Professor Mumford
Econ 360  Fall 2010
[email protected]
Problem Set 11 Answers
(Advanced Topics: Time Series and Panel Data)
True/False
(15 points)
1.
FALSE
The DickeyFuller test can be used to determine if there is evidence that the
speciﬁed time series is
highly
persistent
(also called a unit root)
.
2.
TRUE
Regressing a highly persistent time series on another highly persistent time
series produce spurious results.
3.
TRUE
Fixedeﬀects estimation can be used to estimate causal eﬀects if the unobserved
factors that are correlated with the dependent variable of interest are time invariant.
4.
TRUE
The validity of diﬀerencesindiﬀerences estimation depends on the assumption
that preexisting trends in the treated and control groups are similar.
5.
FALSE
With panel data, estimation in ﬁrst diﬀerences and ﬁxedeﬀects estimation
are
not
computationally identical
except when there are only two time periods
.
1
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View Full DocumentLong Answer Questions
(84 points)
6.
NYSE Index
(a) In a regression of trade volume on day of the week indicators we ﬁnd that Monday
has the lowest trade volume on average and Thursday has the highest trade volume
on average. However, an Ftest of the join signiﬁcance of the day of the week
dummies produces a pvalue of 0.1880 which is not statistically signiﬁcant. So,
while there seems to be some evidence that the day of the week aﬀects volume, it
is not strong evidence.
(b) There is no evidence that the day of the week has any eﬀect on the closing price.
The pvalue from the Ftest is 0.9974. We probably don’t ﬁnd a relationship
because if it were true that the price tended to increase on a certain day of
the week, people would try to buy it the day before, which would drive up the
price then instead. Eﬃcient markets should not exhibit any predictable patterns
because if they did they would be exploited.
(c) Yes. In a regression of the adjusted close on the lagged value of adjusted close
we get an estimate for
ρ
of 0.9967 which is very close to one. The DickeyFuller
test gives a test statistic of 1.571 which gives a pvalue of 0.4979. This means we
cannot reject the null hypothesis that the series is a highly persistent series.
(d) No. In a regression of the volume on the lagged value of volume we get an estimate
for
ρ
of 0.7614 which is not very close to one. The DickeyFuller test gives a test
statistic of 14.208 which gives a pvalue of 0.000. This means we can reject
the null hypothesis that the series is highly persistent and we conclude that it is
simply a weaklypersistent or autocorrelated series.
(e) The regression of closing price on trading volume gives a coeﬃcient estimate of
0.0305894 which seems to indicate that on days where there is a lot of trading,
the price tends to drop. We may be concerned because closing price is a highly
persistent series. However, even in the ﬁrstdiﬀerences regression we still ﬁnd a
statistically signiﬁcant (at the 10 percent level) relationship, although it is much
weaker.
(f) No. In a regression of the rate of return on the lagged value of the rate of return
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 Spring '10
 NA
 Statistics, Statistical hypothesis testing

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