Term 2 lecture notes 1

Question 1

What is the difference between cross-sectional data and time series?

Answer 1

Time-series is collected on the same observation at multiple different points in time.

Question 2

What are the 3 features of time-series

Answer 2

-Trend
-Seasonal
-Cyclical

Question 3

What is the trend component and how would you show this graphically?

Answer 3

Increasing over time

time on x axis yt on y axis.

Question 4

What is a seasonal element in time series data?

Answer 4

associated with the seasons of the year there is a pettern
eg alchol consumption

Question 5

What is the cylical element of time series?

Answer 5

Repeat of upswings and downswings

If you plot the growth it will show a real cycle.

Question 6

What is the difference between interpreting time series coefficients and cross-sectional

Answer 6

Time series:
with no lags you can interpret it normally
However, with lags you must interpret it s

Question 7

What happens to the observations of x1t if there is a lag x1t-2

Answer 7

you have do move the observations two periods down.

Question 8

How do you interpret coefficients in the long run?

Answer 8

in long run x1t = x1t-1 = x1t-2 = x1*
yt=y*

then re write the equation in terms of long run variables

Then collect like terms

Then take deriviative of those collected like terms

Question 9

How do you interpret coefficients in a model with JUST lags of the independent variable (x)

Answer 9

The xt is interpreted as normal
xt-1 can be dellyt/xt-1
or yt+1 / xt

Question 10

How do you interpret coefficients when there is also a lag of independent variable on RHS

What happens after many periods?

Answer 10

There are two effects the direct and indirect coming through the dependent variable.

The first x1t is contamperaneous effect and is normal coefficient

To find the coefficient on xt-1 you need to roll the full model forward one period and then that will make the dependent variable yt then you sub in the derivative of the above into that.

After a certain amount of periods it only becomes the indirect effect.

Question 11

What is the total response at periods?

What is important to remember when looking at the total period effect?

Answer 11

At period 0 its just yt/xt
Over 1 it is yt+1/xt + yt/xt

ALWAYS REMEMBER THE 0 period effect.

Question 12

What happens when you try and use OLS model to estimate time series with lagged dependent variable on RHS?

Answer 12

the first CLRM cannot hold as
et conditional on yt is not equaled to 0
this is because if you increase epsilon t you increase yt

Question 13

If strict exogeneity does not hold in the time series case what should be done instead?

Answer 13

contemporeneous exogeneity

Question 14

What is the difference between contempraneous exogeneity and strict exogeneity?

What does time series do to this?

Answer 14

In contemporenoeus error term is unrelated to everything before that error term E(et | y1,y2,….yt-1) = 0
everything that has happened to date

In strict exogeneity error term is unrelated to everything

Time series means the second cannot hold.

Question 15

1.How do the CLRM have to change under time series with dependent variable with lag?

2.What further conditions are added as well?

Answer 15

1. no longer strict exogeneity but contemporaenous exogeneity E(et | all prior values of y) = 0
2. variance stays as sigma squared
3. cov(et,es | yt-1) = 0
4. still varies normally but not with mean 0! due to strict exogeneity

and all variables must be stationary Stationarity E(yt) = mew for all time

2. E(yt) = mew for all t
   V(yt) = sigma squared for all t
   Cov(yt,yt-1) = gamma h

Weak dependence
Cov( yt, yt-h) = gamma h tends to 0 as gamma gets bigger

Question 16

How would you see from a graph plot if something is stationary?

Answer 16

If the mean does not change and if the variance stays constant for all time

Question 17

What is the condition of weak dependence and why is it useful?

Answer 17

Cov(yt, yt-h) = gamma h as h gets bigger it tends to 0

Therefore you can brake it down into smaller blocks

therefore blocks of data sufficiently far apart are unrelated.

Question 18

In words what are the assumptions when estimating OLS of time series model with dependent variable?

Answer 18

-altered CLRM assumptions\
-Stationarity
-Weak dependency

Question 19

What does it mean if mean is stationary?

Answer 19

Over time it fluctuates around a constant mean

Question 20

What is the implication on OLS estimators when estimating time series model?

Answer 20

-Even though they are biased, as the sample size gets bigger due to weak dependency they are at least consistent.

E(b1) tends to beta 1 as T increases
Distribution of test statistic is no longer normally but N varies a (beta1, v(beta1)).

Hypothesis testing should not use f test but chi squared equivalent test

as obs is large f test becomes scaled chi squared.

Question 21

How do the statistical tests change in time series and what should be used in

Answer 21

tg = N(0/1) / sqroot x^2 g1 / g1
as g tends to inifitinty denominator becomes one so a normal (0,1) can be used instead of t test.

F k,g = x^2 k/k / x^2g / g. as g tends to infintiy f test becomes chi squared.