Startwaarden

Het schatten van een GARCH-model vereist het optimaliseren van de likelihood. Die optimalisatie kan mislukken bij slechte startwaarden. Gelukkig heeft Alexios Ghalanos, de auteur van het R-pakket rugarch, sterke standaardinstellingen gekozen, zodat de optimalisatie in de meeste gevallen nauwkeurig is. Als je twijfelt, kun je de methode setstart() gebruiken om je eigen startwaarden te proberen en te controleren of dit tot vergelijkbare resultaten leidt qua geschatte parameters en likelihood.

Hier kun je dit testen met de dagelijkse EUR/USD-rendementen in EURUSDret, uitgaande van een standaard GARCH-model met constante mean en een Student-t-verdeling. De modelspecificatie staat in de console als garchspec.

Deze oefening maakt deel uit van de cursus

GARCH-modellen in R

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Oefeninstructies

Schat het model garchspec met de standaard startwaarden.
Print de geschatte parameters en de likelihood.
Stel andere startwaarden in en schat opnieuw.
Print de geschatte parameters en de likelihood.

Praktische interactieve oefening

Probeer deze oefening eens door deze voorbeeldcode in te vullen.

# Estimate using default starting values
garchfit <- ___

# Print the estimated parameters and the likelihood
___
___

# Set other starting values and re-estimate
___(garchspec) <- ___(alpha1 = 0.05, beta1 = 0.9, shape = 6) 
garchfit <- ___

# Print the estimated parameters and the likelihood
___
___

Code bewerken en uitvoeren

Deze oefening maakt deel uit van de cursus

GARCH-modellen 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 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: Meebeweging tussen voorspelde volatiliteit en VaR Exercise 4: Gevoeligheid van dekking voor het distributiemodel Exercise 5: Voor productie en simulatie Exercise 6: Werkelijke versus gesimuleerde rendementen Exercise 7: Gebruik in productie Exercise 8: Gebruik in simulatie Exercise 9: Modelrisico Exercise 10: Robustniks Exercise 11: Startwaarden

Huidige oefening

Exercise 12: GARCH-covariantie Exercise 13: Schatting van bèta Exercise 14: Gewichten minimumvariantieportefeuille Exercise 15: GARCH & Co Exercise 16: Gefeliciteerd