The Analysis of Directional Time Series: Applications to Wind Speed and Direction

I: Wind Data Analysis.- 1. Introduction.- 1.1. Surface Wind Observation.- 1.2. General Weather Pattern.- 1.3. Outline of this Monograph.- 2. The Initial Decomposition.- 2.1. General Background.- 2.2. Robust Filtering.- 2.3. Univariate Filter Study.- 2.4. Multivariate Filter Study.- 2.5. Application to Wind Series.- 2.6. Appendix: Mathematical Details.- 3. The Geostrophic Component.- 3.1. The Geostrophic Wind.- 3.2. Estimation of the Geostrophic Wind.- 3.3. Comparison with the Geostrophic Component.- 3.4. Synoptic States.- 3.5. Appendix: Derivation of the Geostrophic Wind Equation.- 4. The Land and Sea Breeze Cycle.- 4.1. The Nature of the Circulation.- 4.2. Statistical Approach.- 4.3. Land and Sea Breeze Pattern.- 5. Short-Term Events.- 5.1. Meteorological Patterns.- 5.2. Wind Classification.- 5.3. Characteristics of Short-Term Events.- 5.4. Appendix: Removal of Storms.- II: Time Series of Directional Data.- 6. Time Series Models for Directional Data.- 6.1. Circular Variables.- 6.2. The von Mises Process.- 6.3. The Wrapped Autoregressive Process.- 7. Measures of Angular Association.- 7.1. Desirable Properties.- 7.2. Bivariate Angular Distributions.- 7.3. Review of Measures of Association.- 7.4. A Proposal for Vector Valued Time Series.- 7.5. Appendix: Non-von Mises Marginals.- 8. Comparison of Different Measures of Association.- 8.1. Independent Bivariate Directional Data.- 8.2. Time Series of Directional Data.- 9. Inference from the Wrapped Autoregressive Process.- 9.1. Introduction.- 9.2. Equating Theoretical and Empirical Circular Variance (EQ).- 9.3. Corrected EQ-Estimation (EC).- 9.4. Bayes Estimation (BA).- 9.5. Maximum Likelihood Estimation (ML).- 9.6. Characteristic Function Estimation (CF).- 9.7. Numerical Comparison of Estimators.- 10. Application to Series of Residual Wind Directions.- 11. Conclusions and Summary of Results.- List of Symbols.