Time Series Analysis Autocorrelation and Partial Autocorrelation 3

Question 1

When both the ACF and PACF of a stationary series show gradual decay, which model class is most likely appropriate?

Accepted Answer

ARMA(p,q) with both p>0 and q>0

Answer

Pure AR(p)

Answer

Pure MA(q)

Answer

Random walk

Question 2

The sample autocorrelation at lag k is computed as the ratio of:

Accepted Answer

The lag-k autocovariance to the lag-0 autocovariance (variance)

Answer

The lag-k autocovariance to the lag-1 autocovariance

Answer

The variance at time t+k to the variance at time t

Answer

The mean at lag k to the overall mean

Question 3

For which of the following series would you expect the ACF to decay very slowly, remaining significantly positive for many lags?

Accepted Answer

A non-stationary series with a unit root

Answer

A stationary AR(1) with coefficient 0.3

Answer

A white noise process

Answer

A stationary MA(2) process

Question 4

In a seasonal ARIMA model, the seasonal ACF and PACF are examined at multiples of the seasonal period S. If S=12 and there is a spike only at lag 12 in the PACF (with the seasonal ACF tailing off), what seasonal component is suggested?

Accepted Answer

Seasonal AR(1)

Answer

Seasonal MA(1)

Answer

Seasonal AR(2)

Answer

No seasonal component

Question 5

The Yule-Walker equations are used to:

Accepted Answer

Relate the theoretical PACF of an AR(p) process to its parameters

Answer

Estimate MA parameters from the sample ACF

Answer

Compute the spectral density from the PACF

Answer

Test for the presence of unit roots using autocorrelations

Question 6

A researcher finds that the PACF of a residual series from a fitted model has a significant spike at lag 4. What does this suggest?

Accepted Answer

An additional AR(4) term or seasonal term may be needed

Answer

The residuals are white noise and the model is adequate

Answer

The model should be re-estimated with fewer parameters

Answer

The series needs to be log-transformed

Question 7

If the partial autocorrelation at lag 2 equals 0.45 and is statistically significant, while the PACF at lags 3 and beyond is near zero, the most parsimonious model to consider is:

Accepted Answer

AR(2)

Answer

MA(2)

Answer

ARMA(1,1)

Answer

ARIMA(0,1,2)