Slide coverage

Question 1

there is a CLRM assumption that can replace two others. elaborate

Answer 1

E[u_t | X_t] = 0

This can replace E[u_t]=0 AND cov(x_t, u_t)=0

Question 2

how to ensure that assumption 1 holds

Answer 2

Include a constant term

Question 3

what is endogeneity? relate to exogeneity

Answer 3

Exogeneity refers to the assumption that exogeneuous variables are not correlated with the error terms. In other words,: E[u | X] = 0

Endogeneity is a condition where exogenity is violated.

Question 4

why would endogeneity be present?

Answer 4

This is the same as asking for reasons why the explanatory variables and error terms might be correlated.

If we are missing an important variable, both the constant term and the explanatory variables can try to explain this movement without actually being related. Unless if completely uncorrelated. in that case, only the constant will be affected.

Measurement error is also a source.

Question 5

Endogeneity is present. What do we do?

Answer 5

The obvious one is to account for missing variables.

if we have panel data, this can help leverage common effects.

IV estimation.

Heckman Correction

Question 6

elaborate on instrumental variables

Answer 6

This is a method for endogeneity.

First we split the X into two parts.
1) the variables not correlated with error term
2) the varibles that are correlated with the error term

Then we extract the part of X that is NOT correlated. We use this to get a consistent estimate of the variation in Y.

We want to use instrumental variables. These are correlated with the endogenuous variables of X, but not the error terms.

We find some other variable, call it Z. we want this to be correlated with the endogenuous variables, but not the error terms.
We would have used this Z directly, but we want to understand the effect that X (endo) has on Y. This is why we go to greater lengths to include it.

We use Z in a spearate regression that will predict values for the endogenuous variable(s). these are then used.

This is referred to as two-stage as well. first regress on the IV, then regress on the real shit.

It is worth noting that good IV’s are usually difficult to find.

Question 7

elaborate on the possible forecasting methods

Answer 7

We have 3)
1) Scaled
2) Iterative
3) Direct

Direct skips directly tpo the forecasting horizon, but iterative goes point by point. This leads to different results.

Scaled predicts 1 step ahead and then scales it with the number of steps we actually want. Does not perform well.

Question 8

what is realized volatility?

Answer 8

Realized volatility entails getting a on-the-spot measure of the volatility by utilizing high frequency returns like 5min intervasl, compute the corresponding volatility and scale to daily. This gives us a daily volatility estimate that represent the current level sort of .

Question 9

what is MIDAS

Answer 9

Mixed Data Sampling

Question 10

what does MIDAS do

Answer 10

it is a regression technique that allows for data sampled at different frequencies to be used in the same model.

Specifically, we sample the depdnent variable at a lower frequency than the independent ones.

Question 11

the price at which electricity is sold is determined by the ?

Answer 11

merit order principle

In europe, it is day ahead markets

Question 12

what is merit order?

Answer 12

a way of ordering available sources of energy.

These are ordered from lowest to highest marginal cost to determine which ones should be produced first to supply a given demand at minimum cost for the system.w

Question 13

give the merit order ordering

Answer 13

solar, wind, nuclear, water, some sort of burning, coal, oil

Question 14

why water not at 0?

Answer 14

Because it is really bad if we exhaust the resource

Question 15

does solar actors and offshore wind actors earn the same?

Answer 15

No, because hte produce electricity at different times of the day. Wind ismostly at night. solar mostly at day. there is also different demand at these times which result in differnet clearing price.

Question 16

elaborate on interpretation of the constant term

Answer 16

we need to be careful with this. It is very common that the constant intercept the y-axis at a point where we basically have no data points. In these chases, it doesnt really makes much sense to interepret any base level.

Question 17

what can we do if we weant to test relationships that are more intricate?

Answer 17

We need to use testng under maximum likelihood.

this includes the 3 boys:
1) Wald
2) LR
3) LM

Question 18

what is the basis for which the ML testing works?

Answer 18

checking if the likelihood value drops when we enforce a restriction

Question 19

what can we do about heteroskedasticity?

Answer 19

If we happen to know the shape, we can do somethin

Question 20

say the hteroskedasticity depends on: var(u_t) = sigma^2 z_t^2

What can we do?

Answer 20

divide the entire regression on z_t^2. this gives us error terms that are constant in variance.

Question 21

elaborate on Durbin Watson

Answer 21

Tests a single lag for autocorrelation.

DW =ish 2(1-p^pred)

Since correlation is between -1 and 1, DW is between 0 and 4.

Values close to 2 represent no correlation.

There are also cirtical values that we need to find, and these will be somewhere between 0 and 2 and between 2 and 4.
There are actually 2 sets of critical values: lower and upper.
We need to be beyond the lower to say that there is autocorrelation

Question 22

what is the error-in-variables problem?

Answer 22

Measurement error in the explanatory variables. this is a serious problem and will cause violation of assumption.

Question 23

what is 2SLS?

Answer 23

two stage least squares.

Refers to first running a regression to predict some endogenuous variable by using some instrumental variable. Then when this is done, we replace the endogenuous, and run a new actual regression.

Question 24

elaborate on Heckman correction

Answer 24

Heckman correction is a technique used in regards to fixing sample bias. It works best when there is a systematic sample bias.

Question 25

what are the stylized facts of financial returns we are working with

Answer 25

1) Nonstationary prices (random walk), stationarity of returns 2) Absence of autocorreltion of returns 3) Autocorrelation in squared returns 4) volatility clustering large returns tend to be followed by large returns and vice versa 5) Fat tailed distribution of returns, kurtusis of larger than 3, (leptokurtosis) 6) Leverage effects, negtive returns tend to increase volatility more than positive returns

Question 26

what specifically are the principal components?

Answer 26

The eigenvectors of the covariance matrix

Question 27

what do principal components represent?

Answer 27

axes along which the data has the most variance

Question 28

how to rank the principal components?

Answer 28

We use their eigenvalues. Largest = largest/first principal component

Question 29

how can we reduce our data but keep say 95% of the variance?

Answer 29

∑lambda_i [i=1, k] / ∑lambda_i [i=1, p] >= 0.95 Here, lambda_i is the eigenvalue of PC i. we assume that the components are ordered.

Question 30

how do we find the covariance matrix that is used for the eigenvalue-vector probkem?

Answer 30

find coviarnace using sample covariance, then center it.

Question 31

after computing the eigenvectors and values ,then wehat?

Answer 31

we project the data we have onto the new axes that we have chosen. if we have a data vector X, we perform: Z_k = X^T v_k where v_k is the k'th principal component vector. More typically, we have a data matrix X and multiply it by the PCA matrix that consist of column stacked eigenvectors. The number of columns of the data matrix will always match the number of rows in the eigenvector matrix, so the matrix product is well defined. The outcome Z_k is a new matrix that has projected the data onto the new axes.

Question 32

how to determine how much variance is caputed by a component?

Answer 32

we use lambda_i, the eigenvalue, and divide on the sum of all eigenvalues. this is the ratio of explained variance.