Term 2 lecture notes serial correlation Flashcards
What is the effect of serial correlation of error term on CLRM assumptions in a model yt = bo +b1X1+ut
error term is serially correlated so ut-j can predict ut
(Has no impact on unbiasedness if there is no lag of dependent variable)
(Variance is wrong as it is normal CLRM variance + something)
So standard errors are wrong
You do not get correct standard errors of coefficients
How do you solve for the variance issues that arises from time serial correlation in error term but no lagged dependent variable.
What is formula?
To get correct se of coefficients you need newey west or transformation
HACSE , Newey West standard errors.
Normal CLRM variance equation + [1 +2gamma sum of (n-j/n) pj
where n is highest order of serial correlation
What is the implication on CLRM of a time series model with a lagged dependent variable and a serially correlated error term?
How do you solve this issue?
What could be the issue with this?
-You use a generalised least squares method which then leads to at least to consistent estimates with correct se.
-you might need to find the type of serial correlation in the error term
What is the Breusch-Godfrey test for serial correlation?
How do you calculate the F statistic?
What is an important caveat from this test?
yt = β0 + β1x1t + β2x2t + . . . + βkxkt + ut
ut = ut = δ0 + δ1ut−1 + . . . + δput−p + ξt
ξt = a well behaved error term
so et is used
H0: that all deltas are equaled to 0 corresponds to CLRM assumption of no serial
H1: then at least one delta is not equal to 0
The f test CV is F p, T-p -(k+1)
The f test = RSSr - RSSu / p / RSSu / T-p - (k+1)
- you must include the explanatory variables in the in the residuals regression to correct for DOF
How do you know what to set p to when you are testing for serial correlation?
If you have annual data 1 or 2
If you have quarterly 4 and 5
If you have monthly data 12 or 13
or look at ACF and PACF and see what order the serial correlation is of
What are the types of test for serial correlation?
Breusch-pagan test
Durbin-watson test
How do you do the Durbin Watson test?
Null is that there is no autocorellation
H0: p = 0 / phi = 0
Test statistic = 2(1-p)
Then draw out a continium going from 0 to 4 with 2 being H0 in the middle to the left of H0 write du and to the left of that dl
Then to the right of 2 is 4-du and then 4-dl to the right of that.
If the test statistic is in one of the extreme regions bounded by the ends reject H0
if it is in the regions between 0 and the du’s then do not reject H0
Anything else is inconclusive
What are the different scenarios in the test statistic of the Durbin Watson test
DW = 2(1-p)
No serial correlation DW = 2
Positive serial correlation DW<2
Perfect positive serial correlation DW = 0
Negative serial correlation DW >2
Perfect negative serial correlation DW>4
What is the difference between Breusch-godfrey and durbin watson test?
What can be done instead of DW test?
Durbin Watson test cannot be used for models with yt-1 as it is biased towards less than 2
Durbin H test can be done
Phi hat times by square root of T/1-Tsbk
which is the variance of the coefficient on the lagged depdendent variable
This is normally distributed so you can compare it to standard normal
What are all the types of tests for serial correlation?
Breusch godfrey the most powerful as it can be done irrespective of lags.
DW cannot be done with lags and has inconclusive
DW H test
