Time Series Analysis Spectral Analysis and Advanced Topics 2 — Questions and Answers
Question 1: What is ARCH (Autoregressive Conditional Heteroscedasticity) in time series modeling?
- A model where the variance of the error term depends on past squared errors (Correct answer)
- A model for series with conditional mean changes
- An autoregressive model with changing coefficients
- A heteroscedastic extension of the MA model
Correct answer: A model where the variance of the error term depends on past squared errors
ARCH models the time-varying variance by making it a function of past squared residuals, capturing volatility clustering in financial data.
Question 2: What does GARCH add beyond the basic ARCH model?
- Lagged conditional variance terms in addition to lagged squared errors (Correct answer)
- Additional AR terms in the mean equation
- A deterministic trend in volatility
- Seasonal heteroscedasticity
Correct answer: Lagged conditional variance terms in addition to lagged squared errors
GARCH includes past conditional variances as predictors, allowing the model to capture longer-memory volatility persistence with fewer parameters than high-order ARCH.
Question 3: What is a 'long memory' process in time series analysis?
- A process where autocorrelations decay slowly (hyperbolically) rather than exponentially (Correct answer)
- A process with a very long historical dataset
- A process requiring many AR lags
- A process with autocorrelations that never decay
Correct answer: A process where autocorrelations decay slowly (hyperbolically) rather than exponentially
Long memory (fractional integration) is characterized by hyperbolic rather than geometric autocorrelation decay, often modeled with ARFIMA models.
Question 4: What is the purpose of an Intervention Analysis in time series?
- To model the effect of known external events (interventions) on a time series (Correct answer)
- To test for structural breaks automatically
- To remove outliers from the series
- To add exogenous variables to an ARIMA model for forecasting
Correct answer: To model the effect of known external events (interventions) on a time series
Intervention analysis explicitly models the impact of known events (policy changes, promotions, disasters) using indicator variables within the ARIMA framework.
Question 5: What is a Transfer Function model?
- An ARIMA model extended with lagged values of one or more input (predictor) variables (Correct answer)
- A Fourier-based frequency domain model
- A model that transfers errors between series
- A changepoint detection model
Correct answer: An ARIMA model extended with lagged values of one or more input (predictor) variables
Transfer function (or dynamic regression) models add filtered versions of external predictors to a noise model, capturing both input-output dynamics and autocorrelated errors.
Question 6: What is 'volatility clustering' commonly observed in financial time series?
- Periods of high volatility tend to follow high-volatility periods, and low follows low (Correct answer)
- Volatility increases linearly over time
- Volatility is constant across all time periods
- High returns always precede high volatility
Correct answer: Periods of high volatility tend to follow high-volatility periods, and low follows low
Volatility clustering means large (small) price changes tend to be followed by large (small) changes, regardless of direction, a stylized fact motivating GARCH models.
Time Series Analysis Spectral Analysis and Advanced Topics 2
What is ARCH (Autoregressive Conditional Heteroscedasticity) in time series modeling?