Test Questions & Answers Ch.13 | Time Series: Dealing With

Chapter 13

True or False Questions:

1. True or False: Time series data is data for many units at a given point in time.
2. True or False: In time series data, if errors are correlated over time, than B1hat is biased.
3. True or False: In autoregressive models, the dependent variable depends directly on the value of the dependent variable in the previous period.
4. True or False: One way to detect autocorrelation is to graph the residuals from a standard OLS model over time.
5. True or False: The interpretation of the coefficient in a dynamic model is the same as in a regular OLS model.
6. True or False: The interpretation of the coefficient in a  transformed model is the same as in a regular OLS model.

Multiple Choice Questions:

1. A stationary variable has:
   1. The same distribution over the entire time series.
   2. The same distribution over each unit.
   3. A different distribution over the entire time series.
   4. A different distribution over each unit.
2. Which of the following is the most serious problem that can arise when dealing with non-stationary data with a unit-root?
   1. The estimates for the variance of the coefficient are wrong.
   2. Regression could give us spurious results.
   3. Heteroscedastic errors
   4. A low R².
3. Which of the following is one way to detect autocorrelation?
   1. Estimate a standard OLS model and look at sign of coefficient.
   2. Graph the residuals over time.
   3. Estimate an auxiliary regression where the value of X is the dependent variable and the lagged value of X is the independent variable.
   4. Estimate an auxiliary regression where the value of e (the residual) is the dependent variable and the lagged value of X is the independent variable.
4. Which of the following is the correct final equation for a p transformed model?
   1. Y_t = B₀(1-) +B₁(X_t-X_t-1) + v_t
   2. Y_t- Y_t-1 = B₀(1-p) +B₁(X_t-X_t-1) + v_t
   3. Y_t-Y_t-1 = B₀ + B₁(X_t- X_t-1) + v_t
   4. Y_t-Y_t-1 = B₀(1-) + B₁X_t + v_t
5. Which of the following is a consequence of failing to use a -transformed model when errors are correlated?
   1. Produces biased coefficient estimates.
   2. Produces incorrect standard errors.
   3. Produces coefficient estimates that cannot be interpreted.
   4. Produces consistent coefficient estimates.
6. Which of the following is not a way in which dynamic models differ from OLS?
   1. Different interpretation of the coefficient.
   2. Correlated errors cause bias in dynamic models.
   3. Will have smaller standard errors than OLS.
   4. Coefficients can be biased if an irrelevant lagged variable is included.
7. Which of the following correctly states concerns about stationarity for the following model:

Y_t = Y_t-1 + ₀ + ₁X_t + _t

• 1. If , the model is stationary and spurious regression results are likely.
  2. If , the model will “blow up” as Y will get larger and larger in every period.
  3. If , the model will “blow up” as Y will get larger and larger in every period.
  4. If , the model is stationary and spurious regression results are likely.

1. We face the largest risk of getting a spurious result when:
   1. Regressing a variable with a unit root against a variable without a unit root.
   2. Regressing a variable with a unit root against a variable with a unit root.
   3. Regressing a variable with 
   4. When errors are autocorrelated.
2. One of the methods of dealing with non-stationary data is:
   1. Using a -transformed model.
   2. Using a dynamic model.
   3. Using a regular OLS model while keeping non-stationarity in mind.
   4. Using a differenced model.
3. Including a lagged dependent variable in an OLS model when autocorrelation exists will:
   1. Will lead to unbiased coefficients.
   2. Will lead to biased coefficients.
   3. Will lead to larger standard errors.
   4. Will lead to smaller standard errors.
4. Please describe the steps involved in diagnosing autocorrelation when using the graphical method.
5. Using equations, describe/show the steps needed to be undertaken in order to p-transform data.

1. Explain the three ways in which a dynamic model differs from a standard OLS model.

A) The interpretation of the coefficients in a dynamic model is not as simple as in an OLS model. In a dynamic model, if X goes up by 1 then Y1 will go up by 1, but Y2 will also go up, because Y2 depends on Y1.

B) Correlated errors will cause a lot more trouble in a dynamic model than in a non-dynamic (OLS) model. In dynamic models, correlated errors cause bias, while in a non-dynamic model, correlated errors will not cause bias but will simply mess up the estimates of the variance of ₁.

C) Including a lagged dependent variable when it is irrelevant (=0) can lead to biased estimates of the coefficient.

1. Describe how you interpret the coefficient results in a dynamic model.
2. Describe, using equations, how you would implement a Dickey-Fuller and an augmented Dickey-Fuller test in order to test for a unit root.

If we reject the null hypothesis that =0, we conclude that the data is stationary and we can therefore use non-transformed data. However, if we fail to reject the null hypothesis that =0, then we conclude that the data is non-stationary and we therefore should use a model with differenced data.