Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.

Influence of accommodation and refractive status on the peripheral refractive profile

AIM: The aim of the study was to determine, objectively and non-invasively, whether changes in accommodative demand modify differentially the peripheral refraction in emmetropic and myopic human eyes. METHODS: Forty subjects (19 male, 21 female) aged 20-30 years (mean 22.7 (SD 2.8) years), 21 emmetropes (mean spherical equivalent refractive error (MSE) -0.13 (SD 0.29) D) and 19 myopes (MSE -2.95 (SD 1.76) D) participated in the study. Ametropia was corrected with soft contact lenses (etafilcon A, 58% water content). Subjects viewed monocularly a stationary, high contrast (85%) Maltese cross at 0.0, 1.0, 2.0 and 3.0 D of accommodative demand and at 0, 10, 20 and 30 degrees field angle (nasal and temporal) through a +3.0 D Badal optical system. Static recordings of the accommodation response were obtained for each accommodative level, at each field angle, with an objective, open-view, infrared optometer. RESULTS: Peripheral mean spherical equivalent (M) data showed that the emmetropic cohort exhibited relative myopic shifts into the periphery, while the myopic group showed hypermetropic shifts. Increasing accommodative demand did not alter the peripheral refractive profile in either the temporal (p = 0.25) or nasal (p = 0.07) periphery with no differential accommodative effect between refractive groups in either the temporal (p = 0.77) or nasal (p = 0.73) field. Significant shifts in the J(0) astigmatic component were seen in the temporal (p<0.0005) and nasal (p<0.0005) fields with increasing eccentricity. Interaction effects between eccentricity and accommodative demand illustrated that increasing accommodative demand significantly altered the peripheral refractive profile in the temporal J(0) astigmatic component (p<0.0005). The nasal periphery, however, failed to show such an effect (p = 0.65). CONCLUSIONS: Alterations in peripheral refraction augmented by changes in ocular accommodation are relatively unaffected by refractive error for young, healthy human eyes.

Line-by-line fiber Bragg grating made by femtosecond laser

In this letter, we report on the inscription of a fourth-order fiber Bragg grating made line-by-line in the optical fiber using a femtosecond laser. Strong Bragg resonance (~17 dB) and low insertion loss (~0.5 dB) were obtained with only 2000 periods. Measured refractive index change of these inscribed lines reaches up to 7 × 10-3. The grating was fully characterized and the low insertion loss together with low polarization-dependent loss were realized compared to gratings made by the point-by-point method. The high temperature annealing experiment shows the grating can survive up to at least 800°C.