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 total correlation between observations k periods apart

Answer

The average autocorrelation up to lag k

Answer

The seasonal correlation at lag k

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

It decays exponentially

Answer

It shows a slow linear decay

Answer

It alternates in sign without cutting off

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

ACF cuts off after lag 2; PACF decays gradually

Answer

Both ACF and PACF cut off after lag 2

Answer

Both ACF and PACF decay gradually

Question 4

The Ljung-Box test statistic is used to:

Accepted Answer

Test whether a group of autocorrelations are jointly zero

Answer

Test whether a single autocorrelation is significant

Answer

Estimate the order of differencing needed

Answer

Measure the strength of seasonal autocorrelation

Question 5

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

Accepted Answer

ACF and PACF plots

Answer

Residual plots and histograms

Answer

AIC and BIC information criteria

Answer

Durbin-Watson and Breusch-Godfrey tests

Question 6

If the ACF of a time series shows a sinusoidal pattern with significant spikes at regular intervals, what does this most likely indicate?

Accepted Answer

The series contains a seasonal component

Answer

The series is integrated of order 1

Answer

The series is purely autoregressive

Answer

The series exhibits heteroskedasticity

Question 7

Which of the following is a key difference between the ACF and the PACF?

Accepted Answer

The PACF removes indirect effects of intermediate lags, while the ACF does not

Answer

The ACF only applies to stationary series, while the PACF does not

Answer

The ACF is bounded between 0 and 1, while the PACF is not

Answer

The PACF is always non-negative, while the ACF can be negative