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Exercises

Choose one or several assets (e.g., stocks or cryptocurrencies) for the following exercises.

Mean Modeling

Exercise 4.1 (Autocorrelation function of returns) Choose one asset and plot the autocorrelation function of the log-returns at different frequencies.

Exercise 4.2 (MA modeling) Choose one asset and try the MA\((q)\) model on the log-returns and log-prices for different values of the lookback \(q\). Compute the mean squared error of the forecast.

Exercise 4.3 (EWMA modeling) Choose one asset and try the EWMA model on the log-returns and log-prices for different values of the memory \(\alpha\). Compute the mean squared error of the forecast.

Exercise 4.4 (ARMA modeling) Choose one asset and experiment with ARMA\((p,q)\) models with different values of \(p\) and \(q\). Compute the mean squared error of the forecast.

Exercise 4.5 (Kalman for mean modeling) Choose one asset and experiment with different state-space models together with Kalman filtering. Compute the mean squared error of the forecast.

Exercise 4.6 (Kalman for ARMA modeling) Choose one asset and compare the results of a direct ARMA model with the corresponding state-space model via Kalman filtering.

Exercise 4.7 (VARMA modeling) Choose several assets and compare the results of asset-by-asset ARMA modeling and VARMA modeling. Discuss the results.

Exercise 4.8 (Kalman for multivariate mean modeling) Choose several assets and compare the results of asset-by-asset Kalman modeling and vector Kalman modeling. Discuss the results.

Volatility Envelope Modeling

Exercise 4.9 (Autocorrelation function of absolute returns) Choose one asset and plot the autocorrelation function of the absolute value of the log-returns at different frequencies.

Exercise 4.10 (MA volatility modeling) Choose one asset and try the MA\((q)\) model on the squared log-returns for different values of the lookback \(q\). Plot the volatility envelope.

Exercise 4.11 (EWMA volatility modeling) Choose one asset and try the EWMA model on the squared log-returns for different values of the memory \(\alpha\). Plot the volatility envelope.

Exercise 4.12 (ARCH volatility modeling) Choose one asset and experiment with ARCH\((q)\) models with different values of \(q\). Plot the volatility envelope.

Exercise 4.13 (GARCH volatility modeling) Choose one asset and experiment with GARCH\((p,q)\) models with different values of \(p\) and \(q\). Plot the volatility envelope.

Exercise 4.14 (SV modeling) Choose one asset and experiment with the SV model. Plot the volatility envelope and compare with the GARCH modeling.

Exercise 4.15 (Kalman SV modeling) Choose one asset and experiment with the SV model via Kalman filtering. Try the AR(1) model and the random walk model. In addition, compare the models under the Gaussian distribution and the heavy-tailed \(t\) distribution.

Exercise 4.16 (Multivariate GARCH modeling) Choose several assets and compare the results of asset-by-asset GARCH modeling and multivariate GARCH modeling via the constant conditional correlation model. Discuss the results.

Exercise 4.17 (Kalman for multivariate SV modeling) Choose several assets and compare the results of asset-by-asset Kalman SV modeling and vector Kalman SV modeling (including correlation among assets). Discuss the results.