Folie 1

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.Chapter 11 - X OLS (Further Issues Using OLS with Time Series Data)Wooldridge: Introductory Econometrics: A Modern Approach, 5e

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (Strict exogeneity), (homoscedasticity), (no serial correlation) , (Statistical inference) (normality) (sample size) (large sample analysis of time series) (time series) (stationary) (weakly dependent) (Stationary time series) (stationary) (stochastic properties) , (temporal dependence structure) : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (Stationary stochastic processes

Covariance stationary processes (stochastic process) (stationary), - (joint distribution) ,

covariance stationary, (expected value), (variance), (covariances) (over time):1) , 2) , 3) .

: OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (Weakly dependent time series)

(weak dependence) weak dependence (correlation) LLN CLT, (strongly related) : (weaker), - (nonstationary) (weakly dependent) (stochastic process) (weakly dependent) , " (almost independent)" ( ).

: OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (weakly dependent time series) 1 (Moving average process of order one) (MA(1)

1 (Autoregressive process of order one) (AR(1))

(weakly dependent) (uncorrelated). (short moving average) i.i.d. et

( iid et) (stability condition) , , (weakly dependent) (serial correlation) .

: OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (Asymptotic) OLS TS.1 (Linear in parameters) TS.1 (dependent) (independent) (variables) (stationary) (weakly dependent) TS.2 (No perfect collinearity) TS.2 TS.3 (Zero conditional mean) (explanatory variables) (only contemporaneously exogenous) (strictly exogenous),

(explanatory variables) (of the same period) (uninformative) (mean) (error term) : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 11.1 ( (Consistency) OLS)

(strict exogeneity); (strict exogeneity) (dynamic relationships) (explanatory variables) (error term), (feedback effects) , (strict exogeneity) (lagged dep. var.)

: (consistency) (suffice) (explanatory variables) (contemporaneously uncorrelated)

: OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (lagged dependent variables) (strict exogeneity);

OLS (estimation) (lagged dependent variables) (contemporaneous exogeneity), OLS (consistent) (biased)

(lagged dependent variable) (Contemporanous exogeneity): (Strict exogeneity): (strict exogeneity) (error term) (uncorrelated) yt, t=1, , n-1

: : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. TS.4 (Homoscedasticity)

TS.5 (No serial correlation)

11.2 ( (Asymptotic normality) OLS) TS.1 TS.5, OLS (estimators) (asymptotically normally distributed). , OLS (standard errors), t-statistics F-statistics (asymptotically valid).

(errors) (contemporaneously homoscedastic)

(Conditional on) (explanatory variables) t s, (errors) (uncorrelated) : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.Example: Efficient Markets Hypothesis (EMH) EMH t t. t.

EMH AR(1) . EMH , TS.3 OLS .

EMH. . : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. trend-stationary series (deterministic time trends) - (nonstationary) (stationary) (trend) (weakly dependent), trend-stationary processesTrend-stationary processes TS.1 (persistent) ( = (strongly dependent)) OLS ( CLM) (weak dependence) : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.Random walks

. random walk (highly persistent): (effect) . random walk random walk yt-1 i.i.d. (random) et random walk covariance stationary (variance) (covariance) .

weakly dependent t. : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. random walk

random walks : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

3 T-bill random walk random walk unit root process.

Unit root processes random walk et (weakly dependent process).

(highly persistent). (highly persistent time series), / (lasting/permanent effects), (weakly dependent) (effects) (transitory). : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.Random walks with drift

(linear time trend) random walk . random walk , (trend). random walk, / (= drift) , random walk drift random walk drift.

Random walks drift covariance statio-nary weakly dependent. : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Sample path of a random walk with drift (trend line).

Random walks drift (time series) (trend) (weakly dependent). : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (highly persistent time series) (Order of integration) (Weakly dependent time series) (integrated of order zero) (= I(0)) (differenced) (weakly dependent) , (integrated of order one) (= I (1)) I(1)

(Differencing) (weak dependence)

(differencing), (weakly dependent) ( et (weakly dependent)). : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (time series) I(1) (time series) I(1) (= unit root tests), (sample first order autocorrelation):

(sample first order autocorrelation) , (highly persistent) (= unit root), (deterministic trend) unit root trend differencing

Measures how strongly adjacent times series observations are related to each other. : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.:

OLS CLM . , (large sample analysis). (large sample analysis), (fertility series) (personal tax exemption) (stationary) (weakly dependent). (highly persistent):

(estimate) (first differences). (levels), (first differences):

: OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.:

detrending, (sample autocorrelations) (first differences) :

(= (productivity)) (trend), (trends). (estimate) . : OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (Dynamically complete models) (dynamically complete) (lagged variables) (explanatory variables) (lags) (dependent variable):

(serial correlation) (lags) (regression), (omission) (serial correlation) ( (variables) (serially correlated)) (dynamic completeness) (lags) , (serial correlation)

: OLS

2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. (Sequential exogeneity) (explanatory variables) (sequentially exogenous) (lagged explanatory variables) :

(sequential exogeneity) (strict exogeneity) (sequential exogeneity) (dynamic completeness) (explanatory variables) (lagged dependent variable) (regression models) (dynamically complete); : (sequential exogeneity), (causal effects) (estimated) : (serial correlation)

: OLS