Time Series Analysis Autocorrelation and Partial Autocorrelation

Question 1

What does the autocorrelation function (ACF) measure in a time series?

Accepted Answer

The correlation between a series and a lagged version of itself

Answer

The ACF measures the linear correlation between a time series and its own lagged values at various lag intervals.

Question 2

In a correlogram (ACF plot), what does a spike at lag 1 that decays slowly suggest?

Accepted Answer

The series is non-stationary or has a trend

Answer

A slowly decaying ACF that remains significant for many lags typically indicates non-stationarity or a trend in the series.

Question 3

What is the range of possible values for the autocorrelation coefficient?

Accepted Answer

-1 to 1

Answer

Autocorrelation coefficients are bounded between -1 and 1, just like Pearson correlation coefficients.

Question 4

For a white noise process, what is the expected value of all autocorrelations at lags greater than zero?

Accepted Answer

0

Answer

White noise is uncorrelated across time, so all autocorrelations at lags > 0 have an expected value of zero.

Question 5

The approximate 95% confidence bounds on an ACF plot for a series of length n are typically drawn at:

Accepted Answer

±2/√n

Answer

The approximate 95% confidence bounds for autocorrelations under the null of white noise are ±1.96/√n ≈ ±2/√n.

Time Series Analysis Practice Test