Solutions to Odd Number Exercises in Chapter 6
|
|
- Francis Mosley
- 5 years ago
- Views:
Transcription
1 1 Soluions o Odd Number Exercises in 6.1 R y eˆ y 6.3 From eˆ ( T K) ˆ R 1 1 SST SST SST (1 R ) 55.36(1.7911) we have, ˆ T K ( ) 6.5 y ye ye y e 1 1 Consider he erms e and xe b b x e y e b e b x e y e e y b b x y Tb b x xe x y b bx xy b x b x The las expressions in each of hese equaions become zero from he normal equaions ha are used o solve for he leas squares esimaors. Subsiuing e = and xe = back ino he original equaion, we obain y ye. 6.7 (a) Knowledge of he relaionship beween he rae of change of wages and he unemploymen rae is very imporan for governmen policy makers and unions. Typically, governmens like o keep he lid on inflaion, bu he cos of doing so may be increasing unemploymen. Unions are always aemping o negoiae pay rises for heir employees. However, hey mus be wary of doing so if wage rises mean ha fewer of heir workers can ge jobs. An economic model for relaing he rae of change in wages o unemploymen was derived in Secion I is called he Phillips' curve and is given by 1 %w 1 u A corresponding saisical model is %w 1 1 e u
2 where some saisical assumpions are needed for he random error e. We assume he e are independen normally disribued random variables wih zero mean and consan variance. To esimae his model, we use a se of 18 observaions on w and u for he period 1949 o The esimaion mehod used is he linear leas squares mehod regressing %w on 1/u. This mehod gives he esimaed equaion as % w 1 = R =.393 (. 355) (. 838) u where sandard errors are in parenheses. We would expec 1 < and >. Thus, from he esimaed equaion, b 1 and b give he expeced signs. The sandard error of b 1 is.355 which is relaively large and leads o b 1 being saisically insignifican. The esimae for b is saisically significan, bu, as we discovered in Exercise 6.(h), is large sandard error leads o a wide confidence inerval ha conveys lile economic informaion. Some of he economic implicaions were discussed in he answers o Exercise 6.. (b) From he Economic Repor o he Presiden we can consruc he following able where u is he unemploymen rae for all workers, w is average gross hourly earnings in curren dollars for he oal privae non-agriculural secor, and % w 1( w w 1) / w 1. Year w u %w (c) The esimaed equaion for he Phillips' curve using he daa for he years 1975 o 1983 is % w 1 = R =.635 ( ) ( ) u where sandard errors are in parenheses. The esimae b 1 =.8311 suggess ha he annual wage increase will never drop below.83%, even as he unemploymen rae becomes very large. This oucome may be unrealisic; we may expec workers o accep a drop in real wages for very high unemploymen raes. If so, b 1 should be negaive. The very high sandard error of b 1, and is consequen insignificance, do no rule ou he possibiliy of 1 being negaive. The esimae b = wih se(b ) = is economically feasible and significan. However, he resuling confidence inerval is sill wide. I conveys lile informaion, alhough he large value of b suggess wage changes are very responsive o he unemploymen rae.
3 3 6.9 In he learning curve model ln( u) 1 ln( q), 1 is he logarihm of he uni cos of producion for he firs uni produced and is he elasiciy of uni cos wih respec o cumulaive producion. A 1% change in he cumulaive producion leads o a % change in he uni cos equal o.
4 The resuls are summarised in he following able. Sandard errors are in parenheses. Changing he unis of y only changes boh b 1 and b, making hem one hundred imes smaller. Changing he unis of x only influences only b, making i 1 imes bigger. When boh x and y are scaled b 1 changes bu no b. Regression b 1 b (i) y on x (.14) (35) (ii) y on x* (.14) (3.5) (iii) y* on x (.14) (35) (iv) y* on x* (.14) (35) 6.13 To es H : normally disribued errors for he preferable equaion, equaion 3, we need values of skewness and kurosis. They are S = and k = The es saisic is T ( k 3) JB S The hypohesis H is rejeced if JB () for a given significance level. Since () a he 5 level of significance, we do no rejec H. Therefore, here is insufficien evidence o conclude ha he normal disribuion assumpion is unreasonable. Differen sofware packages can use differen esimaors for skewness and kurosis; and some repor excess kurosis ( k 3) as he kurosis. For example, SAS yields S.8741 and k 3.411, leading o a es value of JB (a) For households wih 1 child wfood ln( oexp) (41) (9) se For households wih children: (5.19) (-16.7) R.33 wfood ln( oexp) (365) (8) se (6.1) (-16.16) R 6
5 5 (b) In erms of we would expec a negaive value because as he oal expendiure increases he food share should decrease. Boh esimaions give he expeced sign. The sandard errors for b 1 and b from boh esimaions are relaively small resuling in high values of raios and significan esimaes. For households wih 1 child, he average oal expendiure is and b1b ln( oexp) ln(94.848) 1 ˆ.5461 b b ln( oexp) ln(94.848) 1 For households wih children, he average oal expendiure is and b1bln( oexp) ln(11.17) 1 ˆ.6366 b b ln( oexp) ln(11.17) 1 Boh of he elasiciies are less han one; herefore, food is a necessiy.
6 WFOOD X1 X1 Figure 6.4a Figure 6.4b (c) Figures 6.4a and 6.4b are he fied curve and he residual plos for households wih 1 child. The funcion linear in wfood and ln(oexp) seems o be an appropriae one. However, he observaions vary considerably around he fied line, consisen wih he low R value. Also, he absolue magniude of he residuals appears o decline as ln(oexp) increases. In Chaper 11 we discover ha such behavior suggess he exisence of heeroskedasiciy. Figures 6.5a and 6.5b are plos of he fied equaion and he residuals for households wih children. They are similar o he ones wih 1 child, indicaing ha he funcional form is a reasonable one. The values of JB for esing H : errors are normally disribued are and for households wih 1 child and children, respecively. Since boh values are greaer han he criical () 5.991, we rejec H. The p-values obained are 5 and 41, respecively, confirming ha H is rejeced. We conclude ha for boh cases he errors are no normally disribued. (Using SAS esimaes for skewness and excess kurosis, he JB values are 11.6 and 6.65, respecively.) WFOOD X Figure 6.5a Figure 6.5b X
7 (a) For households wih 1 child wfuel ln( oexp) (17) (48) For households wih children: (14.3) (-15) R.1458 se (b) wfuel ln( oexp) (198) (43) se (15.) (-1.71) R.115 We expec fuel o be a necessary good and as oal expendiure increases he fuel share should decrease. Tha is, we expec he sign of o be negaive. Boh esimaions give he expeced sign. The sandard errors for b 1 and b from boh esimaions are relaively small resuling in high values of raios. For households wih 1 child, he average oal expendiure is and b1bln( oexp) ln(94.848) 1 ˆ.4494 b b ln( oexp) ln(94.848) 1 For households wih children, he average oal expendiure is and b1bln( oexp) ln(11.17) 1 ˆ.4647 b b ln( oexp) ln(11.17) 1 Boh of he elasiciies are less han one; herefore, fuel is a necessiy WFUEL X1 Figure 6.6a Figure 6.6b (c) Figures 6.6a and 6.6b are he fied curve and he residual plos for households wih 1 child. The plo of he acual observaions and he fied equaon is in Figure 6.6a. The funcional form is reasonable in he sense ha i is difficul o sugges an alernaive funcion which will be a beer fi o he scaer of poins. On he oher hand, he funcion provides a poor explanaion of variaion in he budge share of fuel. Consisen wih he low R, he observaions vary widely around he fied line. Also he variaion of he observaions around he fied line decreases as he oal X1
8 8 expendiure increases. The posiive residuals vary in magniude from zero o.3 whereas he range of he negaive residuals is zero o.1, suggesing a highly skewed error disribuion. Figures 6.7a and 6.7b are he fied curve and he residual plos for households wih children. They are similar o he ones wih 1 child. While i is difficul o sugges a funcional form which would fi beer han he linear-log one, he funcion is no a good one for explaining variaion in he fuel budge share. Perhaps a muliple regression model wih addiional explanaory variables would be an improvemen WFUEL X Figure 6.7a Figure 6.7b X The values of JB for esing H : errors are normally disribued are and for households wih 1 child and children, respecively. Since boh values are greaer han he criical () 5.991, we rejec H. The p-values are for boh cases confirming ha H is rejeced. We conclude ha for boh cases he errors are no normally disribued (a) Figures 6.1a, 6.1b, 6.1c and 6.1d are he plos of observaions of y agains x, ln(y) agains ln(x), y agains ln(x) and ln(y) agains x, respecively. The funcional forms o choose from are specified in par (b). They are all linear funcions of y and x or he logarihms of hem. The preferable form is he one where he plo of he observaions is bes represened by a linear line. This is he plo of y and x in Figure 6.1a. In all he oher figures a line wih some curvaure would be a beer fi. Thus, he chosen funcional form is he equaion y 1x e. (b) (i) (ii) yˆ x (3) (.691) se (4.5) (.667) R.9753
9 9 ln( y) ln( x) (.3356) (55) se (.5114) (6.6418) R.774 (iii) (iv) yˆ ln( x) (.76) (454) se (5.644) (4.13).5663 ln( y) x (.1556) (3.5589) se (-11.33) (6.5488) R.7674 To check wheher he level of arsenic in he waer influences he level of arsenic in he oenails we es each equaion for wheher,, and are zero. We rejec an H if a raio is greaer han he absolue criical value. A level of significance 5, and 13 degrees of freedom, The calculaed raios for he hypoheses from each equaion are all higher han he criical value. We herefore rejec H and conclude ha here is evidence o sugges ha he level of arsenic in waer does influence he level of arsenic in he oenails. (c) The plos of he residuals from equaion (i) o (iv) are presened in Figures The residuals in Figures 6.1b and 6.13b display a rough U-shape, while hose in Figure 6.14b exhibi a rough invered U-shape. Thus, in hese cases, he residuals for small and large values of x or ln(x) have signs differen o he residuals ha correspond o middle values of x or ln(x). Such paerns sugges inappropriae funcional forms. Since he residuals for he linear funcion do no display such a paern, he plos suppor our choice of funcion in par (a). R Y X Figure 6.11a Figure 6.11b X
10 LNY LNX LNX Figure 6.1a Figure 6.1b Y LNX LNX Figure 6.13a Figure 6.13b LNY X Figure 6.14a Figure 6.14b X
11 (a) The esimaed equaions for dishwasher shipmens as a funcion of durable goods expendiure and as a funcion of privae residenial invesmen are below. DISH DISH DUR (95.5) (.548) R RES (534.7) (1.95) R.7465 The equaion ha gives he beer predicor is he equaion ha has he higher R. In his case i is he equaion wih DUR as he explanaory variable. Hence, DUR is he beer predicor. (b) (c) DISH DISH DUR (8.) RES (67.) 4119 Since he acual DISH , for his fuure observaion RES is a beer predicor han DUR. The residual plos for he wo equaions using DUR and RES as he explanaory variables are in Figures 6.15a and 6.15b, respecively. The residuals appear o be correlaed. There is a endency for posiive residuals o follow posiive residuals and negaive residuals o follow negaive residuals DISH Residuals Figure 6.15a using DUR DISH Residuals Figure 6.15b using RES
Solutions to Exercises in Chapter 12
Chaper in Chaper. (a) The leas-squares esimaed equaion is given by (b)!i = 6. + 0.770 Y 0.8 R R = 0.86 (.5) (0.07) (0.6) Boh b and b 3 have he expeced signs; income is expeced o have a posiive effec on
More informationThe Simple Linear Regression Model: Reporting the Results and Choosing the Functional Form
Chaper 6 The Simple Linear Regression Model: Reporing he Resuls and Choosing he Funcional Form To complee he analysis of he simple linear regression model, in his chaper we will consider how o measure
More informationEcon107 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
More informationR 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,
More informationChapter 11. Heteroskedasticity The Nature of Heteroskedasticity. In Chapter 3 we introduced the linear model (11.1.1)
Chaper 11 Heeroskedasiciy 11.1 The Naure of Heeroskedasiciy In Chaper 3 we inroduced he linear model y = β+β x (11.1.1) 1 o explain household expendiure on food (y) as a funcion of household income (x).
More informationACE 562 Fall Lecture 8: The Simple Linear Regression Model: R 2, Reporting the Results and Prediction. by Professor Scott H.
ACE 56 Fall 5 Lecure 8: The Simple Linear Regression Model: R, Reporing he Resuls and Predicion by Professor Sco H. Irwin Required Readings: Griffihs, Hill and Judge. "Explaining Variaion in he Dependen
More informationEcon Autocorrelation. Sanjaya DeSilva
Econ 39 - Auocorrelaion Sanjaya DeSilva Ocober 3, 008 1 Definiion Auocorrelaion (or serial correlaion) occurs when he error erm of one observaion is correlaed wih he error erm of any oher observaion. This
More informationy = β 1 + β 2 x (11.1.1)
Chaper 11 Heeroskedasiciy 11.1 The Naure of Heeroskedasiciy In Chaper 3 we inroduced he linear model y = β 1 + β x (11.1.1) o explain household expendiure on food (y) as a funcion of household income (x).
More informationTime 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,
More informationEstimation 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
More informationACE 562 Fall Lecture 4: Simple Linear Regression Model: Specification and Estimation. by Professor Scott H. Irwin
ACE 56 Fall 005 Lecure 4: Simple Linear Regression Model: Specificaion and Esimaion by Professor Sco H. Irwin Required Reading: Griffihs, Hill and Judge. "Simple Regression: Economic and Saisical Model
More informationLicenciatura 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
More informationChapter 16. Regression with Time Series Data
Chaper 16 Regression wih Time Series Daa The analysis of ime series daa is of vial ineres o many groups, such as macroeconomiss sudying he behavior of naional and inernaional economies, finance economiss
More informationComparing 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
More informationCHAPTER 9. Exercise Solutions
CHAPTER 9 Exercise Soluions Chaper 9, Exercise Soluions, Principles of Economerics, 3e EXERCISE 9. From he equaion for he AR() error model e = ρ e + v, we have from which we ge and hence ( e ) =ρ ( e )
More informationThe Multiple Regression Model: Hypothesis Tests and the Use of Nonsample Information
Chaper 8 The Muliple Regression Model: Hypohesis Tess and he Use of Nonsample Informaion An imporan new developmen ha we encouner in his chaper is using he F- disribuion o simulaneously es a null hypohesis
More information20. 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
More informationErrata (1 st Edition)
P Sandborn, os Analysis of Elecronic Sysems, s Ediion, orld Scienific, Singapore, 03 Erraa ( s Ediion) S K 05D Page 8 Equaion (7) should be, E 05D E Nu e S K he L appearing in he equaion in he book does
More informationDynamic 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
More informationACE 564 Spring Lecture 7. Extensions of The Multiple Regression Model: Dummy Independent Variables. by Professor Scott H.
ACE 564 Spring 2006 Lecure 7 Exensions of The Muliple Regression Model: Dumm Independen Variables b Professor Sco H. Irwin Readings: Griffihs, Hill and Judge. "Dumm Variables and Varing Coefficien Models
More informationInnova Junior College H2 Mathematics JC2 Preliminary Examinations Paper 2 Solutions 0 (*)
Soluion 3 x 4x3 x 3 x 0 4x3 x 4x3 x 4x3 x 4x3 x x 3x 3 4x3 x Innova Junior College H Mahemaics JC Preliminary Examinaions Paper Soluions 3x 3 4x 3x 0 4x 3 4x 3 0 (*) 0 0 + + + - 3 3 4 3 3 3 3 Hence x or
More informationFinancial 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
More information(a) Set up the least squares estimation procedure for this problem, which will consist in minimizing the sum of squared residuals. 2 t.
Insrucions: The goal of he problem se is o undersand wha you are doing raher han jus geing he correc resul. Please show your work clearly and nealy. No credi will be given o lae homework, regardless of
More informationSolutions: Wednesday, November 14
Amhers College Deparmen of Economics Economics 360 Fall 2012 Soluions: Wednesday, November 14 Judicial Daa: Cross secion daa of judicial and economic saisics for he fify saes in 2000. JudExp CrimesAll
More informationUnit 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
More informationECON 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
More informationVectorautoregressive 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
More informationVehicle Arrival Models : Headway
Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where
More informationChapter 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
More informationDistribution 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
More informationWednesday, November 7 Handout: Heteroskedasticity
Amhers College Deparmen of Economics Economics 360 Fall 202 Wednesday, November 7 Handou: Heeroskedasiciy Preview Review o Regression Model o Sandard Ordinary Leas Squares (OLS) Premises o Esimaion Procedures
More informationRobust estimation based on the first- and third-moment restrictions of the power transformation model
h Inernaional Congress on Modelling and Simulaion, Adelaide, Ausralia, 6 December 3 www.mssanz.org.au/modsim3 Robus esimaion based on he firs- and hird-momen resricions of he power ransformaion Nawaa,
More informationDEPARTMENT OF ECONOMICS
ISSN 0819-6 ISBN 0 730 609 9 THE UNIVERSITY OF MELBOURNE DEPARTMENT OF ECONOMICS RESEARCH PAPER NUMBER 95 NOVEMBER 005 INTERACTIONS IN REGRESSIONS by Joe Hirschberg & Jenny Lye Deparmen of Economics The
More information1. Diagnostic (Misspeci cation) Tests: Testing the Assumptions
Business School, Brunel Universiy MSc. EC5501/5509 Modelling Financial Decisions and Markes/Inroducion o Quaniaive Mehods Prof. Menelaos Karanasos (Room SS269, el. 01895265284) Lecure Noes 6 1. Diagnosic
More informationCHAPTER 17: DYNAMIC ECONOMETRIC MODELS: AUTOREGRESSIVE AND DISTRIBUTED-LAG MODELS
Basic Economerics, Gujarai and Porer CHAPTER 7: DYNAMIC ECONOMETRIC MODELS: AUTOREGRESSIVE AND DISTRIBUTED-LAG MODELS 7. (a) False. Economeric models are dynamic if hey porray he ime pah of he dependen
More informationHypothesis Testing in the Classical Normal Linear Regression Model. 1. Components of Hypothesis Tests
ECONOMICS 35* -- NOTE 8 M.G. Abbo ECON 35* -- NOTE 8 Hypohesis Tesing in he Classical Normal Linear Regression Model. Componens of Hypohesis Tess. A esable hypohesis, which consiss of wo pars: Par : a
More informationThe General Linear Test in the Ridge Regression
ommunicaions for Saisical Applicaions Mehods 2014, Vol. 21, No. 4, 297 307 DOI: hp://dx.doi.org/10.5351/sam.2014.21.4.297 Prin ISSN 2287-7843 / Online ISSN 2383-4757 The General Linear Tes in he Ridge
More informationOn 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
More informationA 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
More information3.1 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
More informationMath 10B: Mock Mid II. April 13, 2016
Name: Soluions Mah 10B: Mock Mid II April 13, 016 1. ( poins) Sae, wih jusificaion, wheher he following saemens are rue or false. (a) If a 3 3 marix A saisfies A 3 A = 0, hen i canno be inverible. True.
More informationOBJECTIVES 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
More informationACE 562 Fall Lecture 5: The Simple Linear Regression Model: Sampling Properties of the Least Squares Estimators. by Professor Scott H.
ACE 56 Fall 005 Lecure 5: he Simple Linear Regression Model: Sampling Properies of he Leas Squares Esimaors by Professor Sco H. Irwin Required Reading: Griffihs, Hill and Judge. "Inference in he Simple
More informationDepartment of Economics East Carolina University Greenville, NC Phone: Fax:
March 3, 999 Time Series Evidence on Wheher Adjusmen o Long-Run Equilibrium is Asymmeric Philip Rohman Eas Carolina Universiy Absrac The Enders and Granger (998) uni-roo es agains saionary alernaives wih
More informationSummer 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:
More informationDiebold, 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
More informationTesting 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
More informationFORECASTING WITH REGRESSION
FORECASTING WITH REGRESSION MODELS Overview of basic regression echniques. Daa analysis and forecasing using muliple regression analysis. 106 Visualizaion of Four Differen Daa Ses Daa Se A Daa Se B Daa
More informationOutline. 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
More informationSTRUCTURAL CHANGE IN TIME SERIES OF THE EXCHANGE RATES BETWEEN YEN-DOLLAR AND YEN-EURO IN
Inernaional Journal of Applied Economerics and Quaniaive Sudies. Vol.1-3(004) STRUCTURAL CHANGE IN TIME SERIES OF THE EXCHANGE RATES BETWEEN YEN-DOLLAR AND YEN-EURO IN 001-004 OBARA, Takashi * Absrac The
More information4.1 Other Interpretations of Ridge Regression
CHAPTER 4 FURTHER RIDGE THEORY 4. Oher Inerpreaions of Ridge Regression In his secion we will presen hree inerpreaions for he use of ridge regression. The firs one is analogous o Hoerl and Kennard reasoning
More informationModeling and Forecasting Volatility Autoregressive Conditional Heteroskedasticity Models. Economic Forecasting Anthony Tay Slide 1
Modeling and Forecasing Volailiy Auoregressive Condiional Heeroskedasiciy Models Anhony Tay Slide 1 smpl @all line(m) sii dl_sii S TII D L _ S TII 4,000. 3,000.1.0,000 -.1 1,000 -. 0 86 88 90 9 94 96 98
More informationChapter 7: Solving Trig Equations
Haberman MTH Secion I: The Trigonomeric Funcions Chaper 7: Solving Trig Equaions Le s sar by solving a couple of equaions ha involve he sine funcion EXAMPLE a: Solve he equaion sin( ) The inverse funcions
More informationFITTING OF A PARTIALLY REPARAMETERIZED GOMPERTZ MODEL TO BROILER DATA
FITTING OF A PARTIALLY REPARAMETERIZED GOMPERTZ MODEL TO BROILER DATA N. Okendro Singh Associae Professor (Ag. Sa.), College of Agriculure, Cenral Agriculural Universiy, Iroisemba 795 004, Imphal, Manipur
More informationMatlab and Python programming: how to get started
Malab and Pyhon programming: how o ge sared Equipping readers he skills o wrie programs o explore complex sysems and discover ineresing paerns from big daa is one of he main goals of his book. In his chaper,
More informationA note on spurious regressions between stationary series
A noe on spurious regressions beween saionary series Auhor Su, Jen-Je Published 008 Journal Tile Applied Economics Leers DOI hps://doi.org/10.1080/13504850601018106 Copyrigh Saemen 008 Rouledge. This is
More informationTypes of Exponential Smoothing Methods. Simple Exponential Smoothing. Simple Exponential Smoothing
M Business Forecasing Mehods Exponenial moohing Mehods ecurer : Dr Iris Yeung Room No : P79 Tel No : 788 8 Types of Exponenial moohing Mehods imple Exponenial moohing Double Exponenial moohing Brown s
More information2.7. Some common engineering functions. Introduction. Prerequisites. Learning Outcomes
Some common engineering funcions 2.7 Inroducion This secion provides a caalogue of some common funcions ofen used in Science and Engineering. These include polynomials, raional funcions, he modulus funcion
More informationLecture 4. Classical Linear Regression Model: Overview
Lecure 4 Classical Linear Regression Model: Overview Regression Regression is probably he single mos imporan ool a he economerician s disposal. Bu wha is regression analysis? I is concerned wih describing
More informationNature Neuroscience: doi: /nn Supplementary Figure 1. Spike-count autocorrelations in time.
Supplemenary Figure 1 Spike-coun auocorrelaions in ime. Normalized auocorrelaion marices are shown for each area in a daase. The marix shows he mean correlaion of he spike coun in each ime bin wih he spike
More informationProperties 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,
More informationChickens vs. Eggs: Replicating Thurman and Fisher (1988) by Arianto A. Patunru Department of Economics, University of Indonesia 2004
Chicens vs. Eggs: Relicaing Thurman and Fisher (988) by Ariano A. Paunru Dearmen of Economics, Universiy of Indonesia 2004. Inroducion This exercise lays ou he rocedure for esing Granger Causaliy as discussed
More informationExplaining 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
More informationMethodology. -ratios are biased and that the appropriate critical values have to be increased by an amount. that depends on the sample size.
Mehodology. Uni Roo Tess A ime series is inegraed when i has a mean revering propery and a finie variance. I is only emporarily ou of equilibrium and is called saionary in I(0). However a ime series ha
More informationCointegration and Implications for Forecasting
Coinegraion and Implicaions for Forecasing Two examples (A) Y Y 1 1 1 2 (B) Y 0.3 0.9 1 1 2 Example B: Coinegraion Y and coinegraed wih coinegraing vecor [1, 0.9] because Y 0.9 0.3 is a saionary process
More informationDEPARTMENT OF STATISTICS
A Tes for Mulivariae ARCH Effecs R. Sco Hacker and Abdulnasser Haemi-J 004: DEPARTMENT OF STATISTICS S-0 07 LUND SWEDEN A Tes for Mulivariae ARCH Effecs R. Sco Hacker Jönköping Inernaional Business School
More informationGDP 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
More informationRegression with Time Series Data
Regression wih Time Series Daa y = β 0 + β 1 x 1 +...+ β k x k + u Serial Correlaion and Heeroskedasiciy Time Series - Serial Correlaion and Heeroskedasiciy 1 Serially Correlaed Errors: Consequences Wih
More informationFinal Exam. Tuesday, December hours
San Francisco Sae Universiy Michael Bar ECON 560 Fall 03 Final Exam Tuesday, December 7 hours Name: Insrucions. This is closed book, closed noes exam.. No calculaors of any kind are allowed. 3. Show all
More informationBias in Conditional and Unconditional Fixed Effects Logit Estimation: a Correction * Tom Coupé
Bias in Condiional and Uncondiional Fixed Effecs Logi Esimaion: a Correcion * Tom Coupé Economics Educaion and Research Consorium, Naional Universiy of Kyiv Mohyla Academy Address: Vul Voloska 10, 04070
More informationKriging 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
More information14 Autoregressive Moving Average Models
14 Auoregressive Moving Average Models In his chaper an imporan parameric family of saionary ime series is inroduced, he family of he auoregressive moving average, or ARMA, processes. For a large class
More information(10) (a) Derive and plot the spectrum of y. Discuss how the seasonality in the process is evident in spectrum.
January 01 Final Exam Quesions: Mark W. Wason (Poins/Minues are given in Parenheses) (15) 1. Suppose ha y follows he saionary AR(1) process y = y 1 +, where = 0.5 and ~ iid(0,1). Le x = (y + y 1 )/. (11)
More informationEconomics 8105 Macroeconomic Theory Recitation 6
Economics 8105 Macroeconomic Theory Reciaion 6 Conor Ryan Ocober 11h, 2016 Ouline: Opimal Taxaion wih Governmen Invesmen 1 Governmen Expendiure in Producion In hese noes we will examine a model in which
More informationChapter 2. Models, Censoring, and Likelihood for Failure-Time Data
Chaper 2 Models, Censoring, and Likelihood for Failure-Time Daa William Q. Meeker and Luis A. Escobar Iowa Sae Universiy and Louisiana Sae Universiy Copyrigh 1998-2008 W. Q. Meeker and L. A. Escobar. Based
More informationGMM - 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...........................................
More informationBiol. 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
More informationLinear Combinations of Volatility Forecasts for the WIG20 and Polish Exchange Rates
Eliza Buszkowska Universiy of Poznań, Poland Linear Combinaions of Volailiy Forecass for he WIG0 and Polish Exchange Raes Absrak. As is known forecas combinaions may be beer forecass hen forecass obained
More informationINTRODUCTION TO MACHINE LEARNING 3RD EDITION
ETHEM ALPAYDIN The MIT Press, 2014 Lecure Slides for INTRODUCTION TO MACHINE LEARNING 3RD EDITION alpaydin@boun.edu.r hp://www.cmpe.boun.edu.r/~ehem/i2ml3e CHAPTER 2: SUPERVISED LEARNING Learning a Class
More informationMacroeconomic 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
More information3.1.3 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
More informationKINEMATICS IN ONE DIMENSION
KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec
More informationMacroeconometrics. Christophe BOUCHER. Session 2 A brief overview of the classical linear regression model 1
Macroeconomerics Chrisophe BOUCHER Session 2 A brief overview of he classical linear regression model 1 Regression Regression is probably he single mos imporan ool a he economerician s disposal. Bu wha
More informationMath 333 Problem Set #2 Solution 14 February 2003
Mah 333 Problem Se #2 Soluion 14 February 2003 A1. Solve he iniial value problem dy dx = x2 + e 3x ; 2y 4 y(0) = 1. Soluion: This is separable; we wrie 2y 4 dy = x 2 + e x dx and inegrae o ge The iniial
More informationNon-uniform circular motion *
OpenSax-CNX module: m14020 1 Non-uniform circular moion * Sunil Kumar Singh This work is produced by OpenSax-CNX and licensed under he Creaive Commons Aribuion License 2.0 Wha do we mean by non-uniform
More informationNCSS Statistical Software. , contains a periodic (cyclic) component. A natural model of the periodic component would be
NCSS Saisical Sofware Chaper 468 Specral Analysis Inroducion This program calculaes and displays he periodogram and specrum of a ime series. This is someimes nown as harmonic analysis or he frequency approach
More informationDerived Short-Run and Long-Run Softwood Lumber Demand and Supply
Derived Shor-Run and Long-Run Sofwood Lumber Demand and Supply Nianfu Song and Sun Joseph Chang School of Renewable Naural Resources Louisiana Sae Universiy Ouline Shor-run run and long-run implied by
More informationState-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
More informationESTIMATION OF DYNAMIC PANEL DATA MODELS WHEN REGRESSION COEFFICIENTS AND INDIVIDUAL EFFECTS ARE TIME-VARYING
Inernaional Journal of Social Science and Economic Research Volume:02 Issue:0 ESTIMATION OF DYNAMIC PANEL DATA MODELS WHEN REGRESSION COEFFICIENTS AND INDIVIDUAL EFFECTS ARE TIME-VARYING Chung-ki Min Professor
More information23.5. Half-Range Series. Introduction. Prerequisites. Learning Outcomes
Half-Range Series 2.5 Inroducion In his Secion we address he following problem: Can we find a Fourier series expansion of a funcion defined over a finie inerval? Of course we recognise ha such a funcion
More informationThe 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:
More informationMath 2142 Exam 1 Review Problems. x 2 + f (0) 3! for the 3rd Taylor polynomial at x = 0. To calculate the various quantities:
Mah 4 Eam Review Problems Problem. Calculae he 3rd Taylor polynomial for arcsin a =. Soluion. Le f() = arcsin. For his problem, we use he formula f() + f () + f ()! + f () 3! for he 3rd Taylor polynomial
More informationWEEK-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
More informationCHAPTER 2 Signals And Spectra
CHAPER Signals And Specra Properies of Signals and Noise In communicaion sysems he received waveform is usually caegorized ino he desired par conaining he informaion, and he undesired par. he desired par
More informationAP CALCULUS AB 2003 SCORING GUIDELINES (Form B)
SCORING GUIDELINES (Form B) Quesion A blood vessel is 6 millimeers (mm) long Disance wih circular cross secions of varying diameer. x (mm) 6 8 4 6 Diameer The able above gives he measuremens of he B(x)
More informationIntroduction 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
More informationExcel-Based Solution Method For The Optimal Policy Of The Hadley And Whittin s Exact Model With Arma Demand
Excel-Based Soluion Mehod For The Opimal Policy Of The Hadley And Whiin s Exac Model Wih Arma Demand Kal Nami School of Business and Economics Winson Salem Sae Universiy Winson Salem, NC 27110 Phone: (336)750-2338
More informationEXERCISES FOR SECTION 1.5
1.5 Exisence and Uniqueness of Soluions 43 20. 1 v c 21. 1 v c 1 2 4 6 8 10 1 2 2 4 6 8 10 Graph of approximae soluion obained using Euler s mehod wih = 0.1. Graph of approximae soluion obained using Euler
More informationSterilization D Values
Seriliaion D Values Seriliaion by seam consis of he simple observaion ha baceria die over ime during exposure o hea. They do no all live for a finie period of hea exposure and hen suddenly die a once,
More informationReliability of Technical Systems
eliabiliy of Technical Sysems Main Topics Inroducion, Key erms, framing he problem eliabiliy parameers: Failure ae, Failure Probabiliy, Availabiliy, ec. Some imporan reliabiliy disribuions Componen reliabiliy
More information