Detecting Multiple Breaks in Financial Market Volatility Dynamics

Samples, T

Kokoszka & Leipus Statistic

Returns Transformations

500

U_maχ^lσ ηac
(^rt)² |^rt|

1000

Umax^lσ HAC
( ^rt ) ² | ^rt |

3000

Umax^lσ HAC

( rt )²

|rt|

H0 : Univariate GARCH, r0,t =

^ξ u 0, tjh 0, t, h 0, t = ω 0

+ α0u2,t_-1 + β0h0,t-1, with (ω0,α0,β0):

DGP1: (0.4, 0.1, 0.5)

0.059 0.072

0.061 0.078

0.061

0.067

DGP2: (0.1, 0.1, 0.8)

0.171 0.165

0.187 0.185

0.212

0.205

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

DGP1: β0 = 0.5 to β1 = 0.6

0.273 0.280

0.492 0.473

0.945

0.926

DGP2: β0 = 0.8 to β1 = 0.9

0.978 0.978

0.999 0.999

1.000

1.000

H₁^A : Break in the dynamics of volatility, β0 (increase of 0.1) at 0.3T.

DGP1: β0 = 0.5 to β1 = 0.6

0.190 0.204

0.382 0.390

0.838

0.825

DGP2: β0 = 0.8 to β1 = 0.9

0.934 0.942

0.996 0.999

1.000

1.000

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

DGP1: ω0 = 0.4 to ω 1 = 0.5

0.210 0.204

0.353 0.353

0.809

0.787

DGP2: ω0 = 0.1 to ω 1 = 0.2

0.718 0.702

0.913 0.915

1.000

1.000

H₁^B : Break in the constant of volatility, ω0 (increase of 0.1) at 0.3T.

DGP1: ω0 = 0.4 to ω 1 = 0.5

0.148 0.153

0.254 0.262

0.674

0.634

DGP2: ω0 = 0.1 to ω 1 = 0.2

0.552 0.573

0.851 0.844

0.999

0.999

H₁^C : Break in the

error, u₀ - N(0,1) (increase σ_{u 1} =

1.1) at 0.5T

DGP1: u ι - N(0,1.1)

0.287 0.277

0.548 0.520

0.921

0.917

DGP2: u 1 - N(0,1.1)

0.449 0.437

0.710 0.700

0.982

0.975

H₁^C : Break in the

error, u₀ - N(0,1) (increase σ_{u 1} =

1.1) at 0.3T

DGP1: u 1 - N(0,1.1)

0.195 0.199

0.329 0.333

0.833

0.804

DGP2: u 1 - N(0,1.1)

0.376 0.386

0.548 0.548

0.932

0.923

HD : Outliers in the error, u₀ - N(0,1) (μ_{u 1}

= 5 every 250 observations).

DGP1: u 1 - N(5,1)

0.019 0.046

0.015 0.039

0.005

0.044

DGP2: u 1 - N(5,1)

0.039 0.115

0.046 0.134

0.062

0.145