Functional Modeling and Forecasting of Complex Time Series Data

Abstract

In today’s world, systematically obtaining several measurements results in a large volume of data collection. Due to non-availability of information on which ones will be appropriate to the phenomenon under study makes the data complex. On the other hand, complex data produce new opportunities for data analysts to present and solve new problems. The data from the energy sector, in general, and from the electricity market, in particular, are an excellent example of such complex data. Data from the electricity market generally exhibit specific features, e.g., the presence of extreme values, spikes or jumps, seasonal patterns, nonlinearity, multiple periodicities, long-trend, mean reversion, and bank holidays effect, etc., and hence, can be considered a complex data set. On the other hand, modeling and forecasting electricity demand and prices are highly important in today’s liberalized electricity markets for effectively managing the power system. In addition, the forecasts are required for a complete next day as electricity prices or demand are determined a day before the physical delivery. The main aim of this research work is to propose and investigate the forecasting perfor mance of models based on functional data analysis, a relatively less explored area in energy research. Functional data analysis deals with the analysis and theory of data that are in the form of functions, images and shapes, or more general objects. In the context of the electricity market, the daily demand or price profile is considered a functional object and the 24 (48) hours (half-hours) are discretized points of this functional curve. Using the functional data analysis approach, this dissertation tackles the modeling and forecasting of electricity demand/price using the following approaches. In the first case (Chapter 4 and Chapter 5), the electricity prices or demand time series is f irst treated for the extreme values. The filtered series is then divided into deterministic and stochastic components. The generalized additive modeling technique is used to model the v deterministic component that accounts for the long-trend, yearly and weekly periodicities, and the effect of bank holidays. Once the deterministic component is estimated, the stochastic component is obtained that is modeled and forecasted using different functional and classical models. In particular, we use functional autoregressive (FAR), FAR with exogenous variable (FARX), classical univariate AR model, and a na¨ıve model to model and forecast the stochastic component. Data from the Italian electricity market and Nord Pool electricity market are used and the one-day ahead out-of-sample forecast is obtained for a whole year. The forecasting performance is evaluated using different forecasting accuracy measures. The results indicate that the functional modeling approach produces superior forecasting results while the FARX outperforms FAR, classical AR models, and na¨ ıve models. In the second approach (Chapter 6), this thesis evaluates the performance of partial and fully functional models for forecasting electricity prices from the British electricity market. In the case of the partial functional model, the electricity price series is divided into deterministic and stochastic components. The deterministic component is modeled using the methodology described earlier, whereas for the stochastic component, FAR and AR models are used to obtain day-ahead out-of-sample electricity price forecasts. On the other hand, the fully functional model jointly estimates the deterministic and stochastic components using the FARX model. The results from partial and fully functional models suggest that the succeeding is superior to proceeding as it produces lower forecasting errors