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CPS2176 Chiraz KARAMTI et al.
between positive and negative shocks on the conditional variance of future
observations. For each detail j, the mean equation of the model is given by:

= + = + √ℎ ~(0,1) (4)

The conditional variance equation (in logarithm) is formulated as follow:
−1 −1

ln(ℎ ) = + | | + + ℎ −1 (5)

√ℎ −1 √ℎ −1
where is the modified wavelet transform (MODWT) return series, ℎ −1 is

the conditional variance or volatility at − 1, while measures the extent to
which a present volatility shock goes into the future volatility and ( + )
measures the rate at which this effect dies in the future. The parameter is the
chief causative agent of the asymmetry in volatility. When > 0, a positive
return shock increases volatility, and when < 0, a positive return shock
reduces volatility. is a standardized error. This implies that the leverage

effect is exponential, rather than quadratic, and the forecasts of the conditional
variance are guaranteed to be non-negative. To evaluate the accuracy of the
models, two performance criteria such as RMAE and MSE. These criteria are
given below:

∑ ( − ̂ ) 2 − ̂

= √ =1 = ∑ | |

=1
Where is the actual and ̂ is the forecasted value of period t, and T is the

number of total observations.
3. Empirical analysis
The data consists of average returns of the exchange rates between the
European Euro vis-à-vis the US dollar. Five minutes observations cover the
period from May 1, 2016 to December 12, 2017 and that makes a sample of
44508 observations. We split the full sample in two sub-periods, pre-Brexit
and post-Brexit referendum to investigate the volatility dynamics in the
presence of high uncertainty.

4. Result
We used 5mn data and our decomposition goes to scale 7. The first level
detail d1 represents the variations within [10;20] mn, while the next level

details d2-d7 represent the variations within [2 , 2 +1 ] (5 minutes) horizon
(Table 1).

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