Description
Book Synopsis
This book presents two new decomposition methods to decompose a time series in intrinsic components of low and high frequencies. The methods are based on Singular Value Decomposition (SVD) of a Hankel matrix (HSVD). The proposed decomposition is used to improve the accuracy of linear and nonlinear auto-regressive models.
Linear Auto-regressive models (AR, ARMA and ARIMA) and Auto-regressive Neural Networks (ANNs) have been found insufficient because of the highly complicated nature of some time series. Hybrid models are a recent solution to deal with non-stationary processes which combine pre-processing techniques with conventional forecasters, some pre-processing techniques broadly implemented are Singular Spectrum Analysis (SSA) and Stationary Wavelet Transform (SWT). Although the flexibility of SSA and SWT allows their usage in a wide range of forecast problems, there is a lack of standard methods to select their parameters.
The proposed decomposition HSVD and Multilevel SVD are described in detail through time series coming from the transport and fishery sectors. Further, for comparison purposes, it is evaluated the forecast accuracy reached by SSA and SWT, both jointly with AR-based models and ANNs.
Table of ContentsPreface
1. Time Series and Forecasting
1.1. Introduction
1.2. Time series
1.3. Linear Autoregressive Models
1.4. Artificial Neural Networks
1.5. Hybrid models
1.5.1. Singular Spectrum Analysis
1.5.2. Wavelet Transform
1.6. Forecasting Accuracy Measures
1.7. Empirical Applications
1.7.1. Traffic Accidents Forecasting based on AR, ANNs and Hybrid models.
1.7.2. Anchovy Stock Forecasting based on AR, ANNs and Hybrid models.
1.7.3. Sardine Stock Forecasting based on AR, ANNs and Hybrid models.
2. Decomposition methods based on Singular Value Decomposition of a Hankel matrix
2.1. Introduction
2.2. Eigenvalues and Eigenvectors
2.3. Theorem of Singular Values Decomposition
2.4. One-level Singular Value Decomposition of a Hankel matrix
2.4.1. Embedding
2.4.2. Decomposition
2.4.3. Unembedding
2.4.4. Window Length Selection
2.5. Multi-level Singular Value Decomposition of a Hankel matrix
2.5.1. Embedding
2.5.2. Decomposition
2.5.3. Unembedding
2.5.4. Singular Spectrum Rate
2.6. Empirical Applications
2.6.1. Extraction of Components from traffic accidents time series based on HSVD and MSVD
2.6.2. Extraction of Components from fishery time series based on HSVD and MSVD
3. Forecasting based on components
3.1. Introduction
3.2. One-step ahead forecasting
3.3. Multi-step ahead forecasting
3.3.1. Direct Strategy
3.3.2. MIMO Strategy
3.4. Empirical Applications
3.4.1. Forecasting of traffic accidents based on HSVD and MSVD
3.4.2. Forecasting of anchovy stock based on HSVD and MSVD
3.4.3. Forecasting of sardine stock based on HSVD and MSVD
List of Figures
List of Tables
List of Acronyms
List of Symbols
References
