An Introduction to Wavelets and Other Filtering Methods in Finance and EconomicsElsevier, 2001 M10 12 - 359 páginas An 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 multi-resolution 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 28
... given by - 7t coS 6 = Sin (94. #). A switch from the frequency domain to the time domain may illustrate some other properties of a sinusoidal signal. Consider the following time series: *-*( : '). t = 0, 1, 2, ... N – 1, (2.7) p where ...
... given by - 7t coS 6 = Sin (94. #). A switch from the frequency domain to the time domain may illustrate some other properties of a sinusoidal signal. Consider the following time series: *-*( : '). t = 0, 1, 2, ... N – 1, (2.7) p where ...
Página 29
... given by X(f) = XD xe". (2.9) t=-oo Equation 2.8 is referred as the inverse Fourier transform, and Equation 2.9 is the Fourier transform of xt. Two equations constitute a Fourier representation of the FIGURE 2.6 Time series ...
... given by X(f) = XD xe". (2.9) t=-oo Equation 2.8 is referred as the inverse Fourier transform, and Equation 2.9 is the Fourier transform of xt. Two equations constitute a Fourier representation of the FIGURE 2.6 Time series ...
Página 30
... Given x, and X(f) as a Fourier transform pair, QX) 1 7t X of =#| |x(f)Faf (2.10) t=-Co --Jr. which is known as Parseval's theorem. The left-hand side in Equation 2.10 is the total energy in the signal, which may be obtained by ...
... Given x, and X(f) as a Fourier transform pair, QX) 1 7t X of =#| |x(f)Faf (2.10) t=-Co --Jr. which is known as Parseval's theorem. The left-hand side in Equation 2.10 is the total energy in the signal, which may be obtained by ...
Página 31
... given by N-1 1. - x =# XX", t = 0, 1, . . . , N – 1 (211) k=0 and N–1 Xk = XD re-". k = 0, 1 . . . , N – 1, (2.12) =0 where f = k/N. Parseval's relation in this case is (Oppenheim and Schafer, 1989, page 574) N–1 1 := * – + 2 XLRA ...
... given by N-1 1. - x =# XX", t = 0, 1, . . . , N – 1 (211) k=0 and N–1 Xk = XD re-". k = 0, 1 . . . , N – 1, (2.12) =0 where f = k/N. Parseval's relation in this case is (Oppenheim and Schafer, 1989, page 574) N–1 1 := * – + 2 XLRA ...
Página 38
... given by 1 ei2RfI(N–M)/2 sin [2t f(M + N + 1)/2] - ——, (2.24) N + M + 1 sin(27tf/2) H(f) = where M is the number of lagged values and N is the number of future values of the input (Oppenheim and Schafer, 1989, Ch. 6). Figure 2.10b plots ...
... given by 1 ei2RfI(N–M)/2 sin [2t f(M + N + 1)/2] - ——, (2.24) N + M + 1 sin(27tf/2) H(f) = where M is the number of lagged values and N is the number of future values of the input (Oppenheim and Schafer, 1989, Ch. 6). Figure 2.10b plots ...
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 |
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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 calculated components computed correlation covariance cycle decomposition defined determined difference discrete distribution dynamics Equation error estimator example exchange feedforward network Figure Fourier transform frequency function gain function Gaussian given Haar hidden units increases indicate input interval 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 transform values variables variance vector volatility wavelet coefficients wavelet details wavelet filter wavelet scale wavelet transform wavelet variance weights zero