LtChapter12 Autocorrelation What happens if Error Terms are Correlated y
Chapter12 Autocorrelation: What Happens if Error Terms are Correlated
12.1 The Nature of autocorrelation 1. Definition (1) CLRM assumption No autocorrelation exist in dishurbances u E(μy)=0 Autocorrelation means E(41)≠0 1 (2) Autocorrelation is usually associated with time series data. but it can also occur in cross-sectional data. which is called spatial correlation (3) Autocorrelation can be positive as well as negative
12.1 The Nature of Autocorrelation 1.Definition （1） CLRM assumption: No autocorrelation exist in dishurbances μi ; E(μiμj )＝ 0 i≠j Autocorrelation means: E(μiμj )≠0 i≠j （2）Autocorrelation is usually associated with time series data, but it can also occur in cross-sectional data, which is called spatial correlation. （3）Autocorrelation can be positive as well as negative
2 Patterns of autocorrelation Figure 12-1, p379
2. Patterns of autocorrelation Figure 12-1, p379
3. Reasons of autocorrelation (1)Inertia or sluggishness Most economic time-series is inertia such as GDP, money supply, price indexes so successive observations are correlated
3. Reasons of autocorrelation (1) Inertia or sluggishness Most economic time-series is inertia, such as GDP, money supply, price indexes, so successive observations are correlated
(2) Model Specification Error(s) . Some important variables that should be included in the model are not included (underspecification) .o The model has the wrong functional form e.g. a linear-in-variable(llv) model is fitted whereas a log-linear model should have been fitted
（2）Model Specification Error(s) ❖ Some important variables that should be included in the model are not included (underspecification) ❖ The model has the wrong functional form e.g. a linear-in-variable(LIV) model is fitted whereas a log-linear model should have been fitted
(3) Cobweb phenomenon The agriculture commodities often reflects the Cobweb phenomenon, where supply reacts to price with a lag of one time period because supply decisions take time to implement, the beginning of this years planting of crops farmers are influenced by the price prevailing last year Supply B+B2P++p
（3）Cobweb phenomenon The agriculture commodities often reflects the Cobweb phenomenon, where supply reacts to price with a lag of one time period because supply decisions take time to implement, the beginning of this year’s planting of crops farmers are influenced by the price prevailing last year Supplyt=B1+B2Pt-1+μt
(4) Data Manipulation Data smoothness can itself lead to a systematic pattern in the disturbances thereby inducing autocorrelation
（4）Data Manipulation Data smoothness can itself lead to a systematic pattern in the disturbances, thereby inducing autocorrelation
12.2 Consequences of autocorrelation (1The OlS estimators are linear and unbiased (2)The OLS estimators are not efficient The error variance of ols estimators is a biased estimator of the true o The estimated variances sometimes underestimate true variances and standard errors, thereby inflating t values (3) The t and f tests are not generally reliable (4) The conventionally computed R2 may be an unreliable measure of true r (5) Variances and standard errors of forecast may also be inefficient
12.2 Consequences of autocorrelation (1)The OLS estimators are linear and unbiased (2)The OLS estimators are not efficient The error variance of OLS estimators is a biased estimator of the true σ2 The estimated variances sometimes underestimate true variances and standard errors, thereby inflating t values （3）The t and F tests are not generally reliable. （4）The conventionally computed R2 may be an unreliable measure of true R2 . （5）Variances and standard errors of forecast may also be inefficient
12.3 Detecting Autocorrelation Because the true u are unobservable. we have to rely on the es obtained from the standard ols procedure to learnsomething about the presence, or lack thereof, of autocorrelation
12.3 Detecting Autocorrelation Because the true ui are unobservable, we have to rely on the et s obtained from the standard OLS procedure to “learn”something about the presence, or lack thereof, of autocorrelation
1. The Graphical Method: Visual examine the ols residuals.e,s (1) Plot residuals against time(time sequence plot (2) Plot the residuals at time t against their values lagged in one period; that is, plot e against et-1:etet-1
1. The Graphical Method: ～ Visual examine the OLS residuals, ets (1) Plot residuals against time（timesequence plot）: ei ～t (2) Plot the residuals at time t against their values lagged in one period; that is, plot et against et-1 : et ～et-1