Table of Contents
CFA Level 2 – Quantitative Analysis, Session 3 – Reading 13, Time-Series Analysis – LOS k
(Practice Questions, Sample Questions)
1. Which of the following statements regarding unit roots in a time series is least accurate?
A) A time series that is a random walk has a unit root.
B) Even if a time series has a unit root, the predictions from the estimated model are valid.
C) A time series with a unit root is not covariance stationary.
<Explanation> The presence of a unit root means that the least squares regression procedure that we have been using to estimate an AR(1) model cannot be used without transforming the data first.
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A time series with a unit root will follow a random walk process. Since a time series that follows a random walk is not covariance stationary, modeling such a time series in an AR model can lead to incorrect statistical conclusions, and decisions made on the basis of these conclusions may be wrong. Unit roots are most likely to occur in time series that trend over time or have a seasonal element.
2. Marvin Greene is interested in modeling the sales of the retail industry. He collected data on aggregate sales and found the following:
Salest = 0.345 + 1.0 Salest-1
The standard error of the slope coefficient is 0.15, and the number of observations is 60. Given a level of significance of 5%, which of the following can we NOT conclude about this model?
A) The model is covariance stationary.
B) The model has a unit root.
C) The slope on lagged sales is not significantly different from one
<Explanation> The test of whether the slope is different from one indicates failure to reject the null H0: b1=1 (t-critical with df = 58 is approximately 2.000, t-calculated = (1.0 – 1.0)/0.15 = 0.0). This is a 2-tailed test and we cannot reject the null since 0.0 is not greater than 2.000. This model is nonstationary because the 1.0 coefficient on Salest-1 is a unit root. Any time series that has a unit root is not covariance stationary which can be corrected through the first-differencing process
3. An AR(1) autoregressive time series model:
A) cannot be used to test for a unit root.
B) can be used to test for a unit root, which exists if the slope coefficient equals one.
C) can be used to test for a unit root, which exists if the slope coefficient is less than one
<Explanation> If you estimate the following model xt = b0 + b1 × xt-1 + et and get b1 = 1, then the process has a unit root and is nonstationary
