Detecting Multiple Breaks in Financial Market Volatility Dynamics



Table 9: Testing for a single change-point in high-frequency volatility filters in the YN/US$
during the period 1986-1996

Volatility
Filters

Change-point Statistics

Kokoszka & Leipus

Inclan & Tiao & extention

k *

max Uk *

max Uk*

^ HAC

max Uk*

GARMA

IT

Bt ( C )

|rt|

26/4/91

0.3538

1.493*

1.589*

1.996*

0.451

( rt )2

^B

0.2676

1.120

1.273

1.151

0.260

QV1

9/2/93

0.3445

1.925*

3.845*

2.302*

^B

QV2

9/2/93

0.3443

1.262

7.685*

2.301*

^B

QV3

9/2/93

0.3442

1.021

11.212*

2.300*

^B

HQV1

8/2/93

0.3428

1.804*

4.222*

2.291*

^B

HQV2

8/2/93

0.3429

1.207

8.467*

2.292*

^B

HQV3

9/2/93

0.3432

0.948

12.435*

2.294*

^B

Notes: (1) The Yen vis-a-vis the US dollar returns over the period 1/12/1986-30/11/1996 at the 5 minute sampling frequency is
analysed for structural changes. The data source is Olsen and Associates. The original sample is 1,052,064 five-minute return
observations (2,653 x 288 five-minute intervals per day). The returns for some days were removed from the sample to avoid having
regular and predictable market closures which affect the characterization of volatility dynamics. The final sample includes 705,024
five-minute returns reflecting N=2448 days. (2) The one-day Quadratic Variation (QV1) is the sum of squared returns r(m),t for the
intraday frequency m, to produce the daily volatility measure: QV1 = ∑m=1 r2m) t+1-j/m, t = 1,..., Tdays, where for the 5-minute sampling
frequency the lag length is = 288 observations for financial markets open 24 hours per day. In QV2 and QV3 the window length is
k = 2,3 days, respectively. The rolling estimation method yields the one-day Historical Quadratic Variation (HQV1) defined as the sum
of m rolling QVestimates: HQV1 = 1/m∑m 1 QV 1(m),t+1-j/m, t = 1,..., Tdays, Whichisalsoextendedtoa k window length, HQVk.(3)
The tests are described in the notes of Table 6.

33



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