FRM Part I · FRM Exam Part I · Stationary Time Series
A weak white noise process has variance σ² = 4. What is the autocovariance at lag 3, and the autocorrelation at lag 3?
Both are zero. White noise has no serial dependence, so the lag-3 autocovariance is 0, and the autocorrelation is 0 divided by the variance of 4, which is 0.
- AAutocovariance 4, autocorrelation 1
- BAutocovariance 0, autocorrelation 0Correct
- CAutocovariance 0, autocorrelation 4
- DAutocovariance 4, autocorrelation 0
Explanation
White noise has zero autocovariance at every non-zero lag, so γ(3)=0. The autocorrelation is γ(3)/γ(0)=0/4=0. The option with autocovariance 4 confuses lag 3 with lag 0.
Did you get it right without looking?
One question tells you little. A timed set on Stationary Time Series shows your real accuracy, how long you take and where you lose marks.
More Stationary Time Series questions
- Which statement correctly describes the sample autocorrelation function (ACF) and partial autocorrelation function (PACF) pattern expected f…
- A monthly series follows the seasonal AR model Y_t = 0.6*Y_{t-12} + e_t, with e_t white noise of variance 1. What is the autocorrelation of …
- An analyst fits an AR(1) model y_t = 2 + 0.6 y_{t-1} + e_t to a stationary series, where e_t is white noise. The latest observation is y_T =…
- An analyst fits a model to monthly data: Y_t = 2 + 0.5*Y_{t-1} + 0.4*Y_{t-12} + e_t, where e_t is white noise. Assuming covariance stationar…
- A risk analyst models monthly trading volume of a commodity exchange and observes a pronounced spike every December. Which feature of the sa…
- A stationary ARMA(1,1) model is Y_t = 3 + 0.6 Y_{t-1} + e_t + 0.5 e_{t-1}. What is the long-run (unconditional) mean of Y, and what does the…