Ahmed S. Abutaleb

A genetic algorithm for the estimation of ridges in fingerprints

A genetic algorithm is developed to find the ridges in paper fingerprints. It is based on the fact that the ridges of the fingerprints are parallel. When scanning the fingerprint, line by line, the ideal noise-free gray level distribution should yield lines of black and white. The widths of these lines are not constant. The proposed genetic algorithm generates black and white lines of different widths. The widths change until we get the best match with the original fingerprint.

Maximum likelihood estimation of time-varying parameters: an application to the Athens Stock Exchange index

The problem of maximum likelihood estimation of time-varying parameters is considered. A hierarchical approach is proposed that involves, first, the estimation of the model order and parameters when they are assumed time-invariant. Second, for each parameter, an autoregressive (AR) model, with constant coefficients, is developed. This allows the parameters to change over time. Finally, the estimates of the AR coefficients for each parameter are used as initial conditions to a time-varying model with AR coefficients, which are allowed to change over time subject to some regularity constraints. This approach is then applied to the Athens Stock Exchange index, where the dominant forces affecting this index are analysed.

Number theory and bootstrapping for phase unwrapping

The problem of the phase unwrapping and the estimation of time-varying frequency is considered. The phase is first modeled as a polynomial in time. Using Lagrange interpolation polynomial approximation, for the modulo operation, where the modulus is a prime, a unique estimate for the phase is obtained. This estimate, however, is sensitive to noise. Using the method of bootstrapping, one is able to obtain good estimate even at SNR values as low as 10 dB. The method is applied to several examples, and compared to the minimum mean square polynomial fit for the phase. It is shown that the proposed approach has superior performance.

A genetic algorithm for the maximum likelihood estimation of the parameters of sinusoids in a noisy environment

An adaptive generic algorithm was developed to solve the optimization problem of the maximum likelihood estimation of the sum of sinusoids in a noisy environment. The algorithm is based on genetic concepts and is extended, with modifications, to this problem. Simulation results were performed to see the effect of different parameters such as permutation and crossover probabilities. The effects of the signal-to-noise ratio (SNR) were also studied. It was found that the key factor for accuracy is the probabilities of permutation and crossover. Thus, we developed an adaptive method to estimate these probabilities, on line, to reduce the error. This was accomplished by considering them as unknown parameters to be estimated with the signal parameters. The mean square error of the frequency estimates was compared favorably to the Cramér-Rao lower bound. Several simulations are shown for SNR values ranging between −7 dB and 20 dB.

Instantaneous frequency estimation using stochastic calculus and bootstrapping

Stochastic calculus methods are used to estimate the instantaneous frequency of a signal. The frequency is modeled as a polynomial in time. It is assumed that the phase has a Brownian-motion component. Using stochastic calculus, one is able to develop a stochastic differential equation that relates the observations to instantaneous frequency. Pseudo-maximum likelihood estimates are obtained through Girsanov theory and the Radon-Nikodym derivative. Bootstrapping is used to find the bias and the confidence interval of the estimates of the instantaneous frequency. An approximate expression for the Cramér-Rao lower bound is derived. An example is given, and a comparison to existing methods is provided.

MALLIAVIN CALCULUS FOR THE ESTIMATION OF TIME-VARYING REGRESSION MODELS USED IN FINANCIAL APPLICATIONS

The paper introduces a new method for the estimation of time-varying regression coefficients employed in financial modeling. We use Malliavin calculus (stochastic calculus of variations) to estimate the time-varying regression coefficients that appear in linear regression models, and the generalized Clark–Ocone formula to derive a closed-form solution for the estimates of the time-varying coefficients. While this approach can be applied to any signal model, we present its application to signals modeled as a Brownian motion and an Ornstein–Uhlenbeck process. Simulation results prove the superiority of the proposed method, as compared to conventional methods.

ESTIMATION AND PREDICTION OF THE JAPANESE YEN/U.S. DOLLAR RATE USING AN ADAPTIVE TIME-VARYING MODEL

This paper presents a new adaptive technique for forecasting the Yen/U.S. Dollar exchange rate. The proposed method assumes a time-varying model to describe the evolution of the exchange rate. Weekly predictions of the Yen/U.S. Dollar rate are dominated by weekly announcements of unexpected changes in the relative unemployment claims between the U.S. and Japan. Monthly predictions are more sensitive to monthly releases of the difference between the expected and announced value of the National Association of Purchasing Managers index. The predictive results of the proposed method are found more accurate than that of conventional ARMA techniques.

Assessing the Impact of the EURO on the Economies of Some MENA Countries: An Empirical Investigation Utilizing a Time-Varying Model to Forecast the Level and Volatility of the US Dollar/EURO Exchange Rate

This paper analyzes qualitatively the impact of changes in the level and variability of the US dollar/EURO exchange rate on the real GDP growth rate and trade balance positions of three MENA countries, namely Egypt, Jordan and Morocco. First, the analytical framework is presented by developing explicit relationships between (1) output growth and the variability of the nominal exchange rate; (2) per capita GDP and the variability and realignment of the real exchange rate; and (3) commodity prices and nominal exchange rate volatility. Then, based on these models, the impacts of (1) an appreciation of the US dollar against the EURO and (2) an increase in the volatility of the US dollar/EURO rate are derived. Our results indicate that an appreciation of the US dollar/EURO rate or an increase in the volatility of this rate leads to a lower real GDP growth rate and worsening of the trade balance positions for Egypt and Jordan, that effectively peg their currencies to the US dollar, and the opposite for Morocco, that effectively pegs its currency to the EURO. In contrast, an appreciation of the EURO against the US dollar encourages imports to and discourages exports from the EMU region to countries that peg their currencies to the US dollar. This appreciation, however, tends to lower inflation in countries with EURO-denominated products, partly because of lower costs for the imported components. In general, a EURO appreciation results in higher economic activity growth of countries that have US dollar-denominated products, and puts competitiveness pressures on countries that have EURO-denominated products.