Search results for: Gaussian%20Dirichlet%20process%20mixture%20model

Authors: Reza Hassanpour, Asadollah Shahbahrami, Stephan Wong

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Skin color based tracking techniques often assume a static skin color model obtained either from an offline set of library images or the first few frames of a video stream. These models can show a weak performance in presence of changing lighting or imaging conditions. We propose an adaptive skin color model based on the Gaussian mixture model to handle the changing conditions. Initial estimation of the number and weights of skin color clusters are obtained using a modified form of the general Expectation maximization algorithm, The model adapts to changes in imaging conditions and refines the model parameters dynamically using spatial and temporal constraints. Experimental results show that the method can be used in effectively tracking of hand and face regions.

Keywords: Face detection, Segmentation, Tracking, Gaussian Mixture Model, Adaptation.

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

Keywords: Human action recognition, Bayesian HMM, Dirichlet process mixture model, Gaussian-Wishart emission model, Variational Bayesian inference, Prior distribution and approximate posterior distribution, KTH dataset.

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Authors: Bahi brahim, El hassane Ibn Elhaj, Driss Aboutajdine

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In this paper we propose a Multiple Description Image Coding(MDIC) scheme to generate two compressed and balanced rates descriptions in the wavelet domain (Daubechies biorthogonal (9, 7) wavelet) using pairwise correlating transform optimal and application method for Generalized Multiple Description Coding (GMDC) to image coding in the wavelet domain. The GMDC produces statistically correlated streams such that lost streams can be estimated from the received data. Our performance test shown that the proposed method gives more improvement and good quality of the reconstructed image when the wavelet coefficients are normalized by Gaussian Scale Mixture (GSM) model then the Gaussian one ,.

Keywords: Multiple description coding (MDC), gaussian scale mixture (GSM) model, joint source-channel coding, pairwise correlating transform, GMDCT.

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Authors: Rasaki O. Olanrewaju

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The driven processes of Wiener and Lévy are known self-standing Gaussian-Markov processes for fitting non-linear dynamical Vasciek model. In this paper, a coincidental Gaussian density stationarity condition and autocorrelation function of the two driven processes were established. This led to the conflation of Wiener and Lévy processes so as to investigate the efficiency of estimates incorporated into the one-dimensional Vasciek model that was estimated via the Maximum Likelihood (ML) technique. The conditional laws of drift, diffusion and stationarity process was ascertained for the individual Wiener and Lévy processes as well as the commingle of the two processes for a fixed effect and Autoregressive like Vasciek model when subjected to financial series; exchange rate of Naira-CFA Franc. In addition, the model performance error of the sub-merged driven process was miniature compared to the self-standing driven process of Wiener and Lévy.

Keywords: Wiener process, Lévy process, Vasciek model, drift, diffusion, Gaussian density stationary.

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Authors: Nima Hatami

Abstract:

In this paper, we use Radial Basis Function Networks (RBFN) for solving the problem of environmental interference cancellation of speech signal. We show that the Second Order Thin- Plate Spline (SOTPS) kernel cancels the interferences effectively. For make comparison, we test our experiments on two conventional most used RBFN kernels: the Gaussian and First order TPS (FOTPS) basis functions. The speech signals used here were taken from the OGI Multi-Language Telephone Speech Corpus database and were corrupted with six type of environmental noise from NOISEX-92 database. Experimental results show that the SOTPS kernel can considerably outperform the Gaussian and FOTPS functions on speech interference cancellation problem.

Keywords: Environmental interference, interference cancellation of speech, Radial Basis Function networks, Gaussian and TPS kernels.

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Authors: R. J. Chang

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A cyclostationary Gaussian linearization method is formulated for investigating the time average response of nonlinear system under sinusoidal signal and white noise excitation. The quantitative measure of cyclostationary mean, variance, spectrum of mean amplitude, and mean power spectral density of noise are analyzed. The qualitative response behavior of stochastic jump and bifurcation are investigated. The validity of the present approach in predicting the quantitative and qualitative statistical responses is supported by utilizing Monte Carlo simulations. The present analysis without imposing restrictive analytical conditions can be directly derived by solving non-linear algebraic equations. The analytical solution gives reliable quantitative and qualitative prediction of mean and noise response for the Duffing system subjected to both sinusoidal signal and white noise excitation.

Keywords: Cyclostationary, Duffing system, Gaussian linearization, sinusoidal signal and white noise.

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Authors: A. H. Fatah, A. H. Ahmed

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Levenberg-Marquardt method (LM) was proposed to be applied as a non-linear least-square fitting in the analysis of a natural gamma-ray spectrum that was taken by the Hp (Ge) detector. The Gaussian function that composed of three components, main Gaussian, a step background function and tailing function in the lowenergy side, has been suggested to describe each of the y-ray lines mathematically in the spectrum. The whole spectrum has been analyzed by determining the energy and relative intensity for the strong y-ray lines.

Keywords: Gamma-Ray, Spectrum analysis, Non-linear leastsquare fitting.

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Authors: Low Khong Teck, Hasan S. M. Al-Khaffaf, Abdullah Zawawi Talib, Tan Kian Lam

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In this paper, an extended study is performed on the effect of different factors on the quality of vector data based on a previous study. In the noise factor, one kind of noise that appears in document images namely Gaussian noise is studied while the previous study involved only salt-and-pepper noise. High and low levels of noise are studied. For the noise cleaning methods, algorithms that were not covered in the previous study are used namely Median filters and its variants. For the vectorization factor, one of the best available commercial raster to vector software namely VPstudio is used to convert raster images into vector format. The performance of line detection will be judged based on objective performance evaluation method. The output of the performance evaluation is then analyzed statistically to highlight the factors that affect vector quality.

Keywords: Performance Evaluation, Vectorization, Median Filter, Gaussian Noise.

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Authors: C. T. Cheung, R. K. P. Ng, T. Y. Lo, Zhou Jinyun

Abstract:

This paper aims at manipulating loop alignment in knitting a three-dimensional (3D) shape by its geometry. Two loop alignment methods are introduced to handle a surface with positive Gaussian curvature. As weft knitting is a two-dimensional (2D) knitting mechanism that the knitting cam carrying the feeders moves in two directions only, left and right, the knitted fabric generated grows in width and length but not in depth. Therefore, a 3D shape is required to be flattened to a 2D plane with surface area preserved for knitting. On this flattened plane, dimensional measurements are taken for loop alignment. The way these measurements being taken derived two different loop alignment methods. In this paper, only plain knitted structure was considered. Each knitted loop was taken as a basic unit for loop alignment in order to achieve the required geometric dimensions, without the inclusion of other stitches which give textural dimensions to the fabric. Two loop alignment methods were experimented and compared. Only one of these two can successfully preserve the dimensions of the shape.

Keywords: 3D knitting, 3D shape, loop alignment, positive Gaussian curvature.

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Authors: Sallama Athab, Hala Bahjat, Zhang Yinghui

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Background detection is essential in video analyses; optimization is often needed in order to achieve real time calculation. Information gathered by dual cameras placed in the front and rear part of an Autonomous Vehicle (AV) is integrated for background detection. In this paper, real time calculation is achieved on the proposed technique by using Priority Regions (PR) and Parallel Processing together where each frame is divided into regions then and each region process is processed in parallel. PR division depends upon driver view limitations. A background detection system is built on the Temporal Difference (TD) and Gaussian Filtering (GF). Temporal Difference and Gaussian Filtering with multi threshold and sigma (weight) value are be based on PR characteristics. The experiment result is prepared on real scene. Comparison of the speed and accuracy with traditional background detection techniques, the effectiveness of PR and parallel processing are also discussed in this paper.

Keywords: Autonomous Vehicle, Background Detection, Dual Camera, Gaussian Filtering, Parallel Processing.

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Authors: Mohammad Rakibul Islam

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In this paper, a Gaussian multiple input multiple output multiple eavesdropper (MIMOME) channel is considered where a transmitter communicates to a receiver in the presence of an eavesdropper. We present a technique for determining the secrecy capacity of the multiple input multiple output (MIMO) channel under Gaussian noise. We transform the degraded MIMOME channel into multiple single input multiple output (SIMO) Gaussian wire-tap channels and then use scalar approach to convert it into two equivalent multiple input single output (MISO) channels. The secrecy capacity model is then developed for the condition where the channel state information (CSI) for main channel only is known to the transmitter. The results show that the secret communication is possible when the eavesdropper channel noise is greater than a cutoff noise level. The outage probability is also analyzed of secrecy capacity is also analyzed. The effect of fading and outage probability is also analyzed.

Keywords: Secrecy capacity, MIMO, wiretap channel, covariance matrix, fading.

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Authors: Turgay Temel, John Hallam

Abstract:

A sequential decision problem, based on the task ofidentifying the species of trees given acoustic echo data collectedfrom them, is considered with well-known stochastic classifiers,including single and mixture Gaussian models. Echoes are processedwith a preprocessing stage based on a model of mammalian cochlearfiltering, using a new discrete low-pass filter characteristic. Stoppingtime performance of the sequential decision process is evaluated andcompared. It is observed that the new low pass filter processingresults in faster sequential decisions.

Keywords: Classification, neuro-spike coding, parametricmodel, Gaussian mixture with EM algorithm, sequential decision.

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Authors: Mario Gianni, Manuel A. Ruiz Garcia, Fiora Pirri

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In this work, we present a Bayesian non-parametric approach to model the motion control of ATVs. The motion control model is based on a Dirichlet Process-Gaussian Process (DP-GP) mixture model. The DP-GP mixture model provides a flexible representation of patterns of control manoeuvres along trajectories of different lengths and discretizations. The model also estimates the number of patterns, sufficient for modeling the dynamics of the ATV.

Keywords: Dirichlet processes, Gaussian processes, robot control learning, tracked vehicles.

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Authors: Adnan Al-Smadi, Mahmoud Smadi

Abstract:

This paper presents an algorithm for reconstructing phase and magnitude responses of the impulse response when only the output data are available. The system is driven by a zero-mean independent identically distributed (i.i.d) non-Gaussian sequence that is not observed. The additive noise is assumed to be Gaussian. This is an important and essential problem in many practical applications of various science and engineering areas such as biomedical, seismic, and speech processing signals. The method is based on evaluating the bicepstrum of the third-order statistics of the observed output data. Simulations results are presented that demonstrate the performance of this method.

Keywords: Cepstrum, bicepstrum, third order statistics

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Authors: Kavita Burse, R.N. Yadav, S.C. Shrivastava, Vishnu Pratap Singh Kirar

Abstract:

During signal transmission, the combined effect of the transmitter filter, the transmission medium, and additive white Gaussian noise (AWGN) are included in the channel which distort and add noise to the signal. This causes the well defined signal constellation to spread causing errors in bit detection. A compact pi neural network with minimum number of nodes is proposed. The replacement of summation at each node by multiplication results in more powerful mapping. The resultant pi network is tested on six different channels.

Keywords: Additive white Gaussian noise, digitalcommunication system, multiplicative neuron, Pi neural network.

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Authors: Worawit Somha, Hiroyuki Yamauchi

Abstract:

This paper proposes, for the first time, how the challenges facing the guard-band designs including the margin assist-circuits scheme for the screening-test in the coming process generations should be addressed. The increased screening error impacts are discussed based on the proposed statistical analysis models. It has been shown that the yield-loss caused by the misjudgment on the screening test would become 5-orders of magnitude larger than that for the conventional one when the amplitude of random telegraph noise (RTN) caused variations approaches to that of random dopant fluctuation. Three fitting methods to approximate the RTN caused complex Gamma mixtures distributions by the simple Gaussian mixtures model (GMM) are proposed and compared. It has been verified that the proposed methods can reduce the error of the fail-bit predictions by 4-orders of magnitude.

Keywords: Mixtures of Gaussian, Random telegraph noise, EM algorithm, Long-tail distribution, Fail-bit analysis, Static random access memory, Guard band design.

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Authors: Kaushalendra K. Khadanga, Lee Hee Hyol

Abstract:

Passenger comfort has been paramount in the design of suspension systems of high speed cars. To analyze the effect of vibration on vehicle ride quality, a vertical model of a six degree of freedom railway passenger vehicle, with front and rear suspension, is built. It includes car body flexible effects and vertical rigid modes. A second order linear shaping filter is constructed to model Gaussian white noise into random rail excitation. The temporal correlation between the front and rear wheels is given by a second order Pade approximation. The complete track and the vehicle model are then designed. An active secondary suspension system based on a Linear Quadratic Gaussian (LQG) optimal control method is designed. The results show that the LQG control method reduces the vertical acceleration, pitching acceleration and vertical bending vibration of the car body as compared to the passive system.

Keywords: Active suspension, bending vibration, railway vehicle, vibration control.

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

Abstract:

The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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Authors: Muhammad Imran Ahmad, Ruzelita Ngadiran, Mohd Nazrin Md Isa, Nor Ashidi Mat Isa, Mohd Zaizu Ilyas, Raja Abdullah Raja Ahmad, Said Amirul Anwar Ab Hamid, Muzammil Jusoh

Abstract:

This paper presents two techniques, local feature extraction using image spectrum and low frequency spectrum modelling using GMM to capture the underlying statistical information to improve the performance of face recognition system. Local spectrum features are extracted using overlap sub block window that are mapped on the face image. For each of this block, spatial domain is transformed to frequency domain using DFT. A low frequency coefficient is preserved by discarding high frequency coefficients by applying rectangular mask on the spectrum of the facial image. Low frequency information is non- Gaussian in the feature space and by using combination of several Gaussian functions that has different statistical properties, the best feature representation can be modelled using probability density function. The recognition process is performed using maximum likelihood value computed using pre-calculated GMM components. The method is tested using FERET datasets and is able to achieved 92% recognition rates.

Keywords: Local features modelling, face recognition system, Gaussian mixture models.

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Authors: Sandipan Chakroborty, Goutam Saha

Abstract:

A state of the art Speaker Identification (SI) system requires a robust feature extraction unit followed by a speaker modeling scheme for generalized representation of these features. Over the years, Mel-Frequency Cepstral Coefficients (MFCC) modeled on the human auditory system has been used as a standard acoustic feature set for speech related applications. On a recent contribution by authors, it has been shown that the Inverted Mel- Frequency Cepstral Coefficients (IMFCC) is useful feature set for SI, which contains complementary information present in high frequency region. This paper introduces the Gaussian shaped filter (GF) while calculating MFCC and IMFCC in place of typical triangular shaped bins. The objective is to introduce a higher amount of correlation between subband outputs. The performances of both MFCC & IMFCC improve with GF over conventional triangular filter (TF) based implementation, individually as well as in combination. With GMM as speaker modeling paradigm, the performances of proposed GF based MFCC and IMFCC in individual and fused mode have been verified in two standard databases YOHO, (Microphone Speech) and POLYCOST (Telephone Speech) each of which has more than 130 speakers.

Keywords: Gaussian Filter, Triangular Filter, Subbands, Correlation, MFCC, IMFCC, GMM.

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Authors: K. Al-Heuseen, M. R. Hashim

Abstract:

The current-voltage (I-V) characteristics of Pd/n-GaN Schottky barrier were studied at temperatures over room temperature (300-470K). The values of ideality factor (n), zero-bias barrier height (φB0), flat barrier height (φBF) and series resistance (Rs) obtained from I-V-T measurements were found to be strongly temperature dependent while (φBo) increase, (n), (φBF) and (Rs) decrease with increasing temperature. The apparent Richardson constant was found to be 2.1x10-9 Acm-2K-2 and mean barrier height of 0.19 eV. After barrier height inhomogeneities correction, by assuming a Gaussian distribution (GD) of the barrier heights, the Richardson constant and the mean barrier height were obtained as 23 Acm-2K-2 and 1.78eV, respectively. The corrected Richardson constant was very closer to theoretical value of 26 Acm-2K-2. 

Keywords: Electrical properties, Gaussian distribution, Pd-GaN Schottky diodes, thermionic emission.

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Authors: Sangjun Park, Jungpyo Hong, Byung-Ok Kang, Yun-keun Lee, Minsoo Hahn

Abstract:

In this paper, an algorithm for detecting and attenuating puff noises frequently generated under the mobile environment is proposed. As a baseline system, puff detection system is designed based on Gaussian Mixture Model (GMM), and 39th Mel Frequency Cepstral Coefficient (MFCC) is extracted as feature parameters. To improve the detection performance, effective acoustic features for puff detection are proposed. In addition, detected puff intervals are attenuated by high-pass filtering. The speech recognition rate was measured for evaluation and confusion matrix and ROC curve are used to confirm the validity of the proposed system.

Keywords: Gaussian mixture model, puff detection and cancellation, speech enhancement.

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Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma

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Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.

Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.

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Authors: Igor Astrov, Mikhail Pikkov, Rein Paluoja

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This paper focuses on a critical component of the situational awareness (SA), the control of autonomous vertical flight for vectored thrust aerial vehicle (VTAV). With the SA strategy, we proposed a linear-quadratic-Gaussian (LQG) flight control procedure for an unmanned helicopter model with vectored thrust configuration. This LQG control for chosen model of VTAV has been verified by simulation of take-off and landing maneuvers using software package Simulink and demonstrated good performance for fast flight stabilization of model, consequently, fast SA with economy in energy can be asserted during search-and-rescue operations.

Keywords: Linear-Quadratic-Gaussian (LQG) controller, situational awareness, vectored thrust aerial vehicle.

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Authors: B. M. Mohan, Sanjeeb Kumar Kar

Abstract:

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

Keywords: Linear quadratic Gaussian control, linear quadratic estimator, linear quadratic regulator, time-invariant systems, orthogonal functions, block-pulse functions, shifted legendre polynomials.

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Authors: Yan Su, L. C. Chan

Abstract:

A novel typical day prediction model have been built and validated by the measured data of a grid-connected solar photovoltaic (PV) system in Macau. Unlike conventional statistical method used by previous study on PV systems which get results by averaging nearby continuous points, the present typical day statistical method obtain the value at every minute in a typical day by averaging discontinuous points at the same minute in different days. This typical day statistical method based on discontinuous point averaging makes it possible for us to obtain the Gaussian shape dynamical distributions for solar irradiance and output power in a yearly or monthly typical day. Based on the yearly typical day statistical analysis results, the maximum possible accumulated output energy in a year with on site climate conditions and the corresponding optimal PV system running time are obtained. Periodic Gaussian shape prediction models for solar irradiance, output energy and system energy efficiency have been built and their coefficients have been determined based on the yearly, maximum and minimum monthly typical day Gaussian distribution parameters, which are obtained from iterations for minimum Root Mean Squared Deviation (RMSD). With the present model, the dynamical effects due to time difference in a day are kept and the day to day uncertainty due to weather changing are smoothed but still included. The periodic Gaussian shape correlations for solar irradiance, output power and system energy efficiency have been compared favorably with data of the PV system in Macau and proved to be an improvement than previous models.

Keywords: Grid Connected, RMSD, Solar PV System, Typical Day.

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Authors: Mukesh Kumar Shah, Tushar Gupta

Abstract:

An Upgraded Cuckoo Search Algorithm is proposed here to solve optimization problems based on the improvements made in the earlier versions of Cuckoo Search Algorithm. Short comings of the earlier versions like slow convergence, trap in local optima improved in the proposed version by random initialization of solution by suggesting an Improved Lambda Iteration Relaxation method, Random Gaussian Distribution Walk to improve local search and further proposing Greedy Selection to accelerate to optimized solution quickly and by “Study Nearby Strategy” to improve global search performance by avoiding trapping to local optima. It is further proposed to generate better solution by Crossover Operation. The proposed strategy used in algorithm shows superiority in terms of high convergence speed over several classical algorithms. Three standard algorithms were tested on a 6-generator standard test system and the results are presented which clearly demonstrate its superiority over other established algorithms. The algorithm is also capable of handling higher unit systems.

Keywords: Economic dispatch, Gaussian selection operator, prohibited operating zones, ramp rate limits, upgraded cuckoo search.

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Authors: Levent Basayigit, Sinan Demir, Yusuf Ucar, Burhan Kara

Abstract:

Many research projects require accurate delineation of the different land cover type of the agricultural area. Especially it is critically important for the definition of specific plants like cannabis. However, the complexity of vegetation stands structure, abundant vegetation species, and the smooth transition between different seconder section stages make vegetation classification difficult when using traditional approaches such as the maximum likelihood classifier. Most of the time, classification distinguishes only between trees/annual or grain. It has been difficult to accurately determine the cannabis mixed with other plants. In this paper, a mixed distribution models approach is applied to classify pure and mix cannabis parcels using Worldview-2 imagery in the Lakes region of Turkey. Five different land use types (i.e. sunflower, maize, bare soil, and cannabis) were identified in the image. A constrained Gaussian mixture discriminant analysis (GMDA) was used to unmix the image. In the study, 255 reflectance ratios derived from spectral signatures of seven bands (Blue-Green-Yellow-Red-Rededge-NIR1-NIR2) were randomly arranged as 80% for training and 20% for test data. Gaussian mixed distribution model approach is proved to be an effective and convenient way to combine very high spatial resolution imagery for distinguishing cannabis vegetation. Based on the overall accuracies of the classification, the Gaussian mixed distribution model was found to be very successful to achieve image classification tasks. This approach is sensitive to capture the illegal cannabis planting areas in the large plain. This approach can also be used for monitoring and determination with spectral reflections in illegal cannabis planting areas.

Keywords: Gaussian mixture discriminant analysis, spectral mixture model, World View-2, land parcels.

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Authors: M.Sujaritha, S. Annadurai

Abstract:

An adaptive spatial Gaussian mixture model is proposed for clustering based color image segmentation. A new clustering objective function which incorporates the spatial information is introduced in the Bayesian framework. The weighting parameter for controlling the importance of spatial information is made adaptive to the image content to augment the smoothness towards piecewisehomogeneous region and diminish the edge-blurring effect and hence the name adaptive spatial finite mixture model. The proposed approach is compared with the spatially variant finite mixture model for pixel labeling. The experimental results with synthetic and Berkeley dataset demonstrate that the proposed method is effective in improving the segmentation and it can be employed in different practical image content understanding applications.

Keywords: Adaptive; Spatial, Mixture model, Segmentation, Color.

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Authors: G. L. C. Yap

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.

Keywords: Long-memory, Gaussian process, Whittle estimator, normalization, volatility, value-at-risk.

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