Comparative Study of Box & Jenkins Methodologies and Singular Spectral Analysis for Forecasting Average Monthly Flows
Name: Michel Trarbach Bleidorn
Type: MSc dissertation
Publication date: 25/04/2023
Advisor:
Name |
Role |
|---|---|
| Antonio Sérgio Ferreira Mendonça | Advisor * |
Examining board:
| Name |
Role |
|---|---|
| Antonio Sérgio Ferreira Mendonça | Advisor * |
| Gutemberg Hespanha Brasil | External Examiner * |
| José Antônio Tosta dos Reis | Internal Examiner * |
| Wanderson de Paula Pinto | External Examiner * |
Summary: Flow forecasting is one of the biggest challenges in hydrology. From the water resources management perspective, flow forecasting is of fundamental importance. The prognosis of liquid discharges can help decision-making about the hydroelectric power generation reservoirs operation and the water multiple uses management, providing information that allows balances computation between availability and future demands of water resources, allowing the contour of potential water use conflicts and the indication of rational use goals. Various forecasting methods have been developed and employed over time. Among them, the one proposed by the statisticians Box and Jenkins stands out, who, in the 1970s, developed the Autoregressive and Moving Averages (ARMA) class of models. One of the most employed in river flow modeling is the Seasonal Autoregressive Integrated Moving Average model (SARIMA) which incorporates seasonality and differentiation to outline nonstationarity. The requirement of assumptions to data and residuals, such as normality, which often makes it necessary to use mathematical transformations, makes its use difficult. On the other hand, methods that do not require distributive assumptions to the data have gained prominence in recent decades, such as Singular Spectral Analysis (SSA). SSA is considered a powerful tool for time series analysis, with its development attributed to the authors Broomhead & King in the 1980s. Despite the technique potential, few applications are observed in the specific literature on forecasting river flows. Therefore, the present study aimed to evaluate the performance of SARIMA time series models and the SSA technique in forecasting flows, in a holistic application for different rivers fluviometric series in Brazil. Based on the performance indicators used in the study (Bias, Mean Squared Error, Mean Absolute Error, Nash and Sutcliffe Coefficients, Pearson Concordance and Correlation Index) and the Relative Percentage Difference of these indicators, it was verified at forecast stage, the superiority of SSA technique in relation to the SARIMA models. The study findings allow inferring that the SSA can be a useful tool to assist in the water resources management.
