An Introduction to Wavelets and Other Filtering Methods in Finance and EconomicsAn Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multiresolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method.

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Página 17
The outputy of a linear filter is the result of the convolution of the input x, with a coefficient vector w.” The elements of the vector w = (... w–2, w_i, ...
The outputy of a linear filter is the result of the convolution of the input x, with a coefficient vector w.” The elements of the vector w = (... w–2, w_i, ...
Página 18
... L M y =XLay: +X w.xi, (2.5) i=1 i=0 where L lagged values of output y, and M lagged values of input xt, as well as the current value of the input, ...
... L M y =XLay: +X w.xi, (2.5) i=1 i=0 where L lagged values of output y, and M lagged values of input xt, as well as the current value of the input, ...
Página 19
Given the unit impulse input in Equation 2.4, the impulse response of the filter is yO = x0 = 1 y1 = ay0 + 0 = a y2 = ay, 40 = a” y = a'.
Given the unit impulse input in Equation 2.4, the impulse response of the filter is yO = x0 = 1 y1 = ay0 + 0 = a y2 = ay, 40 = a” y = a'.
Página 20
... exchange rates for different values of M and N. Since M past values and N future values of the input are required to obtain the filter output at time t, ...
... exchange rates for different values of M and N. Since M past values and N future values of the input are required to obtain the filter output at time t, ...
Página 21
Specifically, given the original input x1, the first step is to filter the input by using the first set of filter coefficients w1: M Zf E ...
Specifically, given the original input x1, the first step is to filter the input by using the first set of filter coefficients w1: M Zf E ...
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Contenido
1  
15  
51  
CHAPTER 4 DISCRETE WAVELET TRANSFORMS  96 
CHAPTER 5 WAVELETS AND STATIONARY PROCESSES  161 
CHAPTER 6 WAVELET DENOISING  202 
CHAPTER 7 WAVELETS FOR VARIANCECOVARIANCE ESTIMATION  235 
CHAPTER 8 ARTIFICIAL NEURAL NETWORKS  272 
NOTATIONS  315 
BIBLIOGRAPHY  323 
INDEX  349 
Otras ediciones  Ver todas
An Introduction to Wavelets and Other Filtering Methods in Finance and Economics Ramazan Gençay,Faruk Selçuk,Brandon Whitcher Sin vista previa disponible  2002 
Términos y frases comunes
analysis applied approximate associated assumed basis beta calculated components computed correlation covariance cycle decomposition defined determined difference discrete distribution dynamics Equation error estimator example feedforward network Figure Fourier transform frequency function gain function Gaussian given Haar hidden units increases indicate input interval Kalman filter known lags length linear matrix mean method MODWT moving average network model neural network noise observations obtained original output parameter performance period phase plotted points prediction presented procedure produce properties random recurrent respectively response returns rule sample scale seasonal sequence shift shows signal simple simulation smooth spectral spectrum squared standard stationary statistical studied term thresholding values variables variance vector volatility wavelet coefficients wavelet details wavelet filter wavelet scale wavelet transform wavelet variance weights zero