Wavelet analysis in economic applications

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 285135, 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

Joanna Bruzda