Parameter bounds and impact on forecasts

Let's take again the flexible GARCH model specification for which the estimated coefficients are printed in the console. Now assume that you believe that the GARCH parameter \(\alpha\) should be between 0.05 and 0.1, while the \(\beta\) parameter is between 0.8 and 0.95. You are asked here to re-estimate the model by imposing those bounds and see the effect on the volatility forecasts for the next ten days obtained using ugarchforecast.

Diese Übung ist Teil des Kurses

GARCH Models in R

Anleitung zur Übung

Impose the c(0.05, 0.2) and c(0.8, 0.95) bounds on alpha1 and beta1.
Estimate the bounded model on the EURUSD returns.
Note how coefficients have changed.
Compare in a table the volatility predictions for the next 10 days using the unrestricted and restricted models.

Interaktive Übung

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# Define bflexgarchspec as the bound constrained version
bflexgarchspec <- flexgarchspec
___(bflexgarchspec) <- list(___ = ___, ___ = ___)

# Estimate the bound constrained model
bflexgarchfit <- ugarchfit(data = EURUSDret, ___ = ___)

# Inspect coefficients
___(___)

# Compare forecasts for the next ten days
cbind(sigma(ugarchforecast(flexgarchfit, n.ahead = ___)),
      sigma(ugarchforecast(bflexgarchfit, n.ahead = ___)))

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Diese Übung ist Teil des Kurses

GARCH Models in R

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We start off by making our hands dirty. A rolling window analysis of daily stock returns shows that its standard deviation changes massively through time. Looking back at the past, we thus have clear evidence of time-varying volatility. Looking forward, we need to estimate the volatility of future returns. This is essentially what a GARCH model does! In this chapter, you will learn the basics of using the rugarch package for specifying and estimating the workhorse GARCH(1,1) model in R. We end by showing its usefulness in tactical asset allocation.

Exercise 1: Analyzing volatility Exercise 2: Computing returns Exercise 3: Standard deviation on subsamples Exercise 4: Roll, roll, roll Exercise 5: The GARCH equation for volatility prediction Exercise 6: GARCH(1,1) reaction to one-off shocks Exercise 7: Prediction errors Exercise 8: The recursive nature of the GARCH variance Exercise 9: The rugarch package Exercise 10: Specify and taste the GARCH model flavors Exercise 11: Out-of-sample forecasting Exercise 12: Volatility targeting in tactical asset allocation

Markets take the stairs up and the elevator down. This Wallstreet wisdom has important consequences for specifying a realistic volatility model. It requires to give up the assumption of normality, as well as the symmetric response of volatility to shocks. In this chapter, you will learn about GARCH models with a leverage effect and skewed student t innovations. At the end, you will be able to use GARCH models for estimating over ten thousand different GARCH model specifications.

Exercise 1: Non-normality of standardized returns Exercise 2: Skewed student t distribution parameters Exercise 3: Estimation of non-normal GARCH model Exercise 4: Standardized returns Exercise 5: Leverage effect Exercise 6: News impact curve Exercise 7: Estimation of GJR garch model Exercise 8: Mean model Exercise 9: Predicting returns Exercise 10: The AR(1)-GJR GARCH dynamics of MSFT returns Exercise 11: Effect of mean model on volatility predictions Exercise 12: Avoid unnecessary complexity Exercise 13: Modeling choices Exercise 14: Fixing GARCH parameters Exercise 15: Parameter bounds and impact on forecasts

Aktuelle Übung

Exercise 16: Variance targeting

GARCH models yield volatility forecasts which serve as input for financial decision making. Their use in practice requires to first evaluate the goodness of the volatility forecast. In this chapter, you will learn about the analysis of statistical significance of the estimated GARCH parameters, the properties of standardized returns, the interpretation of information criteria and the use of rolling GARCH estimation and mean squared prediction errors to analyze the accuracy of the volatility forecast.

Exercise 1: Statistical significance Exercise 2: Significance testing Exercise 3: Analyzing estimation output Exercise 4: A better model for EUR/USD returns Exercise 5: Goodness of fit Exercise 6: Parsimony Exercise 7: Mean squared prediction errors Exercise 8: Comparing likelihood and information criteria Exercise 9: Diagnosing absolute standardized returns Exercise 10: Validation of GARCH model assumptions Exercise 11: Correlogram and Ljung-Box test Exercise 12: Change estimation sample Exercise 13: Backtesting using ugarchroll Exercise 14: ugarchroll arguments Exercise 15: In-sample versus rolling sample vol Exercise 16: Horse race

At this stage, you master the standard specification, estimation and validation of GARCH models in the rugarch package. This chapter introduces specific rugarch functionality for making value-at-risk estimates, for using the GARCH model in production and for simulating GARCH returns. You will also discover that the presence of GARCH dynamics in the variance has implications for simulating log-returns, the estimation of the beta of a stock and finding the minimum variance portfolio.

Exercise 1: Value-at-risk Exercise 2: VaR plot Exercise 3: Comovement between predicted vol and VaR Exercise 4: Sensitivity of coverage to distribution model Exercise 5: For production and simulation Exercise 6: Actual versus simulated returns Exercise 7: Use in production Exercise 8: Use in simulation Exercise 9: Model risk Exercise 10: Robustniks Exercise 11: Starting values Exercise 12: GARCH covariance Exercise 13: Estimation of beta Exercise 14: Minimum variance portfolio weights Exercise 15: GARCH & Co Exercise 16: Congratulations