QUIZ WEEK 9

What is a necessary condition for the stationarity of an ARCH(p) model?

• The sum of the ARCH coefficients must be less than 1.
• The ARCH model must have at least 2 lags.
• All ARCH coefficients must be equal to 0.
• The sum of the ARCH coefficients must be greater than 1.

The ARCH(ρ) model can be considered equivalent to which other type of model, but applied to the squared returns (​r²_t)?

• MA(q)

• AR(ρ)

• ARMA(ρ, q)

• GARCH(1, 1)

What is the main advantage of the GARCH model over the ARCH(ρ) model?

• It is simpler to calculate.

• It considers the dependence of conditional variance on its past values.

• It does not require stationarity of the data.

• It has fewer parameters than the ARIMA model.

What is the general form of the conditional variance in a GARCH(ρ, q) model?

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In the GARCH(1,1) model, what condition must be satisfied for the conditional variance to be stationary?

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• There are no conditions

What is one of the main limitations of the GARCH model?

• It does not capture excess kurtosis.

• It assumes that positive and negative shocks have symmetric effects on volatility.

• It does not consider squared returns.

• It does not require stationarity.

What is the leverage effect in financial models?

• A relationship between past returns and conditional variance.

• An increase in volatility caused by negative returns.

• A decrease in volatility in the presence of positive returns.

• The dependence of variance on past errors.

Which model addresses the asymmetry of shocks in volatility by replacing the squared function with a flexible function?

• GARCH(1, 1)

• tGARCH

• APARCH

• eGARCH

In an eGARCH model, what is the role of the term γ_i(∣ϵ_t-1∣ - E[ϵ_t-1])?

• To determine the size effect.

• To calculate kurtosis.

• To represent the ARCH term.

• To model the leverage effect.

Why is it necessary to square the returns in ARCH and GARCH models?

• To ensure the models capture the magnitude of fluctuations, as volatility measures variance, not direction.

• To remove the impact of extreme events like financial crashes or rallies, ensuring a smoother prediction.

• To transform returns into probabilities that can be directly modeled.

• To cancel out negative returns and focus only on positive ones for simplicity.