Dynamic models for largedimensional. Yields on U.S. Treasury securities (3 months to 10 years) y t
|
|
|
- Eunice Bryan
- 5 years ago
- Views:
Transcription
1 Dynamic models for largedimensional vecor sysems A. Principal componens analysis Suppose we have a large number of variables observed a dae Goal: can we summarize mos of he feaures of he daa using jus a few indicaors? Yields on U.S. Treasury securiies (3 monhs o 10 years) GS3M GS6M GS1 GS2 GS5 GS n 1 vecor of saionary observaions i T 1 T y i (mean of variable i ii T 1 T y i i 2 y i 1/2 ii y i i y 1,..., y n T 1 T (sample correlaion marix) 1
2 Goal is o find a scalar and n 1 vecor h so as o minimize T h h Noe: h and are no unique (h h for h qh, q 1 ) bu h is unique. One normalizaion: h h 1. h Scalar explains as much of variaion of as possible. Soluion is called he "firs principal componen" of (deermined up o arbirary scale facor). Elemens of vecor h are called "facor loadings". min h, 1,..., T T h h Concenrae objecive funcion: (1) for any h, find bes 1,..., T (2) subsiue h ino objecive and min wih respec o h 2
3 (1) for fixed h: min 1,..., T T h h min h h OLS regression of on h h h h 1 h h h I n hh h 1 h (2) minimize over h: min T h h h h h T y I n hh h 1 h max T y hh h 1 h h subjec o h h 1 T h y h h T h Th h max h h h subjec o h h 1 3
4 Consider eigenvalues of x i ix i for i 1,..,n diag 1,.., n X x 1 x n X X I n X X X X max h h subjec o h h 1 h Le h Xh where X X I n and X X max h h subjec o h h 1 h max h X Xh subjec o h h 1 h h X Xh h h h h n 2 n max h h 2 n n h s.. h 1 2 h n 2 1 Soluion: h 1 1 h 2 h 3 h n 0 h x 1 4
5 Conclusion: he facor loadings are given bhe eigenvecor of associaed wih larges eigenvalue. The firs principal componen is given by h, he produc of his eigenvecor wih de-meaned daa vecor. Example: ineres raes for monh for U.S. Treasury securiies wih mauriies 3m, 6m, 1y, 2y, 5y, 10y n :M1-2013:M5 T 1 T Eigenvecor of associaed wih larges eigenvalue: (0.3999, , , , , ) 1/ Conclusion: firs principal componen is esseniallhe average of he 6 yields. 5
6 GS10 GS5 GS2 GS1 GS6M GS3M Fied value for yield i: y i i h i GS3M GS3M_PRED GS10 GS10Y_PRED
7 Could also ask: suppose I could use 2 variables o summarize he 6 yields. Choose 21 vecor for 1,...,T and n 2 marix H o minimize T H H. Again no unique: Q nonsingular 2 2 marix H HQ Q 1 H H. Normalize H H I 2. min H H y I n HH H 1 H max T y HH H 1 H H T raceh H 1 H y H TH H 1 race H H 7
8 Soluion: H is in he linear space spanned bhe eigenvecors of associaed wih he wo larges eigenvalues. Second principal componen refers o h 2 for h 2 he eigenvecor of associaed wih he second larges eigenvalue. Noe second PC is orhogonal o he firs: T h 1 y h 2 Th 1 h 2 T 2h 1 h 2 0 Ineres raes: eigenvalues of Ω Eigenvalue Percen E E
9 GS10 GS5 GS2 GS1 GS6M GS3M Facor loadings associaed wih firs hree principal componens level (facor 1) slope (facor 2) curvaure (facor 3) ineres raes PC PC PC Dynamic models for largedimensional vecor sysems A. Principal componens analysis B. Dynamic facor models 9
10 observed variables unobserved facors u H nr rr D u nn u v D diagd 1, d 2,...,d n H nr Assumpion 1: n 1 H H n u Q H rr wih rank(q H r. Means facors maer for more han jus finie subse of and are differen from each oher (columns of H no oo similar). Assumpion 2: maximum eigenvalue of Eu u is c for all n. Means u does no have is own facor srucure. (e.g., for Eu u 2 11 hen 1 is eigenvecor wih eigenvalue n 10
11 Suppose hese assumpions held and here was ann r marix W such ha: (i) n 1 W W I r (ii) n 1 W H rr (iii) rank( r For yields example and r 1, W 1, 1,..., 1 H nr u n 1 W n 1 rn rn n 1 W u rn W H nr n 1 W u p 0 (e.g., n 1 n i1 u i p 0 Sock and Wason (JASA, 2002) showed ha under relaed assumpions, he firs r principal componens of provide a consisen esimae of for some nonsingular r r marix. 11
12 However, lieraure on erm srucure of ineres raes suggess ha firs 3 PC of ineres raes do no span se of linear combinaions mos useful for forecasing (e.g., Gregory Duffee, "Informaion in (and no in) he erm srucure," Rev Financial Sudies, 2011) Selecing he number of facors r V r H r, r H H nr H, arg min H, 1,..., T subjec o H H I r H H Bai and Ng, Economerica (2002): Choose r o minimize log V r H r, r r nt logminn,t nt 12
13 Ahn and Horensein, Economerica (2013): T 1 T 1 larges eigenvalue of n smalles eigenvalue of Choose r o be value for which r/ is larges. Dynamic models for largedimensional vecor sysems A. Principal componens analysis B. Dynamic facor models C. Nowcasing wih large jagged-edge realime daase Giannone, Reichlin, and Small, JME, 2008 Suppose we have poenially hundreds of differen monhly indicaors, only some of which are currenly available. Wha is he opimal esimae of wha his quarer s GDP growh will urn ou o be? 13
14 n 1 vecor of saionary indicaors ha will evenually be available for monh y i y i y i / i. Calculae firs r PC using larges T for which full sample is available y i i h i w i Ew 2 2 i r i Could calculae analyically or wih OLS regressions for i 1,..., n H nr w Ew w R diagr 1 2,..., r n 2 obs eq for sae-space model F rr Ev v Q v sae eq (could esimae by OLS) 14
15 Conclusion: we could use Kalman filer o obain opimal esimae of facors for las dae T for which we have complee daa, T y T,..., y 1 N T T, P T T, and forecas for T 1: T1 y T,..., y 1 N T1 T, P T1 T. If we had full observaion of y T1, we would updae inference wih T1 T1 T1 T P T1 T HH P T1 T H R 1 T1 T1 y T1 H T1 T If insead for some day T1 we only have some subse of y T1, jus se rows of H and T1 corresponding o missing obs equal o 0: T1 T1 T1 T P T1 T H T1 H T1 P T1 T H T1 R 1 T1 T1 i,t1 T1 i,t1 T1 y i,t1 i h i T1 T if i is observed 0 if i is no observed 15
16 If our goal is o esimae GDP growh for quarer q, regress i on facor value in hird monh of quarer (q using full se of observed daa: y q q e q q 1, 2,..., Q, Q T ŷ q Tk T3 Tk where for example F 2 T3 T1 T1 T1 16
17 Sample of news releases during week of Oc 21, 2013 Dae 21-Oc Time (ET) Saisic For Acual Briefing Marke Forecas Expecs Prior Revised From 10:00 AMExising Home Sales Sep 5.29M 5.15M 5.30M 5.39M 5.48M 22-Oc 8:30 AMNonfarm Payrolls Sep 148K 165K 183K 193K 169K 22-Oc 8:30 AMUnemploymen Rae Sep 7.20% 7.30% 7.30% 7.30% - 22-Oc 8:30 AMHourly Earnings Sep 0.10% 0.20% 0.20% 0.30% 0.20% 24-Oc 8:30 AMIniial Claims Oc 350K 330K 341K 362K 358K 25-Oc 8:30 AMDurable Orders Sep 3.70% 4.20% 3.50% 0.20% 0.10% Durable Goods -ex 25-Oc 8:30 AMransporaion Sep -0.10% 0.30% 0.30% -0.40% -0.10% Michigan Senimen - 25-Oc 9:55 AMFinal Oc Source: hp://biz.yahoo.com/c/e.hml Nowcass of 2013:Q4 U.S. real GDP growh (quarerly rae) Oc 22: 0.81 Oc 24: 0.76 Oc 25: 0.71 Source: Nowcass of 2013:Q3 U.S. real GDP growh rae (quarerly rae) Source: 17
18 Forecass of 2014:Q1 U.S. real GDP growh rae (quarerly rae) Source: Dynamic models for largedimensional vecor sysems A. Principal componens analysis B. Dynamic facor models C. Nowcasing wih large jagged-edge realime daase D. Facor-Augmened Vecor Auoregressions (FAVAR) Bernanke, Boivin and Eliasz, QJE, 2005 n 1 vecor of observed variables n 120 x m 1 subse of of special ineres or imporance. BBE ake x r (he fed funds rae) or x fed funds rae, indusrial producion, and inflaion, in deviaions from heir means. 18
19 Facor-Augmened VAR: x m1 11 L rr 21 L mr 12 L rm 22 L mm x m1 1 2 m1 ij L 1 ij L 1 2 ij L 2 p ij L p Could esimae space spanned by bha spanned by, he firs r principal componens of. Quesion: how o idenify moneary policy shock? Noe: since r is included in, each elemen of H is linear funcion of r. Claim: a moneary policy shock does no affec "slow-moving variables" (wages, prices) in he curren monh. 19
20 y subse of ha is "slow-moving" firs r PC of firs r PC of y (1) regress i i i r e i for i 1,...,r (2) Calculae i i i r (3) Esimae VAR for x,r x Lx (4) Calculae nonorhogonalized impulse-response funcion L I L 1 s x s and Cholesky facorizaion T 1 T P P 20
21 (5) Effec of moneary policy shock (u M on x x is x s u M sp for p he las column of P (6) Since H nr h r r, effec of moneary policy on any variable is s u M H h r sp Effecs of moneary policy shock 21
22 Effecs of moneary policy shock Effecs of moneary policy shock Bu how do we updae his approach now ha fed funds rae is suck a zero? Fischer Black, Journal of Finance, 1995: Can hink of laen or shadow shor rae ha is allowed o be negaive Acual shor rae is maximum of his and (say) 0.25 Wu and Xia (UCSD, 2013) develop convenien algorihm o calculae shadow rae 22
23 Wu and Xia fail o rejec hypohesis ha FAVAR coefficiens since 2009 are same as hose using fed funds for hisorical daa Daa available a hp://econweb.ucsd.edu/~faxia/policyrae.hml 23
Forward guidance. Fed funds target during /15/2017
Forward guidance Fed funds arge during 2004 A. A wo-dimensional characerizaion of moneary shocks (Gürkynak, Sack, and Swanson, 2005) B. Odyssean versus Delphic foreign guidance (Campbell e al., 2012) C.
Affine term structure models
Affine erm srucure models A. Inro o Gaussian affine erm srucure models B. Esimaion by minimum chi square (Hamilon and Wu) C. Esimaion by OLS (Adrian, Moench, and Crump) D. Dynamic Nelson-Siegel model (Chrisensen,
C. Theoretical channels 1. Conditions for complete neutrality Suppose preferences are E t. Monetary policy at the zero lower bound: Theory 11/22/2017
//7 Moneary policy a he zero lower bound: Theory A. Theoreical channels. Condiions for complee neuraliy (Eggersson and Woodford, ). Marke fricions. Preferred habia and risk-bearing (Hamilon and Wu, ) B.
Vectorautoregressive Model and Cointegration Analysis. Time Series Analysis Dr. Sevtap Kestel 1
Vecorauoregressive Model and Coinegraion Analysis Par V Time Series Analysis Dr. Sevap Kesel 1 Vecorauoregression Vecor auoregression (VAR) is an economeric model used o capure he evoluion and he inerdependencies
Time series Decomposition method
Time series Decomposiion mehod A ime series is described using a mulifacor model such as = f (rend, cyclical, seasonal, error) = f (T, C, S, e) Long- Iner-mediaed Seasonal Irregular erm erm effec, effec,
Distribution of Estimates
Disribuion of Esimaes From Economerics (40) Linear Regression Model Assume (y,x ) is iid and E(x e )0 Esimaion Consisency y α + βx + he esimaes approach he rue values as he sample size increases Esimaion
Diebold, Chapter 7. Francis X. Diebold, Elements of Forecasting, 4th Edition (Mason, Ohio: Cengage Learning, 2006). Chapter 7. Characterizing Cycles
Diebold, Chaper 7 Francis X. Diebold, Elemens of Forecasing, 4h Ediion (Mason, Ohio: Cengage Learning, 006). Chaper 7. Characerizing Cycles Afer compleing his reading you should be able o: Define covariance
Inflation Nowcasting: Frequently Asked Questions These questions and answers accompany the technical working paper Nowcasting U.S.
Inflaion Nowcasing: Frequenly Asked Quesions These quesions and answers accompany he echnical working paper Nowcasing US Headline and Core Inflaion by Edward S Knoek II and Saeed Zaman See he paper for
Testing for a Single Factor Model in the Multivariate State Space Framework
esing for a Single Facor Model in he Mulivariae Sae Space Framework Chen C.-Y. M. Chiba and M. Kobayashi Inernaional Graduae School of Social Sciences Yokohama Naional Universiy Japan Faculy of Economics
A Dynamic Model of Economic Fluctuations
CHAPTER 15 A Dynamic Model of Economic Flucuaions Modified for ECON 2204 by Bob Murphy 2016 Worh Publishers, all righs reserved IN THIS CHAPTER, OU WILL LEARN: how o incorporae dynamics ino he AD-AS model
Introduction D P. r = constant discount rate, g = Gordon Model (1962): constant dividend growth rate.
Inroducion Gordon Model (1962): D P = r g r = consan discoun rae, g = consan dividend growh rae. If raional expecaions of fuure discoun raes and dividend growh vary over ime, so should he D/P raio. Since
Linear Gaussian State Space Models
Linear Gaussian Sae Space Models Srucural Time Series Models Level and Trend Models Basic Srucural Model (BSM Dynamic Linear Models Sae Space Model Represenaion Level, Trend, and Seasonal Models Time Varying
Ready for euro? Empirical study of the actual monetary policy independence in Poland VECM modelling
Macroeconomerics Handou 2 Ready for euro? Empirical sudy of he acual moneary policy independence in Poland VECM modelling 1. Inroducion This classes are based on: Łukasz Goczek & Dagmara Mycielska, 2013.
Forecasting optimally
I) ile: Forecas Evaluaion II) Conens: Evaluaing forecass, properies of opimal forecass, esing properies of opimal forecass, saisical comparison of forecas accuracy III) Documenaion: - Diebold, Francis
BOKDSGE: A DSGE Model for the Korean Economy
BOKDSGE: A DSGE Model for he Korean Economy June 4, 2008 Joong Shik Lee, Head Macroeconomeric Model Secion Research Deparmen The Bank of Korea Ouline 1. Background 2. Model srucure & parameer values 3.
Distribution of Least Squares
Disribuion of Leas Squares In classic regression, if he errors are iid normal, and independen of he regressors, hen he leas squares esimaes have an exac normal disribuion, no jus asympoic his is no rue
A Dual-Target Monetary Policy Rule for Open Economies: An Application to France ABSTRACT
A Dual-arge Moneary Policy Rule for Open Economies: An Applicaion o France ABSRAC his paper proposes a dual arges moneary policy rule for small open economies. In addiion o a domesic moneary arge, his
Unit Root Time Series. Univariate random walk
Uni Roo ime Series Univariae random walk Consider he regression y y where ~ iid N 0, he leas squares esimae of is: ˆ yy y y yy Now wha if = If y y hen le y 0 =0 so ha y j j If ~ iid N 0, hen y ~ N 0, he
Vector autoregression VAR. Case 1
Vecor auoregression VAR So far we have focused mosl on models where deends onl on as. More generall we migh wan o consider oin models ha involve more han one variable. There are wo reasons: Firs, we migh
Kriging Models Predicting Atrazine Concentrations in Surface Water Draining Agricultural Watersheds
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Kriging Models Predicing Arazine Concenraions in Surface Waer Draining Agriculural Waersheds Paul L. Mosquin, Jeremy Aldworh, Wenlin Chen Supplemenal Maerial Number
Advanced time-series analysis (University of Lund, Economic History Department)
Advanced ime-series analysis (Universiy of Lund, Economic Hisory Deparmen) 30 Jan-3 February and 6-30 March 01 Lecure 9 Vecor Auoregression (VAR) echniques: moivaion and applicaions. Esimaion procedure.
Estimation Uncertainty
Esimaion Uncerainy The sample mean is an esimae of β = E(y +h ) The esimaion error is = + = T h y T b ( ) = = + = + = = = T T h T h e T y T y T b β β β Esimaion Variance Under classical condiions, where
Testing the Random Walk Model. i.i.d. ( ) r
he random walk heory saes: esing he Random Walk Model µ ε () np = + np + Momen Condiions where where ε ~ i.i.d he idea here is o es direcly he resricions imposed by momen condiions. lnp lnp µ ( lnp lnp
Financial Econometrics Jeffrey R. Russell Midterm Winter 2009 SOLUTIONS
Name SOLUTIONS Financial Economerics Jeffrey R. Russell Miderm Winer 009 SOLUTIONS You have 80 minues o complee he exam. Use can use a calculaor and noes. Try o fi all your work in he space provided. If
Summer Term Albert-Ludwigs-Universität Freiburg Empirische Forschung und Okonometrie. Time Series Analysis
Summer Term 2009 Alber-Ludwigs-Universiä Freiburg Empirische Forschung und Okonomerie Time Series Analysis Classical Time Series Models Time Series Analysis Dr. Sevap Kesel 2 Componens Hourly earnings:
Problem Set 5. Graduate Macro II, Spring 2017 The University of Notre Dame Professor Sims
Problem Se 5 Graduae Macro II, Spring 2017 The Universiy of Nore Dame Professor Sims Insrucions: You may consul wih oher members of he class, bu please make sure o urn in your own work. Where applicable,
Policy regimes Theory
Advanced Moneary Theory and Policy EPOS 2012/13 Policy regimes Theory Giovanni Di Barolomeo giovanni.dibarolomeo@uniroma1.i The moneary policy regime The simple model: x = - s (i - p e ) + x e + e D p
13.3 Term structure models
13.3 Term srucure models 13.3.1 Expecaions hypohesis model - Simples "model" a) shor rae b) expecaions o ge oher prices Resul: y () = 1 h +1 δ = φ( δ)+ε +1 f () = E (y +1) (1) =δ + φ( δ) f (3) = E (y +)
Dynamic Econometric Models: Y t = + 0 X t + 1 X t X t k X t-k + e t. A. Autoregressive Model:
Dynamic Economeric Models: A. Auoregressive Model: Y = + 0 X 1 Y -1 + 2 Y -2 + k Y -k + e (Wih lagged dependen variable(s) on he RHS) B. Disribued-lag Model: Y = + 0 X + 1 X -1 + 2 X -2 + + k X -k + e
Let us start with a two dimensional case. We consider a vector ( x,
Roaion marices We consider now roaion marices in wo and hree dimensions. We sar wih wo dimensions since wo dimensions are easier han hree o undersand, and one dimension is a lile oo simple. However, our
Two Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
Smoothing. Backward smoother: At any give T, replace the observation yt by a combination of observations at & before T
Smoohing Consan process Separae signal & noise Smooh he daa: Backward smooher: A an give, replace he observaion b a combinaion of observaions a & before Simple smooher : replace he curren observaion wih
OBJECTIVES OF TIME SERIES ANALYSIS
OBJECTIVES OF TIME SERIES ANALYSIS Undersanding he dynamic or imedependen srucure of he observaions of a single series (univariae analysis) Forecasing of fuure observaions Asceraining he leading, lagging
Linear state-space models
Linear sae-space models A. Sae-space represenaion of a dynamic sysem Consider following model Sae equaion: F rr r r Observaion equaion: y n A x nkk v r H nr r Observed variables: y,x w n Unobserved variables:,v,w
Chapter 15. Time Series: Descriptive Analyses, Models, and Forecasting
Chaper 15 Time Series: Descripive Analyses, Models, and Forecasing Descripive Analysis: Index Numbers Index Number a number ha measures he change in a variable over ime relaive o he value of he variable
Econ107 Applied Econometrics Topic 7: Multicollinearity (Studenmund, Chapter 8)
I. Definiions and Problems A. Perfec Mulicollineariy Econ7 Applied Economerics Topic 7: Mulicollineariy (Sudenmund, Chaper 8) Definiion: Perfec mulicollineariy exiss in a following K-variable regression
Generalized Least Squares
Generalized Leas Squares Augus 006 1 Modified Model Original assumpions: 1 Specificaion: y = Xβ + ε (1) Eε =0 3 EX 0 ε =0 4 Eεε 0 = σ I In his secion, we consider relaxing assumpion (4) Insead, assume
Final Exam Advanced Macroeconomics I
Advanced Macroeconomics I WS 00/ Final Exam Advanced Macroeconomics I February 8, 0 Quesion (5%) An economy produces oupu according o α α Y = K (AL) of which a fracion s is invesed. echnology A is exogenous
State-Space Models. Initialization, Estimation and Smoothing of the Kalman Filter
Sae-Space Models Iniializaion, Esimaion and Smoohing of he Kalman Filer Iniializaion of he Kalman Filer The Kalman filer shows how o updae pas predicors and he corresponding predicion error variances when
Volatility. Many economic series, and most financial series, display conditional volatility
Volailiy Many economic series, and mos financial series, display condiional volailiy The condiional variance changes over ime There are periods of high volailiy When large changes frequenly occur And periods
R t. C t P t. + u t. C t = αp t + βr t + v t. + β + w t
Exercise 7 C P = α + β R P + u C = αp + βr + v (a) (b) C R = α P R + β + w (c) Assumpions abou he disurbances u, v, w : Classical assumions on he disurbance of one of he equaions, eg. on (b): E(v v s P,
E β t log (C t ) + M t M t 1. = Y t + B t 1 P t. B t 0 (3) v t = P tc t M t Question 1. Find the FOC s for an optimum in the agent s problem.
Noes, M. Krause.. Problem Se 9: Exercise on FTPL Same model as in paper and lecure, only ha one-period govenmen bonds are replaced by consols, which are bonds ha pay one dollar forever. I has curren marke
On Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature
On Measuring Pro-Poor Growh 1. On Various Ways of Measuring Pro-Poor Growh: A Shor eview of he Lieraure During he pas en years or so here have been various suggesions concerning he way one should check
Math 315: Linear Algebra Solutions to Assignment 6
Mah 35: Linear Algebra s o Assignmen 6 # Which of he following ses of vecors are bases for R 2? {2,, 3, }, {4,, 7, 8}, {,,, 3}, {3, 9, 4, 2}. Explain your answer. To generae he whole R 2, wo linearly independen
Outline. lse-logo. Outline. Outline. 1 Wald Test. 2 The Likelihood Ratio Test. 3 Lagrange Multiplier Tests
Ouline Ouline Hypohesis Tes wihin he Maximum Likelihood Framework There are hree main frequenis approaches o inference wihin he Maximum Likelihood framework: he Wald es, he Likelihood Raio es and he Lagrange
The Brock-Mirman Stochastic Growth Model
c December 3, 208, Chrisopher D. Carroll BrockMirman The Brock-Mirman Sochasic Growh Model Brock and Mirman (972) provided he firs opimizing growh model wih unpredicable (sochasic) shocks. The social planner
15. Which Rule for Monetary Policy?
15. Which Rule for Moneary Policy? John B. Taylor, May 22, 2013 Sared Course wih a Big Policy Issue: Compeing Moneary Policies Fed Vice Chair Yellen described hese in her April 2012 paper, as discussed
3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon
3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of
20. Applications of the Genetic-Drift Model
0. Applicaions of he Geneic-Drif Model 1) Deermining he probabiliy of forming any paricular combinaion of genoypes in he nex generaion: Example: If he parenal allele frequencies are p 0 = 0.35 and q 0
International Parity Relations between Poland and Germany: A Cointegrated VAR Approach
Research Seminar a he Deparmen of Economics, Warsaw Universiy Warsaw, 15 January 2008 Inernaional Pariy Relaions beween Poland and Germany: A Coinegraed VAR Approach Agnieszka Sążka Naional Bank of Poland
USP. Surplus-Production Models
USP Surplus-Producion Models 2 Overview Purpose of slides: Inroducion o he producion model Overview of differen mehods of fiing Go over some criique of he mehod Source: Haddon 2001, Chaper 10 Hilborn and
A STRUCTURAL VECTOR ERROR CORRECTION MODEL WITH SHORT-RUN AND LONG-RUN RESTRICTIONS
199 THE KOREAN ECONOMIC REVIEW Volume 4, Number 1, Summer 008 A STRUCTURAL VECTOR ERROR CORRECTION MODEL WITH SHORT-RUN AND LONG-RUN RESTRICTIONS KYUNGHO JANG* We consider srucural vecor error correcion
System of Linear Differential Equations
Sysem of Linear Differenial Equaions In "Ordinary Differenial Equaions" we've learned how o solve a differenial equaion for a variable, such as: y'k5$e K2$x =0 solve DE yx = K 5 2 ek2 x C_C1 2$y''C7$y
Macroeconomic Theory Ph.D. Qualifying Examination Fall 2005 ANSWER EACH PART IN A SEPARATE BLUE BOOK. PART ONE: ANSWER IN BOOK 1 WEIGHT 1/3
Macroeconomic Theory Ph.D. Qualifying Examinaion Fall 2005 Comprehensive Examinaion UCLA Dep. of Economics You have 4 hours o complee he exam. There are hree pars o he exam. Answer all pars. Each par has
Wisconsin Unemployment Rate Forecast Revisited
Wisconsin Unemploymen Rae Forecas Revisied Forecas in Lecure Wisconsin unemploymen November 06 was 4.% Forecass Poin Forecas 50% Inerval 80% Inerval Forecas Forecas December 06 4.0% (4.0%, 4.0%) (3.95%,
Solutions to Odd Number Exercises in Chapter 6
1 Soluions o Odd Number Exercises in 6.1 R y eˆ 1.7151 y 6.3 From eˆ ( T K) ˆ R 1 1 SST SST SST (1 R ) 55.36(1.7911) we have, ˆ 6.414 T K ( ) 6.5 y ye ye y e 1 1 Consider he erms e and xe b b x e y e b
Explaining Total Factor Productivity. Ulrich Kohli University of Geneva December 2015
Explaining Toal Facor Produciviy Ulrich Kohli Universiy of Geneva December 2015 Needed: A Theory of Toal Facor Produciviy Edward C. Presco (1998) 2 1. Inroducion Toal Facor Produciviy (TFP) has become
GMM - Generalized Method of Moments
GMM - Generalized Mehod of Momens Conens GMM esimaion, shor inroducion 2 GMM inuiion: Maching momens 2 3 General overview of GMM esimaion. 3 3. Weighing marix...........................................
Lecture Notes 2. The Hilbert Space Approach to Time Series
Time Series Seven N. Durlauf Universiy of Wisconsin. Basic ideas Lecure Noes. The Hilber Space Approach o Time Series The Hilber space framework provides a very powerful language for discussing he relaionship
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Exam: ECON4325 Moneary Policy Dae of exam: Tuesday, May 24, 206 Grades are given: June 4, 206 Time for exam: 2.30 p.m. 5.30 p.m. The problem se covers 5 pages
Notes on Kalman Filtering
Noes on Kalman Filering Brian Borchers and Rick Aser November 7, Inroducion Daa Assimilaion is he problem of merging model predicions wih acual measuremens of a sysem o produce an opimal esimae of he curren
L07. KALMAN FILTERING FOR NON-LINEAR SYSTEMS. NA568 Mobile Robotics: Methods & Algorithms
L07. KALMAN FILTERING FOR NON-LINEAR SYSTEMS NA568 Mobile Roboics: Mehods & Algorihms Today s Topic Quick review on (Linear) Kalman Filer Kalman Filering for Non-Linear Sysems Exended Kalman Filer (EKF)
A Specification Test for Linear Dynamic Stochastic General Equilibrium Models
Journal of Saisical and Economeric Mehods, vol.1, no.2, 2012, 65-70 ISSN: 2241-0384 (prin), 2241-0376 (online) Scienpress Ld, 2012 A Specificaion Tes for Linear Dynamic Sochasic General Equilibrium Models
A User s Guide to Solving Real Business Cycle Models. by a single representative agent. It is assumed that both output and factor markets are
page, Harley, Hoover, Salyer, RBC Models: A User s Guide A User s Guide o Solving Real Business Cycle Models The ypical real business cycle model is based upon an economy populaed by idenical infiniely-lived
Applying Auto-Regressive Binomial Model to Forecast Economic Recession in U.S. and Sweden
Applying Auo-Regressive Binomial Model o Forecas Economic Recession in U.S. and Sweden Submied by: Chunshu Zhao Yamei Song Supervisor: Md. Moudud Alam D-level essay in Saisics, June 200. School of Technology
Biol. 356 Lab 8. Mortality, Recruitment, and Migration Rates
Biol. 356 Lab 8. Moraliy, Recruimen, and Migraion Raes (modified from Cox, 00, General Ecology Lab Manual, McGraw Hill) Las week we esimaed populaion size hrough several mehods. One assumpion of all hese
An Admissible Macro-Finance Model of the US Treasury Market.
An Admissible Macro-Finance Model of he US Treasury Marke. Peer Spencer* Universiy of York, U.K. This paper develops a macro-finance model of he yield curve and uses his o explain he behavior of he US
Licenciatura de ADE y Licenciatura conjunta Derecho y ADE. Hoja de ejercicios 2 PARTE A
Licenciaura de ADE y Licenciaura conjuna Derecho y ADE Hoja de ejercicios PARTE A 1. Consider he following models Δy = 0.8 + ε (1 + 0.8L) Δ 1 y = ε where ε and ε are independen whie noise processes. In
Exponential Smoothing
Exponenial moohing Inroducion A simple mehod for forecasing. Does no require long series. Enables o decompose he series ino a rend and seasonal effecs. Paricularly useful mehod when here is a need o forecas
t is a basis for the solution space to this system, then the matrix having these solutions as columns, t x 1 t, x 2 t,... x n t x 2 t...
Mah 228- Fri Mar 24 5.6 Marix exponenials and linear sysems: The analogy beween firs order sysems of linear differenial equaions (Chaper 5) and scalar linear differenial equaions (Chaper ) is much sronger
The average rate of change between two points on a function is d t
SM Dae: Secion: Objecive: The average rae of change beween wo poins on a funcion is d. For example, if he funcion ( ) represens he disance in miles ha a car has raveled afer hours, hen finding he slope
The Real Exchange Rate, Real Interest Rates, and the Risk Premium. Charles Engel University of Wisconsin
The Real Exchange Rae, Real Ineres Raes, and he Risk Premium Charles Engel Universiy of Wisconsin How does exchange rae respond o ineres rae changes? In sandard open economy New Keynesian model, increase
The general Solow model
The general Solow model Back o a closed economy In he basic Solow model: no growh in GDP per worker in seady sae This conradics he empirics for he Wesern world (sylized fac #5) In he general Solow model:
Multivariate Markov switiching common factor models for the UK
Loughborough Universiy Insiuional Reposiory Mulivariae Markov swiiching common facor models for he UK This iem was submied o Loughborough Universiy's Insiuional Reposiory by he/an auhor. Addiional Informaion:
ECON 482 / WH Hong Time Series Data Analysis 1. The Nature of Time Series Data. Example of time series data (inflation and unemployment rates)
ECON 48 / WH Hong Time Series Daa Analysis. The Naure of Time Series Daa Example of ime series daa (inflaion and unemploymen raes) ECON 48 / WH Hong Time Series Daa Analysis The naure of ime series daa
10. State Space Methods
. Sae Space Mehods. Inroducion Sae space modelling was briefly inroduced in chaper. Here more coverage is provided of sae space mehods before some of heir uses in conrol sysem design are covered in he
Y, where. 1 Estimate St.error
1 HG Feb 2014 ECON 5101 Exercises III - 24 Feb 2014 Exercise 1 In lecure noes 3 (LN3 page 11) we esimaed an ARMA(1,2) for daa) for he period, 1978q2-2013q2 Le Y ln BNP ln BNP (Norwegian Model: Y Y, where
Online Appendix to Solution Methods for Models with Rare Disasters
Online Appendix o Soluion Mehods for Models wih Rare Disasers Jesús Fernández-Villaverde and Oren Levinal In his Online Appendix, we presen he Euler condiions of he model, we develop he pricing Calvo block,
Math 334 Fall 2011 Homework 11 Solutions
Dec. 2, 2 Mah 334 Fall 2 Homework Soluions Basic Problem. Transform he following iniial value problem ino an iniial value problem for a sysem: u + p()u + q() u g(), u() u, u () v. () Soluion. Le v u. Then
SUPPLEMENTARY APPENDIX. A Time Series Model of Interest Rates With the Effective Lower Bound
SUPPLEMENTARY APPENDIX A Time Series Model of Ineres Raes Wih he Effecive Lower Bound Benjamin K. Johannsen Federal Reserve Board Elmar Merens Bank for Inernaional Selemens April 6, 8 Absrac This appendix
Navneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi
Creep in Viscoelasic Subsances Numerical mehods o calculae he coefficiens of he Prony equaion using creep es daa and Herediary Inegrals Mehod Navnee Saini, Mayank Goyal, Vishal Bansal (23); Term Projec
Comparing Means: t-tests for One Sample & Two Related Samples
Comparing Means: -Tess for One Sample & Two Relaed Samples Using he z-tes: Assumpions -Tess for One Sample & Two Relaed Samples The z-es (of a sample mean agains a populaion mean) is based on he assumpion
GDP Advance Estimate, 2016Q4
GDP Advance Esimae, 26Q4 Friday, Jan 27 Real gross domesic produc (GDP) increased a an annual rae of.9 percen in he fourh quarer of 26. The deceleraion in real GDP in he fourh quarer refleced a downurn
m = 41 members n = 27 (nonfounders), f = 14 (founders) 8 markers from chromosome 19
Sequenial Imporance Sampling (SIS) AKA Paricle Filering, Sequenial Impuaion (Kong, Liu, Wong, 994) For many problems, sampling direcly from he arge disribuion is difficul or impossible. One reason possible
non -negative cone Population dynamics motivates the study of linear models whose coefficient matrices are non-negative or positive.
LECTURE 3 Linear/Nonnegaive Marix Models x ( = Px ( A= m m marix, x= m vecor Linear sysems of difference equaions arise in several difference conexs: Linear approximaions (linearizaion Perurbaion analysis
Properties of Autocorrelated Processes Economics 30331
Properies of Auocorrelaed Processes Economics 3033 Bill Evans Fall 05 Suppose we have ime series daa series labeled as where =,,3, T (he final period) Some examples are he dail closing price of he S&500,
SUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION DOI: 0.038/NCLIMATE893 Temporal resoluion and DICE * Supplemenal Informaion Alex L. Maren and Sephen C. Newbold Naional Cener for Environmenal Economics, US Environmenal Proecion
Fall 2015 Final Examination (200 pts)
Econ 501 Fall 2015 Final Examinaion (200 ps) S.L. Parene Neoclassical Growh Model (50 ps) 1. Derive he relaion beween he real ineres rae and he renal price of capial using a no-arbirage argumen under he
3.1 More on model selection
3. More on Model selecion 3. Comparing models AIC, BIC, Adjused R squared. 3. Over Fiing problem. 3.3 Sample spliing. 3. More on model selecion crieria Ofen afer model fiing you are lef wih a handful of
Article from. Predictive Analytics and Futurism. July 2016 Issue 13
Aricle from Predicive Analyics and Fuurism July 6 Issue An Inroducion o Incremenal Learning By Qiang Wu and Dave Snell Machine learning provides useful ools for predicive analyics The ypical machine learning
PhD Course: Structural VAR models. III. Identification. Hilde C. Bjørnland. Norwegian School of Management (BI)
PhD Course: Srucural VAR models III. Idenificaion Hilde C. Bjørnland Norwegian School of Managemen (BI) Lecure noe III: Idenificaion Conen. Idenificaion (con.) Choleski recursive resricions and implicaion
Module 2 F c i k c s la l w a s o s f dif di fusi s o i n
Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms
Lecture Notes 3: Quantitative Analysis in DSGE Models: New Keynesian Model
Lecure Noes 3: Quaniaive Analysis in DSGE Models: New Keynesian Model Zhiwei Xu, Email: xuzhiwei@sju.edu.cn The moneary policy plays lile role in he basic moneary model wihou price sickiness. We now urn
Nonstationarity-Integrated Models. Time Series Analysis Dr. Sevtap Kestel 1
Nonsaionariy-Inegraed Models Time Series Analysis Dr. Sevap Kesel 1 Diagnosic Checking Residual Analysis: Whie noise. P-P or Q-Q plos of he residuals follow a normal disribuion, he series is called a Gaussian
FACTOR AUGMENTED AUTOREGRESSIVE DISTRIBUTED LAG MODELS. Serena Ng Dalibor Stevanovic. November Preliminary, Comments Welcome
FACTOR AUGMENTED AUTOREGRESSIVE DISTRIBUTED LAG MODELS Serena Ng Dalibor Sevanovic November 212 Preliminary, Commens Welcome Absrac This paper proposes a facor augmened auoregressive disribued lag (FADL)
Discussion of Fuhrer, The Role of Expectations in Inflation Dynamics. August 4, 2011
Discussion of Fuhrer, The Role of Expecaions in Inflaion Dynamics Augus 4, 2011 James H. Sock Deparmen of Economics, Harvard Universiy and he NBER Raional expecaions are a he hear of he DSGE models mainained
Final Spring 2007
.615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o
WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile
Bond Risk Premia. November 6, Abstract
Bond Risk Premia John H. Cochrane and Monika Piazzesi November 6, 2001 Absrac This paper sudies risk premia in he erm srucure. We sar wih regressions of annual holding period reurns on forward raes. We
ψ(t) = V x (0)V x (t)
.93 Home Work Se No. (Professor Sow-Hsin Chen Spring Term 5. Due March 7, 5. This problem concerns calculaions of analyical expressions for he self-inermediae scaering funcion (ISF of he es paricle in