Monday, October 14, 2019
Forecasting Ensemble Empirical Mode Decomposition
Forecasting Ensemble Empirical Mode Decomposition Introduction This chapter introduces the background of time series and the importance of forecasting. Theà motivation behind the project is elaborated and finally the aims and objectives are given. 1.1 Background Time series can be defined as a sequence of observations or measurements that are takenà at equally spaced timed interval (Xu, 2012). Hence, it is a stochastic process and can beà expressed as (Xu, 2012): x(t) = xi; i = 1; 2; :::;N: (1.1) Some examples of time series data include yearly profit, monthly recorded temperature,à hourly electrical consumption. Time series are classified into two categories mainly the stationary time series andà non stationary time series. Stationary time series consist of data which remain fixed irrespectiveà of the whereabouts. A stationary process is one where the mean, varianceà and autocorrelation do not vary with time (Nau, 2014). For example, the financial stockà change of Mauritius remains constant in Mauritius as well as in any other place in theà world. Non stationary time series on the contrary involve data that keeps changing overà time. For instance, if we consider meteorological data of Mauritius, the data collected areà varied considerably from region to region as well as accordingly throughout the year. Forà example, we have more rainfall over regions on the Central Plateau compared with theà coastal regions as demonstrated by Figure (1.1) which illustrates the variation of rainfallà collected for Mauritius over distinct regions from 1960 1990.while figure 1.2 shows theà difference in signal data between the two classes of time series. All meteorological dataà including temperature, wind speed, solar irradiance irradiance, sea pressure and manyà more weather parameters similar to rainfall have variations both in time and location. Hence, we can conclude that meteorological data are non stationary in nature. Figure 1.1: Distribution of rainfall for Mauritius for the year 1961-1990 Source:http://unfccc.int/resource/docs/natc/maunc1/chap1/chapter1.htm Figure 1.2: Difference between stationary and non stationary series , Source:http://en.wikipedia.org/wiki/Stationaryprocess Time series modeling is a vast field of research. The analysis of time series signals canà be extrapolated to meet demands of analytical results and predicting results in variousà fields, such as : Economical Climatological Biological à Financial and others Due to its implementation in various fields, continuous research are been done in order toà design model for forecasting with better accuracy and efficiency. The behaviour of timeà series is governed by four main aspects namely trend, seasonal variation, cyclic variationà and random variation (Xu, 2012). Trend of time series can be pictured as the evolution ofà the series over time and hence gives the forthcoming pathway of the data. Hence, trendà analysis is very efficient in predicting extensive behaviour of data. Phonetically, a generalà assumption in most time series techniques is that the data are stationary. Transformationà of non stationary to stationary is often done to manipulate the data for analysis. Forecasting is of high precedence in application of time series as it can predict futureà events based on past events, specially when using in the field of limited resources. Forecastingà may be classified as a prediction, a projection or estimate of a future activity. Inà fact, we have two types of forecasting methods namely qualitatively and quantitatively. Qualitative methods are non mathematical computations whereas quantitative methodsà are rather objective methods based on mathematical computations. 1.2 Motivation We belong to a world of success in which one of the leading factor to success is our abilityà to predict the result of our choices making all of us in a way or another forecasters. Climate consists of one of the major applications of forecasting. Over years, newer andà better models are been investigated so as to improve forecasting accuracy as much asà possible. Investigating weather parameters is highly necessary so as to be able to predictà weather situations which are required in various fields such as aviation, shipping,à oceanography and agriculture. Moreover, it is helps to evade weather hazards. Mauritiusà has being confronted to drastic changes in weather conditions recently. We haveà already a weather station which is deploying its best methods for weather forecastingà but is unable to predict accurately unexpected changes in weather, for example the recentà flash flood in March 2013 or one of the most worst drought that stroke Mauritiusà in 2002. Therefore, in order to prevent further incidents or life taking calamities, it is ofà high importance to have accurate and early predictive models in order to take preventiveà measures to make sure that the population is safe well before such events occur. Thisà project comprises of investigating a different method for forecasting meteorological data. Throughout this project we will be dealing with time series models based of data whichà has been collected over years and try to foresee future events based on the fundamentalsà patterns confined within those data. The most commonly used forecasting model for time series was the Box Jenkinsà models (ARIMA and ARMA models) (Peel et al., 2014). They are non-static models thatà are beneficial in forecasting changes in a process. Many models have further been developedà among which is listed the Hilbert Huang Transform (Huang and Shen, 2005). Since climate data are of nonlinear and non-stationary nature, Hilbert Huang Transformà is capable of improving accuracy of forecast since most previous traditional methodsà are designed for stationary data while this method is efficient in both cases. On the otherà hand, recognizing all the advantages of Artificial Neural Network, it is of no surprise thatà this methodology has gained so much interest in the this field of application. ANN haveà proven to be more effective, compared to other traditional methods such as Box-Jenkins,à regression models or any other models (Khashei and Bijari, 2009) as a tool for forecasting. Both successful models mentioned however carries their own associated percentageà error. As a means to minimize error, both models can be combined to give rise to a newà hybrid model with better performance capabilities. 1.3 Aims And Objectives 1. In this project, the aim is to develop a combined model from two completely differentà computational models for forecasting namely Ensemble Empirical Mode Decompositionà and Artificial Neural Network so as to improve accuracy of futureà predictions of time series data. 2. EEMD will be adopted as the decomposition technique to obtain a set of Intrinsicà Mode Functions (IMF) and residual for meteorological time series data for Mauritiusà signal while ANN will be the forecasting tool which will take as input parametersà the non obsolete IMFs. The results obtained will be compared with real data inà order evaluate the performance of the model. The idea is to reduce error associatedà with each model when employed separately as both models possess their own skillà in determining trend in complex data. 3. Eventually, the model will be applied to forecast meteorological data mainly rainfallà from MMS and wind speed from studies conducted by fellow colleagues. 1.4 Structure of Reportà 1. Chapter 2 consists of a literature review on the models and their applications 2. Chapter 3 introduces Ensemble Empirical Mode Decomposition and validate theà EMD model. 3. Chapter 4 introduces the Artificial Neural Network and validate the network. 4. Chapter 5 present the results from application of EEMD to meteorological data. Theà EEMD-ANN hybrid model is also introduced and validate. Finally the following isà applied to rainfall and wind speed data. 5. Chapter 6 presents the conclusion and the future work.
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