Licenciatura de ADE y Licenciatura conjunta Derecho y ADE. Hoja de ejercicios 2 PARTE A
|
|
|
- Joleen Stokes
- 5 years ago
- Views:
Transcription
1 Licenciaura de ADE y Licenciaura conjuna Derecho y ADE Hoja de ejercicios PARTE A 1. Consider he following models Δy = ε ( L) Δ 1 y = ε where ε and ε are independen whie noise processes. In wha follows he raes of change are defined as he differences of he logarihms. Mark he correc answers: a) Only he process y is saionary and inverible. b) Boh processes, y and y, have sochasic seasonaliy. c) The process y is saionary, bu is rae of change is no saionary. d) Only he process y is no saionary. e) Boh processes, y and y, are no saionary, bu only he process y has a deerminisic rend. f) None of he above answers is correc.. Consider he following processes: y = ε1 + 0.ε 1 (1 0.L)(1 L)(1 L 1 )log y = (1 0.L) ε where ε and ε are independen whie noise processes. Mark he correc answers: a) Boh processes, y and logy, are saionary bu no inverible. b) The saionary ransformaion of logy does no presen regular auocorrelaion. c) The saionary ransformaion of logy is whie noise. d) The auocorrelaion of order 1 of y is negaive. e) The saionary ransformaion of logy is an AR(1) process. f) The saionary ransformaion of y is a MA(1) process. 3. Le quarerly impors of a counry o be given by he model: 4 ΔΔ log X = (1 0.4L ) ε 4 where ε is a whie noise. In wha follows he raes of change are defined as he differences of he logarihms. Mark he correc answers: a) The quarerly series of raes of change of impors is saionary. b) The annual rae of change of impors is inverible. c) The saionary ransformaion of impors has zero auocorrelaion in all he lags. d) Consider he saionary ransformaion of impors. For he orders greaer han four, he parial auocorrelaions are equal o zero.
2 e) The saionary ransformaion of impors does no presen auocorrelaion in he regular order, bu i has auocorrelaion in he seasonal order. f) None of he above answers is correc. 4. Consider he following quarerly processes: 4 (1 L )log y = 3 + ε 4 (1 L)(1 L )log y 0.4ε 1 = (1 0.6L) ε where ε 1 and ε 1 are independen whie noise processes. Mark he correc answers: 3 1 has mean equal o (b) The annual raes of change, approximaed by he annual differences of logarihmic ransformaions, are saionary in he case of y 1 bu no in he case of y. (c) The saionary ransformaion of y 1 has seasonal correlaion. (d) The auocorrelaion funcion of he saionary ransformaion of y has zero correlaions for lags greaer or equal han he lag. (e) The saionary ransformaions of y 1 and y have zero mean. (a) The series ( L 4 ) log y1
3 5. a) In he nex able are repored he resuls of a Dickey Fuller uni roo es applied o a daily ime series (including Saurdays and Sundays). The daa are daily prices of French elecriciy from 11/8/001 o 5/5/005. Inerpre he resuls of he uni roo es, indicae null and alernaive hypoheses of he es and explain why we need he regression repored in he able. Null Hypohesis: OFFPEAK1 1_8 has a uni roo Exogenous: Consan Lag Lengh: 1 (Fixed) -Saisic Prob.* Augmened Dickey-Fuller es saisic Tes criical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmened Dickey-Fuller Tes Equaion Dependen Variable: D(OFFPEAK1 1_8) Mehod: Leas Squares Dae: 04//08 Time: 1:39 Sample (adjused): 11/9/001 5/5/005 Included observaions: 174 afer adjusmens Variable Coefficien Sd. Error -Saisic Prob. OFFPEAK1 1_8(-1) D(OFFPEAK1 1_8(-1)) C R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa.0660 Prob(F-saisic) Answer: We made a Dickey Fuller uni roo es. The null hypohesis is ha here exiss a uni roo (model I(1), no saionary) and he alernaive hypohesis is ha he model is saionary (I(0)). We es H0: ρ 1 agains H1: ρ 1 in he model y = a + ρ 1 y 1 + ε 1 = 1 0.
4 To perform he es we esimae a regression of he firs differences of he series on he firs lag of he iniial series: Δy = a + a 0 1 y 1 + ε H0: a = 1 0 H1: a 1 0 The saisic ha we ge is = , > , and consequenly we do no accep he null hypohesis. Finally, according o he es, he series has no a uni roo, and i is saionary. b) Below are repored he graphs of he series of he prices and of he esimaed auocorrelaions. Wha are he characerisics of he series of elecriciy prices ha can be derived observing boh graphs? A saionary series have auocorrelaions wih a rapid exponenial decay oward zero. Do you hink ha i is he case for he price of elecriciy?
5 Answer: The auocorrelaions of he series do no decrease exponenially, and his fac suggess ha he series is no saionary, and i is in conradicion wih he resul of he Dickey Fuller es. c) Explain, giving some reasons, if you expec ha daily elecriciy prices have a seasonal paern. Observing he graph and he auocorrelaions of he series, do you hink ha elecriciy prices have a seasonal paern? Answer: We expec ha elecriciy prices have a seasonal paern in erms of days; for example, we expec ha he firms demand for elecriciy decreases on Saurdays and Sundays, while he families demand for elecriciy increases in hese days, and his fac could affec elecriciy prices. Our expecaion is refleced in he correlogram of he series, which seems o be characerized by a cycle in he auocorrelaions (wih a period of 7 observaions, ha is a week). We can also observe ha some parial auocorrelaions are significan, in paricular he ones associaed wih he seasonal lags (7, 14, 1, 8). d) Observing he correlogram, i has been decided o make an augmened Dickey Fuller es, using informaion crieria o decide he number of lags o include in he regression. Using he resuls of quesion c), do you hink ha make sense o include 8 lags in he regression? Inerpre he resuls of he uni roo es and indicae null and alernaive hypoheses. Wha is he resul of he conras now? Commen he resuls, and make a comparison wih he resuls of quesion b).
6 Null Hypohesis: OFFPEAK1 1_8 has a uni roo Exogenous: Consan Lag Lengh: 8 (Auomaic based on SIC, MAXLAG=35) -Saisic Prob.* Augmened Dickey-Fuller es saisic Tes criical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmened Dickey-Fuller Tes Equaion Dependen Variable: D(OFFPEAK1 1_8) Mehod: Leas Squares Dae: 04//08 Time: 1:30 Sample (adjused): 1/6/001 5/5/005 Included observaions: 147 afer adjusmens Variable Coefficien Sd. Error -Saisic Prob. OFFPEAK1 1_8(-1) D(OFFPEAK1 1_8(-1)) D(OFFPEAK1 1_8(-)) D(OFFPEAK1 1_8(-3)) D(OFFPEAK1 1_8(-4)) D(OFFPEAK1 1_8(-5)) D(OFFPEAK1 1_8(-6)) D(OFFPEAK1 1_8(-7)) D(OFFPEAK1 1_8(-8)) D(OFFPEAK1 1_8(-9)) D(OFFPEAK1 1_8(-10)) D(OFFPEAK1 1_8(-11)) D(OFFPEAK1 1_8(-1)) D(OFFPEAK1 1_8(-13)) D(OFFPEAK1 1_8(-14)) D(OFFPEAK1 1_8(-15)) D(OFFPEAK1 1_8(-16)) D(OFFPEAK1 1_8(-17)) D(OFFPEAK1 1_8(-18)) D(OFFPEAK1 1_8(-19)) D(OFFPEAK1 1_8(-0)) D(OFFPEAK1 1_8(-1)) D(OFFPEAK1 1_8(-)) D(OFFPEAK1 1_8(-3))
7 D(OFFPEAK1 1_8(-4)) D(OFFPEAK1 1_8(-5)) D(OFFPEAK1 1_8(-6)) D(OFFPEAK1 1_8(-7)) D(OFFPEAK1 1_8(-8)) C R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared resid Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic) Answer: Observing he resuls of pars b) and c), we noice ha he auocorrelaions of he series do no decrease quickly. Moreover, he series has a seasonal paern, and he model mus include more lags. As consequence, he resul of he Dickey Fuller es can be explained by he fac ha we did no include in he regression model all he necessary dynamic of he series. In fac, i has sense o include 8 lags, which corresponds o 4 weeks. Now, he resul of he Augmened Dickey Fuller es (wih 8 lags of he differences) suggess ha he series is no saionary, and also wih a 10% level we accep he null hypohesis of uni roo: he saisic is , and > The null and alernaive hypoheses of his es are he same of he Dickey Fuller es performed in par a). 6) Consider he following model y = ε σ σ = ω + αy whereε is Normal and independen wih mean 0 and variance 1. a) Assuming saionariy, ha is α<1, compue he mean and he variance of y. We have ha ε and σ are independen: i follows ha E( y ) = E( ε )E( σ ) = 0. Moreover, he process y is saionary, i follows ha i will have a consan marginal variance, sayσ, which can be compued in he following way: E( y ) = E( ε )E( σ ) = E( σ ) = E( ε ) = 1. 1 σ. I is equal o he variance of he process σ, because b) Discuss if he variable y is uncorrelaed and if i is independen. Wha are he differences beween uncorrelaion and independence? The independence beween he processes ε and σ guaranees ha he series y has no auocorrelaion and i is a whie noise process. In fac, he auocovariances of he series are given by: E( y y ) = E( k σ ε σ k k ) = E( ε ε k )E( σ σ k ) = 0, ε
8 because he process ε is independen of is pas values and of he pas and acual values of he process σ. I follows ha he process y will have null auocovariances. However, unlike he common hypoheses of ARIMA models, he series y is no independen of is pas values. In fac, y is relaed o y, and even 1 if hey are no correlaed, in general we will observe dependence in he series y. c) Compue condiional expecaion and condiional variance. Wha are he differences beween he marginal (or uncondiional) momens calculaed in par a) and he condiional momens? The condiional mean of y is E( y y 1 ) = E( ε )E( σ y 1) = 0, and i is equal o he marginal mean. The condiional variance is: Var( y y 1 ) = E( ε )E( σ y 1 ) = σ because E( ε y 1 ) = E( ε ) = 1. Therefore, unlike he marginal variance, which is consan, he condiional variance is no consan, and i changes wih ime. I follows ha he process σ has an ineresing inerpreaion: in each momen, i represens he condiional variance of he series, and i changes wih ime wih a sor of saionary dynamic. 7) Consider he following graphs which represen he observed values of a paricular variable and is sample correlaions Tasas anuales de desempleo
9 Explain how o inerpre he esimaes of he sample mean, he sample variance and he sample auocovariances of his variable. How do you inerpre ha he sample correlaions are ouside he bands of 95%? The series is abou he annual unemploymen rae, and we know ha he variable unemploymen is ransformed by a logarihmic ransformaion. Therefore, he series unemploymen has no a consan variance, and he sample variance will be no a good esimaor of he variance of he populaion (because of he nonsaionariy of he variance of he series unemploymen ). Now, analyzing he problem for he mean, he correlogram shows firs a high dependence in he observaions of he series and second non-saionariy in mean, because of he slow decrease in he FAC. Therefore, also he sample mean will be no a good esimaor of he mean of he populaion. The same hing happens for he sample auocovariances, because hey are second order momens ha depend of he firs order momen. For his reason, he fac ha he sample correlaions are ouside he bands of 95% can no be inerpreed as usually. Finally, because of he non-saionariy, sample mean, sample variance and sample auocovariances are no represenaive for his process.
Stationary Time Series
3-Jul-3 Time Series Analysis Assoc. Prof. Dr. Sevap Kesel July 03 Saionary Time Series Sricly saionary process: If he oin dis. of is he same as he oin dis. of ( X,... X n) ( X h,... X nh) Weakly Saionary
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
Cointegration 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
Regression 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
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,
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
TÁMOP /2/A/KMR
ECONOMIC STATISTICS ECONOMIC STATISTICS Sonsored by a Gran TÁMOP-4..2-08/2/A/KMR-2009-004 Course Maerial Develoed by Dearmen of Economics, Faculy of Social Sciences, Eövös Loránd Universiy Budaes (ELTE)
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,
- The whole joint distribution is independent of the date at which it is measured and depends only on the lag.
Saionary Processes Sricly saionary - The whole join disribuion is indeenden of he dae a which i is measured and deends only on he lag. - E y ) is a finie consan. ( - V y ) is a finie consan. ( ( y, y s
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
Lecture 15. Dummy variables, continued
Lecure 15. Dummy variables, coninued Seasonal effecs in ime series Consider relaion beween elecriciy consumpion Y and elecriciy price X. The daa are quarerly ime series. Firs model ln α 1 + α2 Y = ln X
Econ 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
(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
Chapter 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
Nature 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
Arima Fit to Nigerian Unemployment Data
2012, TexRoad Publicaion ISSN 2090-4304 Journal of Basic and Applied Scienific Research www.exroad.com Arima Fi o Nigerian Unemploymen Daa Ee Harrison ETUK 1, Barholomew UCHENDU 2, Uyodhu VICTOR-EDEMA
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
Modeling 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
(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)
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
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,
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
Section 4 NABE ASTEF 232
Secion 4 NABE ASTEF 3 APPLIED ECONOMETRICS: TIME-SERIES ANALYSIS 33 Inroducion and Review The Naure of Economic Modeling Judgemen calls unavoidable Economerics an ar Componens of Applied Economerics Specificaion
Department 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
Solutions: 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
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
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
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
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
Lecture 5. Time series: ECM. Bernardina Algieri Department Economics, Statistics and Finance
Lecure 5 Time series: ECM Bernardina Algieri Deparmen Economics, Saisics and Finance Conens Time Series Modelling Coinegraion Error Correcion Model Two Seps, Engle-Granger procedure Error Correcion Model
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%,
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
14 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
CHAPTER 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
Types 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
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
5. NONLINEAR MODELS [1] Nonlinear (NL) Regression Models
![5. NONLINEAR MODELS [1] Nonlinear (NL) Regression Models](/thumbs/88/116431777.jpg "5. NONLINEAR MODELS [1] Nonlinear (NL) Regression Models")
5. NONLINEAR MODELS [1] Nonlinear (NL) Regression Models General form of nonlinear or linear regression models: y = h(x,β) + ε, ε iid N(0,σ ). Assume ha he x and ε sochasically independen. his assumpion
Wednesday, 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
Box-Jenkins Modelling of Nigerian Stock Prices Data
Greener Journal of Science Engineering and Technological Research ISSN: 76-7835 Vol. (), pp. 03-038, Sepember 0. Research Aricle Box-Jenkins Modelling of Nigerian Sock Prices Daa Ee Harrison Euk*, Barholomew
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
ACE 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
STAD57 Time Series Analysis. Lecture 5
STAD57 Time Series Analysis Lecure 5 1 Exploraory Daa Analysis Check if given TS is saionary: µ is consan σ 2 is consan γ(s,) is funcion of h= s If no, ry o make i saionary using some of he mehods below:
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
Økonomisk Kandidateksamen 2005(II) Econometrics 2. Solution
Økonomisk Kandidaeksamen 2005(II) Economerics 2 Soluion his is he proposed soluion for he exam in Economerics 2. For compleeness he soluion gives formal answers o mos of he quesions alhough his is no always
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
How to Deal with Structural Breaks in Practical Cointegration Analysis
How o Deal wih Srucural Breaks in Pracical Coinegraion Analysis Roselyne Joyeux * School of Economic and Financial Sudies Macquarie Universiy December 00 ABSTRACT In his noe we consider he reamen of srucural
ACE 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
Chickens 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
Methodology. -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
EXERCISES 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
Robust critical values for unit root tests for series with conditional heteroscedasticity errors: An application of the simple NoVaS transformation
WORKING PAPER 01: Robus criical values for uni roo ess for series wih condiional heeroscedasiciy errors: An applicaion of he simple NoVaS ransformaion Panagiois Manalos ECONOMETRICS AND STATISTICS ISSN
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
Some Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
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
Dynamic Models, Autocorrelation and Forecasting
ECON 4551 Economerics II Memorial Universiy of Newfoundland Dynamic Models, Auocorrelaion and Forecasing Adaped from Vera Tabakova s noes 9.1 Inroducion 9.2 Lags in he Error Term: Auocorrelaion 9.3 Esimaing
Forecast of Adult Literacy in Sudan
Journal for Sudies in Managemen and Planning Available a hp://inernaionaljournalofresearch.org/index.php/jsmap e-issn: 2395-463 Volume 1 Issue 2 March 215 Forecas of Adul Lieracy in Sudan Dr. Elfarazdag
2 Univariate Stationary Processes
Univariae Saionary Processes As menioned in he inroducion, he publicaion of he exbook by GEORGE E.P. BOX and GWILYM M. JENKINS in 97 opened a new road o he analysis of economic ime series. This chaper
Quarterly ice cream sales are high each summer, and the series tends to repeat itself each year, so that the seasonal period is 4.
Seasonal models Many business and economic ime series conain a seasonal componen ha repeas iself afer a regular period of ime. The smalles ime period for his repeiion is called he seasonal period, and
Stability. Coefficients may change over time. Evolution of the economy Policy changes
Sabiliy Coefficiens may change over ime Evoluion of he economy Policy changes Time Varying Parameers y = α + x β + Coefficiens depend on he ime period If he coefficiens vary randomly and are unpredicable,
STAD57 Time Series Analysis. Lecture 17
STAD57 Time Series Analysis Lecure 17 1 Exponenially Weighed Moving Average Model Consider ARIMA(0,1,1), or IMA(1,1), model 1 s order differences follow MA(1) X X W W Y X X W W 1 1 1 1 Very common model
STAD57 Time Series Analysis. Lecture 17
STAD57 Time Series Analysis Lecure 17 1 Exponenially Weighed Moving Average Model Consider ARIMA(0,1,1), or IMA(1,1), model 1 s order differences follow MA(1) X X W W Y X X W W 1 1 1 1 Very common model
Bias 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
The 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
I. Return Calculations (20 pts, 4 points each)
Universiy of Washingon Spring 015 Deparmen of Economics Eric Zivo Econ 44 Miderm Exam Soluions This is a closed book and closed noe exam. However, you are allowed one page of noes (8.5 by 11 or A4 double-sided)
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
Chapter 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).
INVESTIGATING THE WEAK FORM EFFICIENCY OF AN EMERGING MARKET USING PARAMETRIC TESTS: EVIDENCE FROM KARACHI STOCK MARKET OF PAKISTAN
Elecronic Journal of Applied Saisical Analysis EJASA, Elecron. J. App. Sa. Anal. Vol. 3, Issue 1 (21), 52 64 ISSN 27-5948, DOI 1.1285/i275948v3n1p52 28 Universià del Saleno SIBA hp://siba-ese.unile.i/index.php/ejasa/index
ST4064. Time Series Analysis. Lecture notes
ST4064 Time Series Analysis ST4064 Time Series Analysis Lecure noes ST4064 Time Series Analysis Ouline I II Inroducion o ime series analysis Saionariy and ARMA modelling. Saionariy a. Definiions b. Sric
Nonstationary Time Series Data and Cointegration
ECON 4551 Economerics II Memorial Universiy of Newfoundland Nonsaionary Time Series Daa and Coinegraion Adaped from Vera Tabakova s noes 12.1 Saionary and Nonsaionary Variables 12.2 Spurious Regressions
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
Additional material for Chapter 7 Regression diagnostic IV: model specification errors
Table 7.14 OLS resuls of he regression of PCE on income. Dependen Variable: PCE Mehod: Leas Squares Dae: 07/31/10 Time: 10:00 Sample: 1960 2009 Included observaions: 50 Variable Coefficien Sd. Error -Saisic
ACE 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
Lesson 2, page 1. Outline of lesson 2
Lesson 2, page Ouline of lesson 2 Inroduce he Auocorrelaion Coefficien Undersand and define saionariy Discuss ransformaion Discuss rend and rend removal C:\Kyrre\sudier\drgrad\Kurs\series\lecure 02 03022.doc,
1. 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
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
Hypothesis 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
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.
The Effect of Nonzero Autocorrelation Coefficients on the Distributions of Durbin-Watson Test Estimator: Three Autoregressive Models
EJ Exper Journal of Economi c s ( 4 ), 85-9 9 4 Th e Au h or. Publi sh ed by Sp rin In v esify. ISS N 3 5 9-7 7 4 Econ omics.e xp erjou rn a ls.com The Effec of Nonzero Auocorrelaion Coefficiens on he
A Hybrid Model for Improving. Malaysian Gold Forecast Accuracy
In. Journal of Mah. Analysis, Vol. 8, 2014, no. 28, 1377-1387 HIKARI Ld, www.m-hikari.com hp://dx.doi.org/10.12988/ijma.2014.45139 A Hybrid Model for Improving Malaysian Gold Forecas Accuracy Maizah Hura
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
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
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
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
ACE 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
5.1 - Logarithms and Their Properties
Chaper 5 Logarihmic Funcions 5.1 - Logarihms and Their Properies Suppose ha a populaion grows according o he formula P 10, where P is he colony size a ime, in hours. When will he populaion be 2500? We
12: AUTOREGRESSIVE AND MOVING AVERAGE PROCESSES IN DISCRETE TIME. Σ j =
1: AUTOREGRESSIVE AND MOVING AVERAGE PROCESSES IN DISCRETE TIME Moving Averages Recall ha a whie noise process is a series { } = having variance σ. The whie noise process has specral densiy f (λ) = of
Chapter 5. Heterocedastic Models. Introduction to time series (2008) 1
Chaper 5 Heerocedasic Models Inroducion o ime series (2008) 1 Chaper 5. Conens. 5.1. The ARCH model. 5.2. The GARCH model. 5.3. The exponenial GARCH model. 5.4. The CHARMA model. 5.5. Random coefficien
Lecture 10 Estimating Nonlinear Regression Models
Lecure 0 Esimaing Nonlinear Regression Models References: Greene, Economeric Analysis, Chaper 0 Consider he following regression model: y = f(x, β) + ε =,, x is kx for each, β is an rxconsan vecor, ε is
Identification of Trends and Cycles in Economic Time Series. by Bora Isik
Idenificaion of Trends and Cycles in Economic Time Series by Bora Isik An Honours essay submied o Carleon Universiy in fulfillmen of he requiremens for he course ECON 498, as credi oward he degree of Bachelor
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
Applied Time Series Notes White noise: e t mean 0, variance 5 2 uncorrelated Moving Average
Applied Time Series Noes Whie noise: e mean 0, variance 5 uncorrelaed Moving Average Order 1: (Y. ) œ e ) 1e -1 all Order q: (Y. ) œ e ) e â ) e all 1-1 q -q ( 14 ) Infinie order: (Y. ) œ e ) 1e -1 ) e
The Properties of Procedures Dealing with Uncertainty about Intercept and Deterministic Trend in Unit Root Testing
CESIS Elecronic Working Paper Series Paper No. 214 The Properies of Procedures Dealing wih Uncerainy abou Inercep and Deerminisic Trend in Uni Roo Tesing R. Sco Hacker* and Abdulnasser Haemi-J** *Jönköping
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
References are appeared in the last slide. Last update: (1393/08/19)
SYSEM IDEIFICAIO Ali Karimpour Associae Professor Ferdowsi Universi of Mashhad References are appeared in he las slide. Las updae: 0..204 393/08/9 Lecure 5 lecure 5 Parameer Esimaion Mehods opics o be
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
School and Workshop on Market Microstructure: Design, Efficiency and Statistical Regularities March 2011
2229-12 School and Workshop on Marke Microsrucure: Design, Efficiency and Saisical Regulariies 21-25 March 2011 Some mahemaical properies of order book models Frederic ABERGEL Ecole Cenrale Paris Grande
Computer Simulates the Effect of Internal Restriction on Residuals in Linear Regression Model with First-order Autoregressive Procedures
MPRA Munich Personal RePEc Archive Compuer Simulaes he Effec of Inernal Resricion on Residuals in Linear Regression Model wih Firs-order Auoregressive Procedures Mei-Yu Lee Deparmen of Applied Finance,
Mean Reversion of Balance of Payments GEvidence from Sequential Trend Break Unit Root Tests. Abstract
Mean Reversion of Balance of Paymens GEvidence from Sequenial Trend Brea Uni Roo Tess Mei-Yin Lin Deparmen of Economics, Shih Hsin Universiy Jue-Shyan Wang Deparmen of Public Finance, Naional Chengchi
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...........................................
Derived 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