Forecasting Ensemble Empirical Mode Decomposition

Forecasting Ensemble Empirical Mode DecompositionIntroductionThis chapter introduces the background of clipping series and the importance of imageing. Themotivation behind the project is elaborated and finally the aims and objectives be flipn.1.1 BackgroundTime series outhouse be defined as a sequence of observations or measurements that ar takenat equally spaced clippingd interval (Xu, 2012). Hence, it is a stochastic process and can beexpressed as (Xu, 2012)x(t) = xi i = 1 2 N (1.1)Some examples of age series entropy include socio-economic classly profit, monthly record temperature,hourly electrical consumption.Time series are classified into two categories mainly the unmoving time series andnon stationary time series. Stationary time series consist of data which remain fixed irrespectiveof the whereabouts. A stationary process is one where the mean, varianceand autocorrelation do not vary with time (Nau, 2014). For example, the financial stockchange of Mauritius remains constant in Mauritius as well as in any other place in theworld. Non stationary time series on the contrary involve data that keeps changing overtime. For instance, if we consider meteoric data of Mauritius, the data collected are vary considerably from region to region as well as accordingly throughout the year. Forexample, we have more rain over regions on the Central plateau compared with thecoastal regions as demonstrated by Figure (1.1) which illustrates the variation of rainfallcollected for Mauritius over distinct regions from 1960 1990.while figure 1.2 shows thedifference in signal data between the two classes of time series. All meteorological dataincluding temperature, wind speed, solar irradiance irradiance, sea pressure and manymore weather condition 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 1961-1 990Sourcehttp//unfccc.int/resource/docs/natc/maunc1/chap1/chapter1.htmFigure 1.2 Difference between stationary and non stationary series ,Sourcehttp//en.wikipedia.org/wiki/StationaryprocessTime series modeling is a vast orbital cavity of research. The analysis of time series signals canbe extrapolated to meet demands of analytical results and look toing results in variousfields, such as EconomicalClimatologicalBiologicalFinancial and others delinquent to its implementation in various fields, continuous research are been done in order todesign model for forecasting with better true statement and efficiency. The deportment of timeseries is governed by four main aspects namely trend, seasonal variation, cyclic variationand random variation (Xu, 2012). Trend of time series can be pictured as the evolution ofthe series over time and hence gives the forthcoming pathway of the data. Hence, trendanalysis is very efficient in predicting extensive behaviour of data. Phonetically, a genera lassumption in most time series techniques is that the data are stationary. Transformationof non stationary to stationary is very much done to manipulate the data for analysis.Forecasting is of high precedence in application of time series as it can predict futureevents ground on past events, specially when using in the field of limited resources. Forecastingmay be classified as a prediction, a expulsion or estimate of a future activity. Infact, we have two types of forecasting regularitys namely qualitatively and quantitatively.Qualitative rules are non mathematical computations whereas quantitative methodsare rather objective methods based on mathematical computations.1.2 MotivationWe belong to a world of achievement in which one of the leading factor to success is our abilityto 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 andbetter models are been inves tigated so as to improve forecasting accuracy as much aspossible. Investigating weather parameters is highly necessary so as to be able to predictweather situations which are required in various fields such as aviation, shipping,oceanography and agriculture. Moreover, it is helps to evade weather hazards. Mauritiushas being confronted to drastic changes in weather conditions recently. We havealready a weather station which is deploying its best methods for weather forecastingbut is unable to predict accurately unexpected changes in weather, for example the recentflash flood in March 2013 or one of the most worst drought that stroking Mauritiusin 2002. Therefore, in order to prevent further incidents or life taking calamities, it is ofhigh importance to have accurate and early predictive models in order to take preventivemeasures to make sure that the population is safe well before such events occur. Thisproject comprises of investigating a different method for forecasting meteorolo gical data.Throughout this project we will be dealing with time series models based of data whichhas been collected over years and essay to foresee future events based on the fundamentalspatterns confined within those data.The most commonly used forecasting model for time series was the recess Jenkinsmodels (ARIMA and ARMA models) (Peel et al., 2014). They are non-static models thatare beneficial in forecasting changes in a process. Many models have further been developedamong which is listed the Hilbert Huang Transform (Huang and Shen, 2005).Since climate data are of nonlinear and non-stationary nature, Hilbert Huang Transformis capable of improving accuracy of forecast since most previous traditional methodsare designed for stationary data while this method is efficient in both cases. On the otherhand, recognizing all the advantages of Artificial Neural Network, it is of no surprise thatthis methodology has gained so much interest in the this field of application. ANN haveprove n to be more effective, compared to other traditional methods such as Box-Jenkins,regression models or any other models (Khashei and Bijari, 2009) as a tool for forecasting.Both successful models mentioned however carries their own associated percentageerror. As a means to minimize error, both models can be combined to give rise to a newhybrid model with better performance capabilities.1.3 Aims And Objectives1. In this project, the aim is to develop a combined model from two entirely differentcomputational models for forecasting namely Ensemble Empirical Mode Decompositionand Artificial Neural Network so as to improve accuracy of futurepredictions of time series data.2. EEMD will be adopted as the decomposition technique to obtain a set of IntrinsicMode Functions (IMF) and remainder for meteorological time series data for Mauritiussignal while ANN will be the forecasting tool which will take as input parametersthe non antiquated IMFs. The results obtained will be compared with rea l data inorder evaluate the performance of the model. The idea is to reduce error associatedwith each model when employed one at a time as both models possess their own skillin determining trend in complex data.3. Eventually, the model will be applied to forecast meteorological data mainly rainfallfrom MMS and wind speed from studies conducted by fellow colleagues.1.4 Structure of Report1. Chapter 2 consists of a literature review on the models and their applications2. Chapter 3 introduces Ensemble Empirical Mode Decomposition and validate theEMD 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. TheEEMD-ANN hybrid model is also introduced and validate. Finally the following isapplied to rainfall and wind speed data.5. Chapter 6 presents the conclusion and the future work.