TSII Fall 2008 1 / 16 More on AR(1) In AR(1) model (Y t = µ + ρy t 1 + u t ) with ρ = 1, the series is said to have a unit root or a
More informationTesting methodology. It often the case that we try to determine the form of the model on the basis of data
Testing methodology It often the case that we try to determine the form of the model on the basis of data The simplest case: we try to determine the set of explanatory variables in the model Testing for
More informationNonstationary Time Series:
Nonstationary Time Series: Unit Roots Egon Zakrajšek Division of Monetary Affairs Federal Reserve Board Summer School in Financial Mathematics Faculty of Mathematics & Physics University of Ljubljana September
More informationLikely causes: The Problem. E u t 0. E u s u p 0
Autocorrelation This implies that taking the time series regression Y t X t u t but in this case there is some relation between the error terms across observations. E u t 0 E u t E u s u p 0 Thus the error
More information1 Regression with Time Series Variables
1 Regression with Time Series Variables With time series regression, Y might not only depend on X, but also lags of Y and lags of X Autoregressive Distributed lag (or ADL(p; q)) model has these features:
More informationMonte Carlo Simulations and the PcNaive Software
Econometrics 2 Monte Carlo Simulations and the PcNaive Software Heino Bohn Nielsen 1of21 Monte Carlo Simulations MC simulations were introduced in Econometrics 1. Formalizing the thought experiment underlying
More informationIntroduction to Eco n o m et rics
2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Introduction to Eco n o m et rics Third Edition G.S. Maddala Formerly
More informationVector Auto-Regressive Models
Vector Auto-Regressive Models Laurent Ferrara 1 1 University of Paris Nanterre M2 Oct. 2018 Overview of the presentation 1. Vector Auto-Regressions Definition Estimation Testing 2. Impulse responses functions
More informationEmpirical Macroeconomics
Empirical Macroeconomics Francesco Franco Nova SBE April 21, 2015 Francesco Franco Empirical Macroeconomics 1/33 Growth and Fluctuations Supply and Demand Figure : US dynamics Francesco Franco Empirical
More informationEconometrics - 30C00200
Econometrics - 30C00200 Lecture 11: Heteroskedasticity Antti Saastamoinen VATT Institute for Economic Research Fall 2015 30C00200 Lecture 11: Heteroskedasticity 12.10.2015 Aalto University School of Business
More informationVAR Models and Applications
VAR Models and Applications Laurent Ferrara 1 1 University of Paris West M2 EIPMC Oct. 2016 Overview of the presentation 1. Vector Auto-Regressions Definition Estimation Testing 2. Impulse responses functions
More informationDynamic Regression Models
Università di Pavia 2007 Dynamic Regression Models Eduardo Rossi University of Pavia Data Generating Process & Models Setup y t denote an (n 1) vector of economic variables generated at time t. The collection
More informationThe Number of Bootstrap Replicates in Bootstrap Dickey-Fuller Unit Root Tests
Working Paper 2013:8 Department of Statistics The Number of Bootstrap Replicates in Bootstrap Dickey-Fuller Unit Root Tests Jianxin Wei Working Paper 2013:8 June 2013 Department of Statistics Uppsala
More information13. Time Series Analysis: Asymptotics Weakly Dependent and Random Walk Process. Strict Exogeneity
Outline: Further Issues in Using OLS with Time Series Data 13. Time Series Analysis: Asymptotics Weakly Dependent and Random Walk Process I. Stationary and Weakly Dependent Time Series III. Highly Persistent
More informationEmpirical Market Microstructure Analysis (EMMA)
Empirical Market Microstructure Analysis (EMMA) Lecture 3: Statistical Building Blocks and Econometric Basics Prof. Dr. Michael Stein michael.stein@vwl.uni-freiburg.de Albert-Ludwigs-University of Freiburg
More informationChapter 2. Dynamic panel data models
Chapter 2. Dynamic panel data models School of Economics and Management - University of Geneva Christophe Hurlin, Université of Orléans University of Orléans April 2018 C. Hurlin (University of Orléans)
More informationLecture: Simultaneous Equation Model (Wooldridge s Book Chapter 16)
Lecture: Simultaneous Equation Model (Wooldridge s Book Chapter 16) 1 2 Model Consider a system of two regressions y 1 = β 1 y 2 + u 1 (1) y 2 = β 2 y 1 + u 2 (2) This is a simultaneous equation model
More informationEconometrics Honor s Exam Review Session. Spring 2012 Eunice Han
Econometrics Honor s Exam Review Session Spring 2012 Eunice Han Topics 1. OLS The Assumptions Omitted Variable Bias Conditional Mean Independence Hypothesis Testing and Confidence Intervals Homoskedasticity
More informationEconometrics Summary Algebraic and Statistical Preliminaries
Econometrics Summary Algebraic and Statistical Preliminaries Elasticity: The point elasticity of Y with respect to L is given by α = ( Y/ L)/(Y/L). The arc elasticity is given by ( Y/ L)/(Y/L), when L
More informationProblem Set 1 Solution Sketches Time Series Analysis Spring 2010
Problem Set 1 Solution Sketches Time Series Analysis Spring 2010 1. Construct a martingale difference process that is not weakly stationary. Simplest e.g.: Let Y t be a sequence of independent, non-identically
More informationLecture 2: Univariate Time Series
Lecture 2: Univariate Time Series Analysis: Conditional and Unconditional Densities, Stationarity, ARMA Processes Prof. Massimo Guidolin 20192 Financial Econometrics Spring/Winter 2017 Overview Motivation:
More informationUnit Root and Cointegration
Unit Root and Cointegration Carlos Hurtado Department of Economics University of Illinois at Urbana-Champaign hrtdmrt@illinois.edu Oct 7th, 016 C. Hurtado (UIUC - Economics) Applied Econometrics On the
More informationGMM, HAC estimators, & Standard Errors for Business Cycle Statistics
GMM, HAC estimators, & Standard Errors for Business Cycle Statistics Wouter J. Den Haan London School of Economics c Wouter J. Den Haan Overview Generic GMM problem Estimation Heteroskedastic and Autocorrelation
More informationMonte Carlo Simulations and PcNaive
Econometrics 2 Fall 2005 Monte Carlo Simulations and Pcaive Heino Bohn ielsen 1of21 Monte Carlo Simulations MC simulations were introduced in Econometrics 1. Formalizing the thought experiment underlying
More informationApplied Econometrics (MSc.) Lecture 3 Instrumental Variables
Applied Econometrics (MSc.) Lecture 3 Instrumental Variables Estimation - Theory Department of Economics University of Gothenburg December 4, 2014 1/28 Why IV estimation? So far, in OLS, we assumed independence.
More informationCovers Chapter 10-12, some of 16, some of 18 in Wooldridge. Regression Analysis with Time Series Data
Covers Chapter 10-12, some of 16, some of 18 in Wooldridge Regression Analysis with Time Series Data Obviously time series data different from cross section in terms of source of variation in x and y temporal
More informationA Non-Parametric Approach of Heteroskedasticity Robust Estimation of Vector-Autoregressive (VAR) Models
Journal of Finance and Investment Analysis, vol.1, no.1, 2012, 55-67 ISSN: 2241-0988 (print version), 2241-0996 (online) International Scientific Press, 2012 A Non-Parametric Approach of Heteroskedasticity
More informationThis note analyzes OLS estimation in a linear regression model for time series
LINEAR REGRESSION WITH TIME SERIES DATA Econometrics C LectureNote2 Heino Bohn Nielsen February 6, 2012 This note analyzes OLS estimation in a linear regression model for time series data. We first discuss
More information