Time Series Analysis Spectral Analysis and Advanced Topics

Question 1

What does spectral analysis of a time series reveal?

Accepted Answer

The distribution of variance across different frequencies (periodicities)

Answer

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?

Accepted Answer

A plot of the squared amplitude of each frequency component against frequency

Answer

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?

Accepted Answer

A test whether past values of series X improve predictions of series Y beyond Y's own past

Answer

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?

Accepted Answer

A multivariate model where each variable is regressed on its own lags and the lags of all other variables

Answer

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?

Accepted Answer

Functions showing how each variable responds over time to a shock in one variable

Answer

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.

Time Series Analysis Practice Test

Time Series Analysis Practice Test

Time Series Analysis Spectral Analysis and Advanced Topics