Forecasting Ensemble Empirical Mode Decomposition

Forecasting Ensemble a posteriori regularity DecompositionIntroductionThis chapter introduces the background of clip series and the importance of forecasting. Theindigence behind the pick up is elaborated and fin in ally the aims and objectives ar given.1.1 Background cartridge holder series can be defined as a season of observations or measurements that be takenat equally spaced time interval (Xu, 2012). Hence, it is a stochastic process and can be explicit as (Xu, 2012)x(t) = xi i = 1 2 N (1.1) about examples of time series data include yearly profit, monthly preserve temperature,hourly electrical consumption.Time series atomic number 18 classified into devil categories mainly the nonmoving time series andnon stationary time series. unmoving time series consist of data which remain fixed regardlessof 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 Ma uritius remains eternal in Mauritius as well as in each otherwise place in theworld. Non stationary time series on the black eye involve data that keeps changing all overtime. For instance, if we consider meteorological data of Mauritius, the data collected argonvaried considerably from orbit to region as well as accordingly throughout the year. Forexample, we have oft pelting over regions on the Central Plateau compared with thecoastal regions as demonstrated by Figure (1.1) which illustrates the variation of peltingcollected for Mauritius over distinct regions from 1960 1990. period figure 1.2 shows thedifference in signal data amidst the two classes of time series. All meteorological dataincluding temperature, wind hurrying, solar irradiance irradiance, sea pressure and many more(prenominal) go parameters similar to rainfall have variations both(prenominal) 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 1961-1990Sourcehttp//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 exampleing is a vast plain of research. The analysis of time series signals canbe extrapolated to meet demands of analytical burdens and predicting results in variousfields, such as economicClimatologicalBiologicalFinancial and othersDue to its implementation in various fields, constant research are been done in erect todesign feigning for forecasting with better accuracy and efficiency. The behaviour of timeseries is governed by four main aspects namely trend, seasonal variation, cyclic variationand hit-or-miss variation (Xu, 2012). Trend of time series can be conceive of as the evolution ofthe series over time and hence gives the extravertive pathway of the data. Hence, trendanalysis is very efficient in predicting gigantic behaviour of data. Phonetically, a generalassumption in most time series techniques is that the data are stationary. Transformationof non stationary to stationary is a lot done to manipulate the data for analysis.Forecasting is of high precedence in application of time series as it can predict prospectiveevents found on past events, specially when using in the field of limited resources. Forecastingmay be classified as a prediction, a projection or estimate of a emerging activity. Infact, we have two types of forecasting methods namely qualitatively and quantitatively.Qualitative methods are non mathematical computations whereas quantitative methodsare rather objective methods based on mathematical computations.1.2 MotivationWe belong to a world of success 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, unexampleder andbetter types are been investigated so as to improve forecasting accuracy as oftentimes 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 ineffective to predict completely unexpected changes in weather, for example the recent fool away flood in March 2013 or one of the most whip drought that stroke Mauritiusin 2002. Therefore, in order to prevent bring forward incidents or life taking calamities, it is ofhigh importance to have accurate and early predictive models in order to take preventivemeasures to find sure that the population is safe well before such events occur. Thispro ject comprises of investigating a different method for forecasting meteorological data.throughout this project we give be dealing with time series models based of data whichhas been collected over years and try to foresee approaching events based on the fundamentalspatterns confined within those data.The most usually used forecasting model for time series was the Box Jenkinsmodels (ARIMA and ARMA models) (Peel et al., 2014). They are non-static models thatare beneficial in forecasting changes in a process. many a(prenominal) models have further been createedamong 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 slushy Neural intercommunicate, it is of no surpris e thatthis methodology has gained so much interest in the this field of application. ANN haveproven 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 nevertheless 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 completely 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 go forth be adopted as the guff technique to obtain a set of IntrinsicMode Functions (IMF) and oddment for meteorological time series data for Mauritiussignal while ANN will be the forecasting tool which will take as stimulus parametersthe non obsolete IMFs. The results obtained will be compared with real data inorder evaluate the performance of the model. The idea is to reduce error associatedwith each model when employed separately as both models possess their own dexterityin 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.