Detecting Multiple Breaks in Financial Market Volatility Dynamics

Table 2: Nominal Size and Power of the Inclan and Tiao (1994) test for a single change-point in
the volatility based on a GARCH process.

H₁^A : Break in the dynamics of volatility, β0 (increase of 0.1) at 0.5T

DGP1: β0 = 0.5, β1 = 0.6      0.404 0.001  0.047     0.633 0.023 0.047     0.966 0.294 0.058

DGP2: β0 = 0.8,β1 = 0.9      0.989 0.621  0.047     1.000 0.969 0.046     1.000  1.000 0.047

H₁^B : Break in the constant of volatility, ω0 (increase of 0.1) at 0.5T

DGP1: ω0 = 0.4, ω1 = 0.5     0.276 0.002 0.047     0.519 0.014 0.043     0.883 0.131  0.044

DGP2: ω0 = 0.1, ω1 = 0.2     0.786 0.121  0.043     0.959 0.385 0.047     1.000 0.981  0.032

H C : Break in the error, u 0 - N(0,1) (increase σ _{u 1} = 1.1)at0.5 Γ

DGP1: uι - N(0,1.1)          0.610 0.057 0.242     0.806 0.133 0.461     0.993 0.685 0.910

DGP2: u 1 - N(0,1.1)          0.599 0.046 0.247     0.823 0.128 0.432     0.994 0.668 0.929

H^d : Outliers in the error, u₀ - N(0,1) (μ_{u 1} = 5 every 250 observations).

DGP1: u 1 - N(5,1)            0.357 0.000 0.231     0.271  0.000 0.112     0.219 0.000 0.079

DGP2: u 1 - N(5,1)            0.505 0.001 0.257     0.500 0.002 0.136     0.481  0.002 0.079

Notes: The Inclan and Tiao (1994) statistic IT = T//2 max∣D_k| where D_k = [ζ∑^k r2/∑^τ r2) - -T- J is specified for independent
processes. It also converges to the sup ofa Brownian Bridge with asymptotic critical value 1.36 at the 5% significance level.

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