FRM Part I · FRM Exam Part I · Nonstationary Time Series
A log price series is a random walk, so ln P_t = ln P_(t-1) + e_t. An analyst differences the log price series to obtain the series Δln P_t. Which description is correct?
It is the continuously compounded return and it is stationary. The difference of log prices equals the log of the price ratio, which for a random walk reduces to the white noise shock, so no unit root remains.
- AIt is the continuously compounded return and is stationaryCorrect
- BIt is the price level and is nonstationary
- CIt is the simple return and has a unit root
- DIt is a trend-stationary series with a deterministic trend
Explanation
The first difference of log prices equals ln(P_t/P_(t-1)), the continuously compounded return. For a random walk this equals e_t, which is white noise and therefore stationary. It is not the simple return, which is P_t/P_(t-1) − 1.
Did you get it right without looking?
One question tells you little. A timed set on Nonstationary Time Series shows your real accuracy, how long you take and where you lose marks.
More Nonstationary Time Series questions
- An analyst fits Y_t = 0.2 + Y_{t-1} + e_t, where e_t is white noise with variance 1.00 and Y_0 = 50. What are the expected value and varianc…
- A risk analyst models monthly retail sales of a department store, which spike every December. She wants to capture the seasonal pattern usin…
- An analyst models the log of a stock index as Y_t = Y_{t-1} + e_t, where e_t is white noise with variance 0.0004. Which statement correctly …
- An analyst models monthly returns of an equity index and suspects that the relationship between returns and a risk factor changed after a re…
- A series grows at a roughly constant percentage rate. An analyst estimates ln(y_t) = 2.0 + 0.03t. Which statement about the model is correct…
- An analyst fits an AR(1) model to monthly changes in a bond spread over 2005-2023 and suspects that the intercept and slope changed after a …