Time Series Analysis Autocorrelation and Partial Autocorrelation 1 — Questions and Answers
Question 1: What does the autocorrelation function (ACF) measure in a time series?
- The correlation between a series and a lagged version of itself (Correct answer)
- The correlation between two different time series at the same time point
- The rate of change of a series over time
- The variance of a series at different time points
Correct answer: The correlation between a series and a lagged version of itself
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?
- The series has a seasonal component
- The series is non-stationary or has a trend (Correct answer)
- The series follows a pure MA(1) process
- The series has no autocorrelation
Correct answer: The series is non-stationary or has a trend
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?
- 0 to 1
- -1 to 1 (Correct answer)
- -∞ to +∞
- 0 to +∞
Correct answer: -1 to 1
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?
- 1
- -1
- 0 (Correct answer)
- 0.5
Correct answer: 0
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:
- ±1/n
- ±1/√n
- ±2/√n (Correct answer)
- ±2/n
Correct answer: ±2/√n
The approximate 95% confidence bounds for autocorrelations under the null of white noise are ±1.96/√n ≈ ±2/√n.
Question 6: Which of the following best describes the theoretical ACF of a pure MA(q) process?
- It cuts off to zero after lag q (Correct answer)
- It decays exponentially without cutting off
- It oscillates between positive and negative values indefinitely
- It equals 1 at all lags
Correct answer: It cuts off to zero after lag q
A pure MA(q) process has autocorrelations that are exactly zero for all lags beyond q, causing a sharp cutoff.
Question 7: What does a negative autocorrelation at lag 1 in a time series indicate?
- The series has a positive trend
- High values tend to be followed by low values and vice versa (Correct answer)
- The series is non-stationary
- The series is perfectly predictable
Correct answer: High values tend to be followed by low values and vice versa
A negative autocorrelation at lag 1 means that above-average values tend to be followed by below-average values, indicating mean-reverting oscillation.
Time Series Analysis Autocorrelation and Partial Autocorrelation 1
What does the autocorrelation function (ACF) measure in a time series?