Topic 12: Time Series Analysis

Question 1

What test do you use to test if a series is highly persistent?

Answer 1

The Dickey-Fuller Test

Question 2

How do you run a Dickey-Fuller test?

Answer 2

Make sure the regression is set for time series with tsset time, then use the command “dfuller varname” for the variable of interest. The null hypothesis is unit root, so small p values reject unit root.

Question 3

What does it mean to say a series has a unit root?

Answer 3

When a time series rho value is close to or equal to 1, a highly persistent series. yt = py(t-1) + et. Can cause spurious regression problems. Not much change from year to year.

Question 4

What does it mean to say a series is highly persistent?

Answer 4

It means that distant-future outcomes are highly correlated with current outcomes in the time series.

Question 5

What is serial correlation?

Answer 5

Also called auto-correlation, when a time series or panel data model has correlation between errors in different time periods.

Question 6

What is a spurious regression problem?

Answer 6

Occurs when two series when regressing two unit root series. A high persistence in the regression is picked up and spuriously strongly statistically significant, but not actually from the data, from the persistence.

Question 7

What is a consequence of serially correlated errors?

Answer 7

Inconsistent standard errors. As long as there is a zero conditional mean, the estimates are unbiased.

Question 8

What is the null hypothesis of the Dickey-Fuller test?

Answer 8

Unit root

Question 9

What kind of estimation would you do to correct for serial correlation in a time series regression model?

Answer 9

The Cochrane-Orcutt/Prais-Winsten estimation process to correct the standard errors.

Question 10

Stata: How to run a Cochran-Orcutt process?

Answer 10

Set the regression to run a time series “tsset time, year”, run a regression, predict the residuals, reg uhat l.uhat, the L1 value indicates how much correlation. Gen new x and y variables: gen newy=(y - L1*l.y), then reg newy newx. Is it statistically significant? Do it again if not.

Question 11

What is long run propensity?

Answer 11

In a distributed lag model, it is the overall change in y given a permanent one unit increase in x, as given by the sum of all the coefficients current and lagged.

Question 12

Does serial correlation cause bias and inconsistency in the OLS estimates?

Answer 12

No, it causes inconsistency in the standard errors and variances though.

Question 13

What will regressing a highly persistent time series on another cause?

Answer 13

Spurious results.

Question 14

How can you make a highly persistent time series weakly dependent?

Answer 14

By using first differencing.

Question 15

What is first differencing?

Answer 15

A transformation done on time series by taking the difference of two adjacent time periods, earlier from the later.

Question 16

Does using first differencing change how you interpret the variable of interest?

Answer 16

No.

Question 17

Stata: How do you run a regression on models with differences and lags of -1 or more?

Answer 17

Use the “reg” command then “d.” before the variable, if using lags use “l.”, “l2.”, “l3.” and so on for more lags. For both use “d.l.”

Question 18

When using several lagged variables, what is the interpretation for when only one lag is statistically significant?

Answer 18

For every one unit increase in x, there is a L increase in y, holding other factors constant.

Question 19

What makes time series estimation different from the previous estimation of cross sectional data?

Answer 19

The order of the entries matter, thus violating the random variable assumption.

Question 20

Can you run a regular regression on time series data?

Answer 20

No, use the command “tsset var, year”

Question 21

When would we use a finite distributed lag model?

Answer 21

When we want to see if the timing of x affects y, is it immediate or does it take time?

Question 22

What is impact propensity?

Answer 22

In a distributed lag model, the immediate change in y given a one unit increase in x.

Question 23

What is seasonality?

Answer 23

Seasonality refers to a time series showing changes that have to do with the time of year, affected by things like holidays and weather.

Question 24

How can we test for seasonality?

Answer 24

By including seasonal dummy variables and then performing a joint f-test for their significance. Can be done similarly for days of the week, month, etc.

Question 25

What is random walk?

Answer 25

A value equal to last year’s value plus some noise (no rho) yt = y(t-1) + et

Question 26

What is drift?

Answer 26

Trending up or down, with random walk drift is a: yt = a + y(t-1) + et

Question 27

How do you test for a highly persistent series without a drift (alpha) term?

Answer 27

Use the command “, noconst” with either your lagged regression or dfuller command, if the graph looks like it has up or down trend.

Question 28

How to test for serial correlation?

Answer 28

Run the regression, save residuals, regress uhat on l.uhat if close to = no problem, not equal to 0, serial correlation, =0 unit root.