9.) Serial Correlation Flashcards
Pure Serial Correlation
occurs when Classical Assumption IV, which assume uncorrelated observations of the error term, is violated in a correctly specified equation.
If the expected value of the simple correlation coefficient between any two observations of the error term that are…
not equal to zero.
The most commonly assumed kind of serial correlation is ….
first-order serial correlation, in which the current value of the error term is a function of the previous value of the error term.
The first order autocorrelation coefficient (p) …
measures the functional relationship between the value of an observation of the error term and th evalue of the previous observation of the error term
The magnitude of p indicates…
the strength of the serial correlation in an equation.
A p approaches one in absolute value..
the value of the previous observation of the error term becomes more important in determining the curret value of the stochastic error term, and a high degree of serial correlation exists.
The sighn of p indicates…
the nature of the serial correlation in an equation.
A positive value for p implies…
that the error term tends to have the same sign from one time period to the next.
Positive Serial Correlation indicates…
that the error term tends to have the same sign from one time period to the next.
A negative value of p implies…
that the error term has a tendency to switch signs from negative to positive and back again in consecutive observations
Negative Serial Correlation signals…
that there is some sort of cycle (like a pendulum) behind the drawings of the stochastic disturbances.
By impure serial correlation the authors mean…
serial correlation is caused by a specification error such as an omitted variable or an incorrect functional form.
Pure Serial Correlation is caused by…
the underlying distribution of the error term of the true specification of an equation
Impure Serial Correlation is caused by…
a specification error that often can be corrected.
An omitted variable can cause…
the error term to be serially correlated
The proper remedy for serial correlation depends on …
whether the serial correlation is likely to be pure or impure
the new error term e* will tend to be serially correlated when…
- ) X2 itself is serially correlated (this is quite likely in a time series) and
- ) the size of e is small compared to the size of B2Xbarred2
An incorrect functional form is a common cause of…
the error term being serially correlated
Using a linear functional form when a nonlinear one is appropriate will…
usually result in positive impure serial correlation
What generally results in positive impure serial correlation?
Using a linear functional form when a nonlinear one is appropriate.
The existence of serial correlation in the error term of an equation violates Classical Assumption IV, and the estimation of the equation with OLS has at least three consequences…
- ) Pure serial correlation does not cause bias in the coefficient estimates.
- ) Serial correlation causes OLS to no longer be the minimum variance estimator (of all the linear unbiased estimators).
- ) Serial correlation causes the OLS estimates of the SE(Bestiamted) to be biased, leading to unreliable hypothesis testing.
When we have pure serial correlation…
hypothesis testing becomes both biased and unreliable
What sort of bias does serial correlation tend to cause?
Typically, the bias in the estimate of SE(Best) is negative, meaning that OLS underestimates the size of the standard error of the coefficients
What will happen to hypothesis testing if OLS understimates the SE(Best) and therefore overestimates the t-scores?
The “too low) SE(Best) will cause a “too-high” t-score for a particular coefficient
The Durbin-Watsin d statistic is used to…
determine if there is first-order serial correlation in the error term of an equation by examining the residuals of a particular estimation of that equation.
It’s important to use the Durbin-Watson d statistic only when the assumptions that underlies its derivation are met…
- ) The regression model includes an intercept term.
- ) The serial correlation is first-order in nature.
- ) The regression model does not include a lagged dependent variable as an independent variable.
Serial correlation is first-order in nature when…
et = pet-1 + ut
where p is the autocorrelation coefficient and u is a classical (normally distributed) error term
With extreme positive correlation the Durbin-Watson d statistic for extreme positive correlation is…
d = 0
In what two respects is the Durbin-Watson d statistic unusual?
- ) Econometricians almost never test test the one-sided null hypothesis that there is . Its existence usually means that impure serial correlation has been caused by some error of specification.
- ) The Durbin-Watson test is sometimes inconclusive, because there is a third possibility called the inconclusive region
To test for positive serial correlation with the Durbin-Watson d test, the following steps are required.
- ) Obtain OLS residuals from the equation to be tested and calculate the d statistic
- ) Determine the sample size and the number of explanatory variables then consult Stat Tables B-4, B-5, or B-6 in Appendix B to find the upper critical d value, dU, and the lower critical d value, dI, respectively.
- ) relate to null hypothesis and decide whether to reject or fail to reject
The reordering of the data …
does not get rid of the serial correlation; it just makes the problem harder to detect
Generalized Least Squares (GLS) is …
a method of ridding an equation of pure first-order serial correlation and in the process restoring the minimum variance property to its estimation
GLS starts with
an equation that does not meet the Classical Assumptions (due in this case to the pure serial correlation in the error term) and transforms it inot one that does.
The detection of negative serial correlation is often a strong hint that…
the serial correlation is impure
The AR(1) method estimates…
a GLS equation by estimating B0, B1, and p simultaneously with iterative non linear regression techniques that are well beyond the scope of this chapter
The AR(1) method tends to …
produce the same coefficient estimates as Cochrane-Orcutt but with superior estimates of the standard errors, so we recommend the AR(1)
Generalized Least Squares have at least two problems…
- ) Even though serial correlation causes no bias in the estimats of the Best, the GLS estimates usually are different form the OLS ones.
- ) (More Important) It turns out that GLS works quite well if pest is close to the actual p, but the GLS ppest is biased in small samples
If pest is biased,
then the biased pest introduces bias into the GLS estiamtes of the Bests,
What is the remedy for serial correlation that avoids both of the problems of GLS?
New-West Standard Errors
Newey-West standard errors are…
SE(Best)s that take account of serial correlation without changing the Bs themselves in any way.
Newey-West standard errors can be used for
t-tests and other hypothesis tests in most samples without the errors of inference potentially caused by serial correlation
p is “rho” the..
autocorrelation coefficient
pure serial correlation in economics or business situations is almost always…
positive
The first step in ridding an equation of serial correlation is to ..
check for possible specification errors.
