Time Series Analysis Autocorrelation and Partial Autocorrelation 2

Question 1

What does the Partial Autocorrelation Function (PACF) measure at lag k?

Accepted Answer

The correlation between observations k periods apart after removing the effect of intervening lags

Answer

The PACF at lag k measures the correlation between observations separated by k periods after controlling for all shorter lags.

Question 2

For a pure AR(p) process, which of the following correctly describes the PACF?

Accepted Answer

It cuts off to zero after lag p

Answer

The PACF of an AR(p) process cuts off sharply to zero after lag p, making the PACF the primary tool for identifying AR order.

Question 3

Which combination of ACF and PACF patterns suggests an AR(2) model is appropriate?

Accepted Answer

ACF decays gradually; PACF cuts off after lag 2

Answer

An AR(p) model is indicated when the PACF cuts off after lag p while the ACF decays gradually (tails off).

Question 4

The Ljung-Box test statistic is used to:

Accepted Answer

Test whether a group of autocorrelations are jointly zero

Answer

The Ljung-Box Q statistic tests the null hypothesis that the first m autocorrelations are jointly equal to zero, useful for model diagnostics.

Question 5

In the Box-Jenkins methodology, which tools are primarily used in the model identification stage?

Accepted Answer

ACF and PACF plots

Answer

The Box-Jenkins identification stage relies on examining the patterns in the ACF and PACF to determine the appropriate AR and MA orders.

Time Series Analysis Practice Test