Abstract: Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.
Abstract: Logarithms reduce products to sums and powers to products; they play an important role in signal processing, communication and information theory. They are primarily
used for hardware calculations, handling multiplications, divisions,
powers, and roots effectively. There are three commonly
used bases for logarithms; the logarithm with base-10 is called
the common logarithm, the natural logarithm with base-e and
the binary logarithm with base-2. This paper demonstrates different
methods of calculation for log2 showing the complexity
of each and finds out the most accurate and efficient besides
giving insights to their hardware design. We present a new
method called Floor Shift for fast calculation of log2, and
then we combine this algorithm with Taylor series to improve
the accuracy of the output, we illustrate that by using two
examples. We finally compare the algorithms and conclude
with our remarks.
Abstract: Recently, many existing partially blind signature scheme based on a single hard problem such as factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. However sooner or later these systems will become broken and vulnerable, if the factoring or discrete logarithms problems are cracked. This paper proposes a secured partially blind signature scheme based on factoring (FAC) problem and elliptic curve discrete logarithms (ECDL) problem. As the proposed scheme is focused on factoring and ECDLP hard problems, it has a solid structure and will totally leave the intruder bemused because it is very unlikely to solve the two hard problems simultaneously. In order to assess the security level of the proposed scheme a performance analysis has been conducted. Results have proved that the proposed scheme effectively deals with the partial blindness, randomization, unlinkability and unforgeability properties. Apart from this we have also investigated the computation cost of the proposed scheme. The new proposed scheme is robust and it is difficult for the malevolent attacks to break our scheme.