ECON-3342

if the Ljung-Box test for a particular time series is Q3 = 22.676, and the critical value in the chi-square distribution at the 5% significance level is 7.81, this is evidence that

Statistically, we conclude that at least one of the Autocorrelation Coefficients (rho1, rho2 or rho3) are different from zero

The Dow Jones index (for the period discussed in the videos) is a time series that is non-stationary

True

The model given by Y = b0 + b1*(1/X) + u is linear in parameters

True

Under certain assumptions, the OLS estimators are BLUE. What does the U stand for in BLUE?

Unbiasedness

"If a variable X Granger-causes a variable Y, this means that"

X and its lags helps predict Y

Consider the estimation of the model Y[t] = c + phi*Y[t-1] + e[t] + theta1*e[t-1] + theta2*e[t-2] , where Y[t] represents the value of some variable at time t, Y[t-1] is the value of Y at time [t-1], e[t] is a white noise innovation at time t, and the parameters are {c, phi, theta1, theta2}. When specifying the estimating equation in Eviews you would specify

Y c ar(1) ma(1) ma(2)

"A researcher estimates an AR(1) model for the time series of some variable Y. The one-period ahead forecast (when using the conditional mean) for the relevant variable yields a value of 5.2. The variance of the forecasting error is estimated to be 2.25. With this information, the 95% confidence interval for the forecast is given by the interval"

[2.26, 8.14]

"A model is given by: Y = b0 +b1* trend + b2*(trend^2) , where b0, b1 and b2 are constants and ""t"" is trend, this is an example of "

a quadratic trend model

One of the most pieces of information with a VAR is whether each estimated coefficient for the lags are statistically significant (t-tests)

false

The optimal forecast of any symmetric loss function is the conditional mean

false

optimal forecasts are always unbiased

false

According to the Wold Theorem, any covariance stationary process

has a unique representation which is the sum of a deterministic component and an infinite MA term

An I(1) process is one that

has a unit root

"A researcher is choosing between 4 models, and is using a fixed forecast environment in order to make a decision. The models have the following summary statistics in the following order (Model #, MSE, MAE, MAPE): (Model1, 4.23, 1.58, 80.6); (Model2, 5.26, 1.70, 70.9); (Model3, 5.30, 1.87, 125.2); (Model4, 3.92, 1.623, 65.2). If the forecaster has a loss function that is the ABSOLUTE VALUE LOSS FUNCTION, then most preferred model is"

idk but not model 4

"For an MA(1) process and under quadratic loss function, the 2-step periods ahead forecast of a time series is the unconditional mean of the process"

true

"Given a typical linex loss function L( e ) = exp(a*e) +a*e - 1 where a is a parameter different from zero, then the optimal forecast is biased"

true

"If a model is trend-stationary, one can apply the ARMA methodology to a time series once a deterministic trend is removed"

true

"If the model is well-specified, the residuals in the estimation process should resemble a white noise"

true

"In a VAR system, all equations have exactly the same regressors"

true

"In a VAR, each equation is estimated with Ordinary Least Squares"

true

"The correlogram of an AR(1) process has typically only one significant spike for the partial autocorrelation coefficient (PAC) of order one , and the rest are not significant"

true

"The model Y = b0 + b1*trend + error, where b0 and b1 are constants, Y refers to some time series at time t. This model is classified as a linear trend model"

true

"The model Y[t] = b0 + b1*trend + b2*Y[t-1] + e[t], where e[t] is a white noise innovation is an example of a trend-stationary model"

true

"The typical correlogram of a random walk without drift has a very high spike in the PAC of order 1, and a AC function that slowly dies out after many periods"

true

A cycle is a time series pattern of periodic fluctuations (see section 7.1 in textbook)

true

A necessary and sufficient condition for an AR(1) model to be covariance stationary is that the persistence parameter (greek letter phi in our notes) is less than 1 in absolute value

true

A process is strongly stationary if all of the random variables in the stochastic process have the same pdf

true

MA processes are always stationary

true

The Mean Squared Error (MSE) is computed as the Sum of Squared Errors of Prediction divided by the number of observations in the prediction sample

true

The Schwarz information criterion (SIC) typically selects more parsimonious models than the Akaike information criterion (AIC).

true

The uncertainty of a forecast of a Random Walk model increases with time

true

There are no Moving Average Terms in a VAR

true

When a lag operator is applied to a random variable, this operation returns the random variable of the previous period

true

Consider the following data collection {100, 102, 104, 106, 105, 108} where the first element (100) is the value of some random variable in year 2015, then 102 is the value of the random variable in year 2016 and so on. If one were to construct differences, the new series corresponds to

{NA,2,2,2,-1,3}

The marginal probability distribution of a variable is always equal to the conditional probability distribution of the same variable

False

If the R-squared is 0, we would typically say that the explanatory variable doesn't explain the variation in the dependent variable

True

In the model Y = b0+b1*X + u, when b1 is positive implies that higher levels of X are associated with higher levels of Y

True

A particular random variable follows a process given by Y[t] = 1 + 0.4*E[t-1] + E[t] , where E[t] is a Gaussian White Noise innovation with mean 0 and variance of 1 (This process is not estimated, but rather we know the true data generating process as described here). Theoretically, the first order autocorrelation coefficient is approximately

0

"In an estimated VAR model of 2 variables, the impulse response function"

Shows the persistence and magnitude of a single shock

A particular random variable follows a process given by Y[t] = 1 + 0.4*E[t-1] + E[t] , where E[t] is a Gaussian White Noise innovation with mean 0 and variance of 1 (This process is not estimated, but rather we know the true data generating process as described here). Theoretically, the second order autocorrelation coefficient is

0.345

Two of the roots in an estimated ARMA process include -.01 -.65i and -.01 + .65i. The modulus of this root is

0.4226

"In a given regression model, the TOTAL SUM OF SQUARES (SST) is 800, and the SUM OF SQUARED OF ERRORS (SSError) is 200. Then the R-squared of this model is "

0.75

"If two random variables are independent, then their covariance is 0"

True

"When the correlation coefficient between 2 variables is close to 0, it means that the linear association between the 2 variables is weak"

True

"If Cov(X,Y)>0, then the correlation coefficient between X and Y is 1"

False

A white noise process is characterized by a high degree of time dependence

False

The correlation coefficient can never be negative

False

"A random variable X has the following probability distribution. X can take the values of {1,2,3,4}, each of them with equal probability. The Variance of X is "

1.25

The process Y[t] = 1.5 + 0.5*E[t-1] + E[t] , where E[t] is a Gaussian White Noise innovation with mean 0 and variance of 2. The unconditional mean of this process is

1.5

[Consult a table with the t-Distribution] You estimate a regression model Y = b0 + b1*X + u by using 40,000 observations. For the null hypothesis that b1 = 0 (and the alternative hypothesis that b1 is different from 0), the critical value of the t-statistic at the 5% significance level is

1.96

"Assume that the annual returns of a stock are either 1) 50% with probability of 0.25, and 2) 10% with probability of 0.75. The STANDARD DEVIATION OF THIS RETURN is"

17.32%

Consider the following data collection {100, 102, 104, 106, 105, 108} where the first element (100) is the value of some random variable in year 2015, then 102 is the value of the random variable in year 2016 and so on. The growth rate between 2015 and 2016 of this random variable was (in %)

2

"A random variable X has the following probability distribution. X can take the values of {1,2,3,4}, each of them with equal probability. The expected value of X is"

2.5

"Assume that the annual returns of a stock are either (1) 50% with probability of 0.25, or (2) 10% with probability of 0.75. The expected return of this stock is "

20%

"X and Y are two random variables. The values that they can take are the following. If X=0, then Y=0. If X=1, then Y=0. And when X=2, then Y=9. Each of these 3 points are equally likely ( Prob = 1/3). The covariance between X and Y is"

3

If a parameter is estimated to be 3.15, and the standard deviation of this estimated parameter is 1.05, then the t-statistic for this estimated parameter is

3

"You estimate the model Y = -12.28 + 2.79*X, where Y is wage per hour in US dollars and X is years of schooling (e.g. X = 10 means 10 years of schooling). According to this regression, a person with 18 years of schooling has a PREDICTED wage per hour of

37.94

"Assume that you are interested in estimating a VAR(1) for equations X and Y. Ignoring the intercepts, how many coefficients need to be estimated in this system?"

4

Consider the following estimated model, which uses Eviews notation (lagged values appear for example as Y(-1) and so on ): Y = 2 + 0.5*Y(-1) . The unconditional mean of such process is estimated to be

4

"Consider the following estimated model, which uses Eviews notation (lagged values appear for example as Y(-1) and so on ): Y = 2 + 0.5*Y(-1) . Assume that the current value of Y is 4.2. The one period ahead forecast for Y (assuming we want to use the conditional mean) is"

4.1

"In practice, the number of lags p selected for a VAR(p) system, is typically determined by"

AIC or SIC

"Using the notation as in Eviews [lagged values appear for example as Y(-1) and so on ], the estimated model given by Y = 1.2 + 0.35*Y(-1) + 0.2*Y(-2) is which type of model?"

AR(2)

"You estimate the model Y[t] = 1.5 + 0.5Y(t-1) + e[t] + 0.25e(t-1) - .01e(t-2), where Y(t) represents the value of some variable at time t, and e(t) represents a white noise innovation at time t. This type of model is a "

ARMA(1, 2)

"The relationship between Fahrenheit (F) and Celsius ( C ) degrees is given by the relationship C = (F - 32) * 5/9 . If we had exact data of the temperatures in any given city measured both in F and C degrees, a regression of Celsius on Fahrenheit degrees would yield"

An R-squared of 1

Consider the model Y = b0 + b1*X + u. One can to rewrite the OLS estimator for b1 is given by

Cov(X,Y) / Var(X)

The process Y[t] = 1 + E[t] + 0.7*E[t-1] + 0.1*E[t-2] , where E[t] is a Gaussian White Noise innovation at time [t] with mean 0. This process is an example of an

MA(2) process

"Assume that you have estimated 2 different models which have good properties with respect to other metrics. Model (1) has a SIC (Schwarz information criterion) of 4.69 and an Akaike information criterion (AIC) of 4.58 , while model (2) has a SIC of 4.76 and an AIC of 4.61. Which of the following is correct?"

according to both information criteria, model 1 is preferred to model 2

Which of the following things about an MA(1) process are correct (choose only 1)

all but the first autocorrelation are 0

"In the regression model lnY=b0+b1*lnX+u , the coefficient b1 is interpreted as

an elasticity

"You use quarterly data in order to estimate a model JOBS = 27700 + 386*trend + error, where JOBS represents thousands of US Non-farm employment (e.g. if JOBS = 100,000, it really represents 100 million of jobs). The coefficient multiplying the trend (386) represents"

an increase of 386,000 jobs per quarter in the US

"A researcher estimates the model Y[t] = b0 + b1 * trend + error[t], where Y[t] refers to a variable at time t in years, and b0 and b1 are constants. Using this model, the 2 - period ahead conditional mean forecast for Y[t+2] is given by (Hint: today is year t, you are forecasting Y for 2 years into the future)."

b0 + b1*(trend + 2)

You estimate the following equation in Eviews. Y = c(1) + c(2)*Y(-1) + c(3)*Y(-2). The coefficient that represents the partial autocorrelation coefficient of order 2 (k=2) is

c(3)

"You estimate the model Y = -12.28 + 2.79*X, where Y is wage per hour in US dollars and X is years of schooling (e.g. X = 10 means 10 years of schooling). The coefficient in schooling says that

each extra year of schooling is associated with an increase in wage per hour by $2.79 dollars

"For an AR(2) process that is covariance stationary, shocks will"

eventually die away

"A Random Walk with drift is first-order stationary, but not covariance-stationary"

false

"In a VAR, each extra lag requires many more coefficients to estimate. For example, if the VAR has 2 variables, an extra lag adds 8 parameters"

false

"In a model that has a stochastic trend, the shocks are ""temporary"""

false

"When estimating an ARMA model, covariance - stationary is obtained if all the autocorrelation coefficients in the ACF are less than or equal to 1 in absolute value"

false

A process {Yt} is said to be first order weakly stationary if and only if the autocovariances do not depend on time

false

A statistical test yields a p-value of .0001, then at the 5% level of significance you CANNOT reject the null hypothesis

false

Deterministic trend models always have linear trends

false

"A researcher is choosing between 4 models, and is using a fixed forecast environment in order to make a decision. The models have the following summary statistics in the following order (Model #, MSE, MAE, MAPE): (Model1, 4.23, 1.58,80.6); (Model2, 5.26, 1.70, 70.9); (Model3, 5.30, 1.87, 125.2); (Model4, 3.92, 1.623, 65.2). If the forecaster has a loss function that is QUADRATIC, then most preferred model is"

model 4

Assume that the loss function is quadratic. There are 4 competing models that a researcher is considering. Which model would the researcher choose (each MSE refers to a particular model)

model w MSE = 12.96 model w MSE = 14.28 model w MSE = 19.21 * model w MSE = 7.28 *

Of the 7 assumptions studied on linear regression, which one that is not required for the Gauss-Markov Theorem to hold?

normality of error

The most common loss function used by forecasters is

quadratic

Under the Dickey Fuller family of tests (choose the appropriate answer)

rejecting the null hypothesis represents statistical evidence that the time series DOES NOT contain a unit root

A collection of random variables indexed by time is a

stochastic process

"Assume you estimate the model Y = b0 + b1*trend , where b0 and b1 are constants, Y refers to annual GDP in billions of dollars. The interpretation of the coefficient b1 is"

the average billions of dollars that GDP changes each year

"An ARIMA(2,1,2) is a model such that"

the dependent variable is differenced and the resulting (differenced) series is estimated with an ARMA(2, 2) model

"If the researcher has a quadratic loss function, the metric that the researcher could use in order to judge forecasts is"

the mean squared error (MSE)

Which of the following is True

the optimal forecast is the forecast that minimizes the expected loss

Optimal linear combination of forecasts are obtained when

the researcher takes an average of the forecasts of each model considered

A collection of observations ordered by time is a

time series

"A Random Walk and a Random Walk with drift are also called ""difference stationary"" models"

true

"A process that contains a stochastic trend is called a ""unit-root"" process"

true

"An estimated MA(4) had the following roots: .41+.71i, .41 - .71i , -.59 -.58i , -.59 + .58i. This model is covariance stationary"

true

"Assume that the true data generating process of a variable is given by a linear trend model Y = b0 + b1*trend + error. In such environment, the uncertainty associated to the 1-period ahead forecast is the same as the uncertainty associated to the 5-year forecast "

true