# 9.) Serial Correlation Flashcards

1
Q

Pure Serial Correlation

A

occurs when Classical Assumption IV, which assume uncorrelated observations of the error term, is violated in a correctly specified equation.

2
Q

If the expected value of the simple correlation coefficient between any two observations of the error term that are…

A

not equal to zero.

3
Q

The most commonly assumed kind of serial correlation is ….

A

first-order serial correlation, in which the current value of the error term is a function of the previous value of the error term.

4
Q

The first order autocorrelation coefficient (p) …

A

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

5
Q

The magnitude of p indicates…

A

the strength of the serial correlation in an equation.

6
Q

A p approaches one in absolute value..

A

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.

7
Q

The sighn of p indicates…

A

the nature of the serial correlation in an equation.

8
Q

A positive value for p implies…

A

that the error term tends to have the same sign from one time period to the next.

9
Q

Positive Serial Correlation indicates…

A

that the error term tends to have the same sign from one time period to the next.

10
Q

A negative value of p implies…

A

that the error term has a tendency to switch signs from negative to positive and back again in consecutive observations

11
Q

Negative Serial Correlation signals…

A

that there is some sort of cycle (like a pendulum) behind the drawings of the stochastic disturbances.

12
Q

By impure serial correlation the authors mean…

A

serial correlation is caused by a specification error such as an omitted variable or an incorrect functional form.

13
Q

Pure Serial Correlation is caused by…

A

the underlying distribution of the error term of the true specification of an equation

14
Q

Impure Serial Correlation is caused by…

A

a specification error that often can be corrected.

15
Q

An omitted variable can cause…

A

the error term to be serially correlated

16
Q

The proper remedy for serial correlation depends on …

A

whether the serial correlation is likely to be pure or impure

17
Q

the new error term e* will tend to be serially correlated when…

A
1. ) X2 itself is serially correlated (this is quite likely in a time series) and
2. ) the size of e is small compared to the size of B2Xbarred2
18
Q

An incorrect functional form is a common cause of…

A

the error term being serially correlated

19
Q

Using a linear functional form when a nonlinear one is appropriate will…

A

usually result in positive impure serial correlation

20
Q

What generally results in positive impure serial correlation?

A

Using a linear functional form when a nonlinear one is appropriate.

21
Q

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…

A
1. ) Pure serial correlation does not cause bias in the coefficient estimates.
2. ) Serial correlation causes OLS to no longer be the minimum variance estimator (of all the linear unbiased estimators).
3. ) Serial correlation causes the OLS estimates of the SE(Bestiamted) to be biased, leading to unreliable hypothesis testing.
22
Q

When we have pure serial correlation…

A

hypothesis testing becomes both biased and unreliable

23
Q

What sort of bias does serial correlation tend to cause?

A

Typically, the bias in the estimate of SE(Best) is negative, meaning that OLS underestimates the size of the standard error of the coefficients

24
Q

What will happen to hypothesis testing if OLS understimates the SE(Best) and therefore overestimates the t-scores?

A

The “too low) SE(Best) will cause a “too-high” t-score for a particular coefficient

25
Q

The Durbin-Watsin d statistic is used to…

A

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.

26
Q

It’s important to use the Durbin-Watson d statistic only when the assumptions that underlies its derivation are met…

A
1. ) The regression model includes an intercept term.
2. ) The serial correlation is first-order in nature.
3. ) The regression model does not include a lagged dependent variable as an independent variable.
27
Q

Serial correlation is first-order in nature when…

A

et = pet-1 + ut

where p is the autocorrelation coefficient and u is a classical (normally distributed) error term

28
Q

With extreme positive correlation the Durbin-Watson d statistic for extreme positive correlation is…

A

d = 0

29
Q

In what two respects is the Durbin-Watson d statistic unusual?

A
1. ) 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.
2. ) The Durbin-Watson test is sometimes inconclusive, because there is a third possibility called the inconclusive region
30
Q

To test for positive serial correlation with the Durbin-Watson d test, the following steps are required.

A
1. ) Obtain OLS residuals from the equation to be tested and calculate the d statistic
2. ) 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.
3. ) relate to null hypothesis and decide whether to reject or fail to reject
31
Q

The reordering of the data …

A

does not get rid of the serial correlation; it just makes the problem harder to detect

32
Q

Generalized Least Squares (GLS) is …

A

a method of ridding an equation of pure first-order serial correlation and in the process restoring the minimum variance property to its estimation

33
Q

GLS starts with

A

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.

34
Q

The detection of negative serial correlation is often a strong hint that…

A

the serial correlation is impure

35
Q

The AR(1) method estimates…

A

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

36
Q

The AR(1) method tends to …

A

produce the same coefficient estimates as Cochrane-Orcutt but with superior estimates of the standard errors, so we recommend the AR(1)

37
Q

Generalized Least Squares have at least two problems…

A
1. ) Even though serial correlation causes no bias in the estimats of the Best, the GLS estimates usually are different form the OLS ones.
2. ) (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
38
Q

If pest is biased,

A

then the biased pest introduces bias into the GLS estiamtes of the Bests,

39
Q

What is the remedy for serial correlation that avoids both of the problems of GLS?

A

New-West Standard Errors

40
Q

Newey-West standard errors are…

A

SE(Best)s that take account of serial correlation without changing the Bs themselves in any way.

41
Q

Newey-West standard errors can be used for

A

t-tests and other hypothesis tests in most samples without the errors of inference potentially caused by serial correlation

42
Q

p is “rho” the..

A

autocorrelation coefficient

43
Q

pure serial correlation in economics or business situations is almost always…

A

positive

44
Q

The first step in ridding an equation of serial correlation is to ..

A

check for possible specification errors.