Structural Breakpoints in Volatility in International Markets

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hypothetical linear cumulative energy trend. The D-statistic is compared to the critical
value of the distribution of D, for a given significance level, under the null hypothesis of
variance homogeneity.

3.2.2 The ICSS Algorithm

The idea behind the Inclan and Tiao’s ICSS algorithm can be summarized as
follows. A time series of interest has a stationary unconditional variance over an initial time

period until a sudden break takes place. The unconditional variance is then stationary until
the next sudden change occurs. This process repeats through time, giving a time series of
observations with a number of M breakpoints in the unconditional variance in n
observations:

In order to estimate the number of changes and the point in time of variance shifts, a
k

cumulative sum of square residuals is used, C_k = ∑ε_t² , k=1, 2, .., n, where {εt} is a series
t=1

of uncorrelated random variables with zero mean and unconditional variance σ_t² , as in (12).

Inclan and Tiao define the statistic:

Ck

Dk = —--       k=1, 2,.., n,   Do=Dn=O.                        (13)

C_n n

If there are no changes in variance over the whole sample period, Dk will oscillate
around zero. Otherwise, if there are one or more shifts in variance, Dk will departure from
zero. The ICSS algorithm systematically looks for breaks in variance at different points in
the series. A full description of the algorithm is given in Inclan and Tiao’s paper.

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