Opis książki:
The book Wavelet analysis in economic applications summarises a five-year research project financed by the Polish Ministry of Science and Higher Education under the grant no. N N111 [zasłonięte]135, entitled Wavelet decompositions in economic applications: exploratory analysis, business cycle synchronisation and forecasting. It can serve as a concise and accessible guide to different types of wavelet transformations: the continuous wavelet transform, the decimated and non-decimated discrete wavelet transform as well as the wavelet packet transform. It also covers many original applications of mainly the discrete wavelet methodology like portfolio optimisation, examining comovements and lead-lag relations, transfer function modelling, estimation of stochastic signals and forecasting, offering both a new perspective as well as practical solutions for certain statistical modelling problems in finance, economics and marketing.
Acknowledgements / 5 Abbreviations and notation / 9 Chapter I Introduction / 15 1.1. Waves and wavelets in economics / 15 1.2. From Fourier to wavelet transform / 20 1.3. Other places where 'time meets frequency' / 29 1.4. What is this book about? / 32 Chapter II The discrete wavelet transforms / 36 2.1. Introduction / 36 2.2. The DWT and MODWT / 37 2.3. The Daubechies filters / 47 2.4. Exploratory data analysis with discrete wavelets / 56 2.5. The decorrelation property of the DWT / 60 Chapter III Beyond the DWTs / 70 3.1. Introduction / 70 3.2. The discrete wavelet packet transforms / 71 3.3. The multiresolution approximation / 79 3.4. The continuous wavelet transform / 91 Chapter IV Wavelet analysis of variance and covariance / 101 4.1. Introduction / 101 4.2. The wavelet variance / 102 4.3. Testing for change in variance / 105 4.4. The wavelet covariance, cross-covariance, correlation and cross-correlation / 108 4.5. Efficient frontiers and stability of minimum variance portfolios across scales / 113 4.6. Summary and discussion / 119 Chapter V Discrete wavelet analysis of bivariate spectra / 124 5.1. Introduction / 124 5.2. The maximal overlap discrete Hilbert wavelet transform / 125 5.3. Discrete wavelet analysis of coherence and phase spectra / 132 5.4. Estimation and confidence intervals / 142 5.5. Wavelet time delay estimation - comparison of approaches / 150 5.6. An empirical illustration - the dependence between business and stock market cycles / 155 5.7. Summary and discussion / 163 Chapter VI Modelling and forecasting with wavelets / 170 6.1. Introduction / 170 6.2. The Haar transfer function model / 173 6.3. Empirical examples of Haar transfer function models / 180 6.4. Wavelet forecasting of univariate time series / 194 6.5. Signal estimation via wavelet smoothing / 199 6.6. Forecasting via wavelet smoothing / 207 6.7. Summary and discussion / 217 References / 231
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