Time Series Analysis Spectral Analysis and Advanced Topics 1 — Questions and Answers
Question 1: What does spectral analysis of a time series reveal?
- The distribution of variance across different frequencies (periodicities) (Correct answer)
- The autocorrelation at each lag
- The trend and seasonality components
- The stationarity of the series
Correct answer: The distribution of variance across different frequencies (periodicities)
Spectral analysis decomposes a time series into frequency components, showing which cycles contribute most to the overall variance.
Question 2: What is a periodogram in spectral analysis?
- A plot of the squared amplitude of each frequency component against frequency (Correct answer)
- A plot of autocorrelation vs lag
- A histogram of time series values
- A plot of forecast errors over time
Correct answer: A plot of the squared amplitude of each frequency component against frequency
The periodogram estimates the spectral density by computing and squaring the Fourier transform coefficients at each frequency.
Question 3: What is Granger causality in time series analysis?
- A test whether past values of series X improve predictions of series Y beyond Y's own past (Correct answer)
- A test for unit roots in bivariate systems
- A measure of cross-correlation between two series
- A cointegration test
Correct answer: A test whether past values of series X improve predictions of series Y beyond Y's own past
Granger causality tests whether lagged values of X add statistically significant predictive power for Y after controlling for Y's own lags.
Question 4: What is a Vector Autoregression (VAR) model?
- A multivariate model where each variable is regressed on its own lags and the lags of all other variables (Correct answer)
- A univariate AR model with variable lag length
- A seasonal ARIMA model
- A random forest model applied to time series
Correct answer: A multivariate model where each variable is regressed on its own lags and the lags of all other variables
VAR models capture the dynamic interdependencies among multiple time series, with each equation modeling one variable as a function of all variables' lagged values.
Question 5: What are 'impulse response functions' (IRFs) in VAR analysis?
- Functions showing how each variable responds over time to a shock in one variable (Correct answer)
- Functions showing seasonal responses to external inputs
- Forecasting functions for long horizons
- Functions measuring parameter sensitivity
Correct answer: Functions showing how each variable responds over time to a shock in one variable
IRFs trace the dynamic effect of a one-unit shock to one variable on itself and all other variables in the system over subsequent time periods.
Question 6: What is 'changepoint detection' in time series analysis?
- Identifying time points where the statistical properties of the series change abruptly (Correct answer)
- Detecting outliers using z-scores
- Finding seasonal peaks in the data
- Locating the start of an upward trend
Correct answer: Identifying time points where the statistical properties of the series change abruptly
Changepoint detection algorithms locate times when the mean, variance, or other properties of the series shift, indicating structural changes.
Time Series Analysis Spectral Analysis and Advanced Topics 1
What does spectral analysis of a time series reveal?