Dissertations / Theses on the topic 'ARIMA/SARIMA'

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Esta dissertação tem como principal objetivo apresentar os modelos de previsão de arrecadação do ICMS, por segmento econômico, para a Secretaria da Fazenda do Estado de Pernambuco, utilizando as técnicas econométricas. Objetiva-se, com essa pesquisa, disponibilizar aos gestores púbicos do Estado mais um modelo de previsão consistente e com certo grau de confiabilidade. Para tanto, utilizou-se da metodologia Box-Jenkins, mais especificamente os modelos: ARIMA - modelo autorregressivo integrado de média móvel, e SARIMA - modelo autorregressivo integrado de média móvel sazonal, e o software RATS (Regression Analyse Time Series). O trabalho apresenta o comportamento da arrecadação de ICMS no Estado e uma revisão da literatura, onde são abordados os principais conceitos teóricos utilizados, bem como uma análise dos resultados obtidos. Conclui-se que o modelo de previsão utilizando séries temporais, em função de sua capacidade preditiva, pode se transformar em um valioso instrumento para auxiliar na elevação da receita tributária no Estado de Pernambuco, dentro da capacidade contributiva de cada contribuinte

Two real time series, one discussing the area of energy, other discussing the area of economy. By the energetic area we will be dealing with the electric power consumption in the USA, by the economic area we will be dealing with the progress of index PX50. We will try to approve the validity of hypothesis that with some test functions we will be able to set down the accidental unit distribution in these two time series.

This work concerns the creation of automatized procedure of ARIMA and SARIMA class model choice according to Box-Jenkins methodology and in this connection, also deals with force testing of unit roots and analysis of applying of informatics criteria when choosing a model. The goal of this work is to create an application in the environment R that can automatically choose a model of time array generating process. The procedure is verified by a simulation study. In this work an effect of values of generating ARMA (1,1) model processes parameters is examined, for his choice and power of KPSS test, augmented Dickey-Fuller and Phillips-Peron test of unit roots.

I denna uppsats har olika metoder för att göra prognoser för ekonomiska tidsserier med säsongsmönster jämförts och utvärderats. Frågan som undersökningen har kretsat kring är: Vilken metod är bäst lämpad för att göra prognoser av tidsserier med säsongsmönster? De metoder som jämförs är säsongsrensningsmetoderna Census II och TRAMO/SEATS, säsongsmodellerna SARIMA och ARIMA med dummyvariabler för säsong samt en metod där medelvärdena från de fyra första metoderna används som prognoser. För att genomföra undersökningen har dessa metoder tillämpats på fyra ekonomiska tidsserier, nämligen: konsumtion, BNP, export samt byggstarter. Resultatet från undersökningen är att säsongsmodellerna är bäst för konsumtionsserien, säsongsrensningsmetoderna är bäst för BNP- och exportserien och den ena säsongsmodellen (SARIMA) är bäst för byggstartsserien medan den andra (ARIMA-dummy) är den sämsta. Val av prognosmetod beror med andra ord på vilken serie som ska prognostiseras.

Os processos espaço-temporais vêm ganhando destaque nos últimos anos, em razão do aumento de estudos compreendendo variáveis que apresentam interação entre as dimensões espacial e temporal. Com o objetivo de modelar esses processos, Pfeifer e Deutsch (1980a) propuseram uma extensão da classe de modelos univariados de Box-Jenkins, denominada por modelo espaço-temporal autoregressivo de média móvel (STARMA). Essa classe de modelos é utilizada para descrever dados de séries temporais espacialmente localizadas. Os processos passíveis de modelagem via classe de modelos STARMA são caracterizados por observações de variáveis aleatórias, em que os locais a serem incorporados no modelo são fixos no espaço. A dependência entre as n séries temporais é modelada por meio da matriz de ponderação, de modo que os modelos da classe STARMA expressem cada observação no tempo t e na localização i como uma média ponderada de combinações lineares das observações anteriores e a inovação defasada no espaço e no tempo conjuntamente. Dada a nova classe de modelos, os objetivos deste estudo foram apresentar a classe de modelos STARMA, implentar computacionalmente, no software R, rotinas que permitam a análise de dados espaço-temporais, com as rotinas implementadas estabelecer e testar modelos de séries temporais aos dados de temperaturas mínimas médias mensais de 8 estações meteorológicas situadas no Paraná e comparar a classe de modelos STARMA com a classe de modelos univariados proposta por Box e Jenkins (1970). Com este estudo verificou-se que na apresentação da classe de modelos STARMA há complexidade no conceito de ordens de vizinhança e na identificação dos modelos espaço-temporais. Em relação a criação de rotinas responsáveis pelas análises de dados espaço-temporais observou-se dificuldades em sua implementação, principalmente no momento de estimação dos parâmetros. Na comparação da classe de modelos STARMA, multivariada, com a classe de modelos SARIMA, univariada, constatou-se que ambos os modelos se ajustaram de maneira satisfatória aos dados, produzindo previsões acuradas.
Spatio-temporal processes have been highlighted lately, due to the increase of studies approaching variables that present interactions between the spatial and temporal dimensions. In order to model these processes, Pfeifer e Deutsch (1980a) have suggested an extension of the Box-Jenkins univariate model class, named spatio-temporal autoregressive moving-average model (STARMA). This model class is used to describe spatially located time series data. The processes prone to be modeled via the STARMA model class are characterized by observations of random variables, in which the locations to be incorporated in the model are spatially fixed. The dependence between the n time series is modeled through the weighing matrix. So STARMA models express each observation at time t and location i as a weighed mean of linear combinations of the previous observations and the jointly lagged innovation in space and time. Given the new class models, the objectives of this study were to present a class of models STARMA, implentar computationally, in textit R software, routines that allow the analysis of spatio-temporal data with the routines implemented to establish and test models time series data of monthly average minimum temperatures of 8 meteorological stations located in Paraná and compare the class of models STARMA with the class of univariate models proposed by Box e Jenkins (1970). With this study it was found that the presentation of the class of models STARMA no complexity in the concept of ordered neighborhood and identification of spatio-temporal models. Regarding the creation of routines responsible for the analysis of spatio-temporal observed difficulties in its implementation, especially at the time of estimation of parameters. In comparison class STARMA models, multivariate, with the class of SARIMA models, univariate, it was found that both models were adjusted satisfactorily to the data, producing accurate forecasts.

n the electrical power grid, the power load is not constant but continuouslychanging. This depends on many different factors, among which the habits of theconsumers, the yearly seasons and the hour of the day. The continuous change inenergy consumption requires the power grid to be flexible. If the energy provided bygenerators is lower than the demand, this is usually compensated by using renewablepower sources or stored energy until the power generators have adapted to the newdemand. However, if buffers are depleted the output may not meet the demandedpower and could cause power outages. The currently adopted practice in the indus-try is based on configuring the grid depending on some expected power draw. Thisanalysis is usually performed at a high level and provide only some basic load aggre-gate as an output. In this thesis, we aim at investigating techniques that are able topredict the behaviour of loads with fine-grained precision. These techniques couldbe used as predictors to dynamically adapt the grid at run time. We have investigatedthe field of time series forecasting and evaluated and compared different techniquesusing a real data set of the load of the Swedish power grid recorded hourly throughyears. In particular, we have compared the traditional ARIMA models to a neuralnetwork and a long short-term memory (LSTM) model to see which of these tech-niques had the lowest forecasting error in our scenario. Our results show that theLSTM model outperformed the other tested models with an average error of 6,1%.

This study aims to investigate short-to-medium forecasting and simulation of streamflow, water levels, and sediments in Canada using Seasonal Autoregressive Integrated Moving Average (SARIMA) time series models. The methodology can account for linear trends in the time series that may result from climate and environmental changes. A Universal Canadian forecast Application using python web interface was developed to generate short-term forecasts using SARIMA. The Akaike information criteria was used as performance criteria for generating efficient SARIMA models. The developed models were validated by analyzing the residuals. Several stations from the Canadian Hydrometric Database (HYDAT) displaying a linear upward or downward trend were identified to validate the methodology. Trends were detected using the Man-Kendall test. The Nash-Sutcliffe efficiency coefficients (Nash ad Sutcliffe, 1970) of the developed models indicate that they are acceptable. The models can be used for short term (1 to 7 days) and medium-term (7 days to six months) forecasting of streamflow, water levels and sediments at all Canadian hydrometric stations. Such a forecast can be used for water resources management and help mitigate the effects of floods and droughts. The models can also be used to generate long time-series that can be used to test the performance of water resources systems. Finally, we have automated the process of analysis, model-building and forecasting streamflow, water levels, and sediments by building a python-based application easily extendable and user-friendly. Therefore, automating the SARIMA calibration and forecasting process for all Canadian stations for the HYDAT database will prove to be a very useful tool for decision-makers and other entities in the field of hydrological study.

Nella presente tesi, si è discusso sul corretto trattamento dei dati di posizione, provenienti da una stazione permanente GPS in PPP, per studiarne l’andamento e successivamente elaborarne le previsioni per il futuro. E' stato utlizzato un approccio con la classe del Modelli ARIMA implementati su linguaggio Python.

The mobile traffic in cellular networks is increasing in a steady rate as we go intoa future where we are connected to the internet practically all the time in one wayor another. To map the mobile traffic and the volume pressure on the base stationduring different time periods, it is useful to have the ability to predict the trafficvolumes within cellular networks. The data in this work consists of 4G cellular trafficdata spanning over a 7 day coherent period, collected from cells in a moderately largecity. The proposed method in this work is ARIMA modeling, in both original formand with an extension where the coefficients of the ARIMA model are re-esimated byintroducing some user characteristic variables. The re-estimated coefficients produceslightly lower forecast errors in general than a isolated ARIMA model where thevolume forecasts only depends on time. This implies that the forecasts can besomewhat improved when we allow the influence of these variables to be a part ofthe model, and not only the time series itself.

Intelligenta Transportsystem (ITS) utgör idag en central del i arbetet att försöka höja kvaliteten i transportnätverken, genom att exempelvis ge stöd i arbetet att leda trafik i realtid och att ge trafikanter större möjlighet att ta informerade beslut gällandes sin körning. Kortsiktig prediktion av trafikdata, däribland trafikvolym, spelar en central roll för de tjänster ITS-systemen levererar. Den starka teknologiska utvecklingen de senaste decennierna har bidragit till en ökad möjlighet till att använda datadriven modellering för att utföra kortsiktiga prediktioner av trafikdata. Säsongsbaserad ARIMA (SARIMA) är en av de vanligaste datadrivna modellerna för modellering och predicering av trafikdata, vilken använder mönster i historisk data för att predicera framtida värden. Vid modellering med SARIMA behöver en mängd beslut tas gällandes de data som används till modelleringen. Exempel på sådana beslut är hur stor mängd träningsdata som ska användas, vilka dagar som ska ingå i träningsmängden och vilket aggregationsintervall som ska användas. Därtill utförs nästintill enbart enstegsprediktioner i tidigare studier av SARIMA-modellering av trafikdata, trots att modellen stödjer predicering av flera steg in i framtiden. Besluten gällandes de parametrar som nämnts saknar ofta teoretisk motivering i tidigare studier, samtidigt som det är högst troligt att dessa beslut påverkar träffsäkerheten i prediktionerna. Därför syftar den här studien till att utföra en känslighetsanalys av dessa parametrar, för att undersöka hur olika värden påverkar precisionen vid prediktion av trafikvolym. I studien utvecklades en modell, med vilken data kunde importeras, preprocesseras och sedan modelleras med hjälp av SARIMA. Studien använde trafikvolymdata som insamlats under januari och februari 2014, med hjälp av kameror placerade på riksväg 40 i utkanten av Göteborg. Efter differentiering av data används såväl autokorrelations- och partiell autokorrelationsgrafer som informationskriterier för att definiera lämpliga SARIMA-modeller, med vilka prediktioner kunde göras. Med definierade modeller genomfördes ett experiment, där åtta unika scenarion testades för att undersöka hur prediktionsprecisionen av trafikvolym påverkades av olika mängder träningsdata, vilka dagar som ingick i träningsdata, längden på aggregationsintervallen och hur många tidssteg in i framtiden som predicerades. För utvärdering av träffsäkerheten i prediktionerna användes MAPE, RMSE och MAE. Resultaten som experimentet visar är att definierade SARIMA-modeller klarar att predicera aktuell data med god precision oavsett vilka värden som sattes för de variabler som studerades. Resultaten visade dock indikationer på att en träningsvolym omfattande fem dagar kan generera en modell som ger mer träffsäkra prediktioner än när volymer om 15 eller 30 dagar används, något som kan ha stor praktisk betydelse vid realtidsanalys. Därtill indikerar resultaten att samtliga veckodagar bör ingå i träningsdatasetet när dygnsvis säsongslängd används, att SARIMA-modelleringen hanterar aggregationsintervall om 60 minuter bättre än 30 eller 15 minuter samt att enstegsprediktioner är mer träffsäkra än när horisonter om en eller två dagar används. Studien har enbart fokuserat på inverkan av de fyra parametrarna var för sig och inte om en kombinerad effekt finns att hitta. Det är något som föreslås för framtida studier, liksom att vidare utreda huruvida en mindre träningsvolym kan fortsätta att generera mer träffsäkra prediktioner även för andra perioder under året.
Intelligent Transport Systems (ITS) today are a key part of the effort to try to improve the quality of transport networks, for example by supporting the real-time traffic management and giving road users greater opportunity to take informed decisions regarding their driving. Short-term prediction of traffic data, including traffic volume, plays a central role in the services delivered by ITS systems. The strong technological development has contributed to an increased opportunity to use data-driven modeling to perform short-term predictions of traffic data. Seasonal ARIMA (SARIMA) is one of the most common models for modeling and predicting traffic data, which uses patterns in historical data to predict future values. When modeling with SARIMA, a variety of decisions are required regarding he data used. Examples of such decisions are the amount of training data to be used, the days to be included in training data and the aggregation interval to be used. In addition, one-step predictions are performed most often in previous studies of SARIMA modeling of traffic data, although the model supports multi-step prediction into the future. Often, in previous studies, decisions are made concerning mentioned variables without theoretical motivation, while it is highly probable that these decisions affect the accuracy of the predictions. Therefore, this study aims at performing a sensitivity analysis of these parameters to investigate how different values affect the accuracy of traffic volume prediction. The study developed a model with which data could be imported, preprocessed and then modeled using a SARIMA model. Traffic volume data was used, which was collected during January and February 2014, using cameras located on highway 40 on the outskirts of Gothenburg. After differentiation of data, autocorrelation and partial autocorrelation graphs as well as information criteria are used to define appropriate SARIMA models, with which predictions could be made. With defined models, an experiment was conducted in which eight unique scenarios were tested to investigate how the prediction accuracy of traffic volume was influenced by different amount of exercise data, what days was included in training data, length of aggregation intervals, and how many steps into the future were predicted. To evaluate the accuracy of the predictions, MAPE, RMSE and MAE were used. The results of the experiment show that developed SARIMA models are able to predict current data with good precision no matter what values were set for the variables studied. However, the results showed indications that a training volume of five days can generate a model that provides more accurate predictions than when using 15 or 30-day volumes, which can be of great practical importance in real-time analysis. In addition, the results indicate that all weekdays should be included in the training data set when daily seasonality is used, SARIMA modeling handles aggregation intervals of 60 minutes better than 30 or 15 minutes, and that one-step predictions are more accurate than when one or two days horizons are used. The study has focused only on the impact of the four parameters separately and not if a combined effect could be found. Further research is proposed for investigating if combined effects could be found, as well as further investigating whether a lesser training volume can continue to generate more accurate predictions even for other periods of the year.

The interest in modeling non-maturing deposits has skyrocketed ever since thefinancial crisis 2008. Not only from a regulatory and legislative perspective,but also from an investment and funding perspective.Modeling of non-maturing deposits is a very broad subject. In this thesis someof the topics within the subject are investigated, where the greatest focus inon the modeling of the deposit volumes. The main objective is to providethe bank with an analysis of the majority of the topics that needs to be cov-ered when modeling non-maturing deposits. This includes short-rate model-ing using Vasicek’s model, deposit rate modeling using a regression approachand a method proposed by Jarrow and Van Deventer, volume modeling usingSARIMA, SARIMAX and a general additive model, a static replicating port-folio based on Maes and Timmerman’s to model the behaviour of the depositaccounts and finally a liquidity risk model that was suggested by Kalkbrenerand Willing. All of these models have been applied on three different accounttypes: private transaction accounts, savings accounts and corporate savingsaccounts.The results are that, due to the current market, the static replicating portfoliodoes not achieve the desired results. Furthermore, the best volume model forthe data provided is a SARIMA model, meaning the effect of the exogenousvariables are seemingly already embedded in the lagged volume. Finally, theliquidity risk results are plausible and thus deemed satisfactory.
Intresset för att modellera inlåningsvolymer utan en kontrakterad förfallodaghar ökat markant sedan finanskrisen 2008. Inte bara sett utifrån ett perspek-tiv att uppfylla krav som ställs av tillsynsmyndigheter, men också sett utifrånbankens investerings-och finansieringsperspektiv.Målet med det här arbetet är att förse banken med en analys av majoritetenav de olika områdena som man behöver ta hänsyn till när man ska model-lera inlåningar utan förfallodatum, men med ett fokus på volymmodellering.I den här rapporten modelleras räntor (kortränta och kontoränta), kontovoly-merna, kontobeteendet samt likviditetsrisken. Detta görs med hjälp av Vasicekför korträntan, en regressionsmetod samt en metod som föreslagits av Jarrowoch Van Deventer för kontoräntan, SARIMA, SARIMAX och en generell ad-ditiv regressionsmetod för volymerna, en statisk replikeringsportfölj baseradpå Maes och Timmermans modell för att imitera kontona och slutligen så mo-delleras likviditetsrisken med ett ramverk som föreslagits av Kalkbrener ochWilling. Alla dessa nämnda modeller appliceras, där det är möjligt, på de treolika kontotyperna: privatkonton, sparkonton samt företagssparkonto.Resultatet är att räntemodelleringen samt replikeringsportföljen inte ger ade-kvata resultat på grund av den rådande marknaden. Vidare så ger en SARIMA-modell den bästa prediktionen, vilket gör att slutsatsen är att andra exogenavariabler redan är inneslutna i den fördröjda volymvariabeln. Avslutningsvisså ger likviditetsmodellen tillfredsställande resultat och antas vara rimlig.

This work aims to explore practical one-step-ahead forecasting of structurally changing data, an unstable behaviour, that real-life data connected to human activity often exhibit. This setting can be characterized as monitoring process. Various forecast models, methods and approaches can range from being simple and computationally "cheap" to very sophisticated and computationally "expensive". Moreover, different forecast methods handle different data-patterns and structural changes differently: for some particular data types or data intervals some particular forecast methods are better than the others, something that is usually not known beforehand. This raises a question: "Can one design a forecast procedure, that effectively and optimally switches between various forecast methods, adapting the forecast methods usage to the changes in the incoming data flow?" The thesis answers this question by introducing optimality concept, that allows optimal switching between simultaneously executed forecast methods, thus "tailoring" forecast methods to the changes in the data. It is also shown, how another forecast approach: combinational forecasting, where forecast methods are combined using weighted average, can be utilized by optimality principle and can therefore benefit from it. Thus, four classes of forecast results can be considered and compared: basic forecast methods, basic optimality, combinational forecasting, and combinational optimality. The thesis shows, that the usage of optimality gives results, where most of the time optimality is no worse or better than the best of forecast methods, that optimality is based on. Optimality reduces also scattering from multitude of various forecast suggestions to a single number or only a few numbers (in a controllable fashion). Optimality gives additionally lower bound for optimal forecasting: the hypothetically best achievable forecast result. The main conclusion is that optimality approach makes more or less obsolete other traditional ways of treating the monitoring processes: trying to find the single best forecast method for some structurally changing data. This search still can be sought, of course, but it is best done within optimality approach as its innate component. All this makes the proposed optimality approach for forecasting purposes a valid "representative" of a more broad ensemble approach (which likewise motivated development of now popular Ensemble Learning concept as a valid part of Machine Learning framework).
Denna avhandling syftar till undersöka en praktisk ett-steg-i-taget prediktering av strukturmässigt skiftande data, ett icke-stabilt beteende som verkliga data kopplade till människoaktiviteter ofta demonstrerar. Denna uppsättning kan alltså karakteriseras som övervakningsprocess eller monitoringsprocess. Olika prediktionsmodeller, metoder och tillvägagångssätt kan variera från att vara enkla och "beräkningsbilliga" till sofistikerade och "beräkningsdyra". Olika prediktionsmetoder hanterar dessutom olika mönster eller strukturförändringar i data på olika sätt: för vissa typer av data eller vissa dataintervall är vissa prediktionsmetoder bättre än andra, vilket inte brukar vara känt i förväg. Detta väcker en fråga: "Kan man skapa en predictionsprocedur, som effektivt och på ett optimalt sätt skulle byta mellan olika prediktionsmetoder och för att adaptera dess användning till ändringar i inkommande dataflöde?" Avhandlingen svarar på frågan genom att introducera optimalitetskoncept eller optimalitet, något som tillåter ett optimalbyte mellan parallellt utförda prediktionsmetoder, för att på så sätt skräddarsy prediktionsmetoder till förändringar i data. Det visas också, hur ett annat prediktionstillvägagångssätt: kombinationsprediktering, där olika prediktionsmetoder kombineras med hjälp av viktat medelvärde, kan utnyttjas av optimalitetsprincipen och därmed få nytta av den. Alltså, fyra klasser av prediktionsresultat kan betraktas och jämföras: basprediktionsmetoder, basoptimalitet, kombinationsprediktering och kombinationsoptimalitet. Denna avhandling visar, att användning av optimalitet ger resultat, där optimaliteten för det mesta inte är sämre eller bättre än den bästa av enskilda prediktionsmetoder, som själva optimaliteten är baserad på. Optimalitet reducerar också spridningen från mängden av olika prediktionsförslag till ett tal eller bara några enstaka tal (på ett kontrollerat sätt). Optimalitet producerar ytterligare en nedre gräns för optimalprediktion: det hypotetiskt bästa uppnåeliga prediktionsresultatet. Huvudslutsatsen är följande: optimalitetstillvägagångssätt gör att andra traditionella sätt att ta hand om övervakningsprocesser blir mer eller mindre föråldrade: att leta bara efter den enda bästa enskilda prediktionsmetoden för data med strukturskift. Sådan sökning kan fortfarande göras, men det är bäst att göra den inom optimalitetstillvägagångssättet, där den ingår som en naturlig komponent. Allt detta gör det föreslagna optimalitetstillvägagångssättetet för prediktionsändamål till en giltig "representant" för det mer allmäna ensembletillvägagångssättet (något som också motiverade utvecklingen av numera populär Ensembleinlärning som en giltig del av Maskininlärning).

This study uses aspects of time series methodology to model and forecast major taxes such as Personal Income Tax (PIT), Corporate Income Tax (CIT), Value Added Tax (VAT) and Total Tax Revenue(TTAXR) in the South African Revenue Service (SARS). The monthly data used for modeling tax revenues of the major taxes was drawn from January 1995 to March 2010 (in sample data) for PIT, VAT and TTAXR. Due to higher volatility and emerging negative values, the CIT monthly data was converted to quarterly data from the rst quarter of 1995 to the rst quarter of 2010. The competing ARIMA/SARIMA and Holt-Winters models were derived, and the resulting model of this study was used to forecast PIT, CIT, VAT and TTAXR for SARS fiscal years 2010/11, 2011/12 and 2012/13. The results show that both the SARIMA and Holt-Winters models perform well in modeling and forecasting PIT and VAT, however the Holt-Winters model outperformed the SARIMA model in modeling and forecasting the more volatile CIT and TTAXR. It is recommended that these methods are used in forecasting future payments, as they are precise about forecasting tax revenues, with minimal errors and fewer model revisions being necessary.
Statistics
M.Sc. (Statistics)

Голуб М. С. Використання методології теорії часових рядів у вивченні та обробці багаторічних змін метеорологічних даних : кваліфікаційна робота магістра спеціальності 113 "Прикладна математика" / наук. керівник В. В. Леонтьєва. Запоріжжя : ЗНУ, 2020. 69 с.
UA : Робота викладена на 69 сторінках друкованого тексту, містить 18 рисунків, 24 джерела, 2 додатки. Об’єкт дослідження – метеорологічні показники міста Запоріжжя. Мета роботи: провести аналіз ряду метеорологічних даних та, використовуючи методи прогнозування, побудувати прогноз погоди на 5 років. Метод дослідження – статичний аналіз ряду, прогнозування часових рядів методами ARIMA та SARIMA. У кваліфікаційній роботі розглядаються методи аналізу та прогнозування часових рядів. Основною задачею роботи є вивчення та обробка багаторічних змін метеорологічних даних, використовуючи методологію теорії часових рядів. Проведено статичний аналіз ряду: виявлення та усунення аномальних рівнів ряду, перевірено на наявність тренду та сезонної компоненти. Побудовано моделі прогнозування ARIMA та SARIMA, зроблено прогноз погоди на 5 років вперед.
EN : The work is presented on 69 pages of printed text, 18 figures, 24 references, 2 supplements. The object of the study is meteorological indicators of the city. The aim of the study is to to analyze a number of meteorological meters and, using forecasting methods, to build a weather forecast for 5 years. The methods of research are static series analysis, time series forecasting by ARIMA and SARIMA methods. Methods of analysis and forecasting of time series are considered in the qualification work. The main task of the work is to study and process long-term changes in meteorological data, using the methodology of time series theory. Static analysis of the series was performed: detection and elimination of abnormal levels of the series, checked for the presence of trend and seasonal component. ARIMA and SARIMA forecasting models have been built, and the weather forecast for the next 5 years has been made.

Relatório Final de Estágio do Mestrado em Engenharia Informática apresentado à Faculdade de Ciências e Tecnologia da Universidade de Coimbra.
A previsão do consumo energético é uma necessidade para a gestão eficiente das smart grids, dos programas de demand response e da gestão da eficiência energética de uma habitação. Isto deve-se ao facto de, ao obter informação sobre o eventual estado futuro do sistema elétrico, ser possível tomar medidas preventivas que permitam ao produtor de energia uma melhor gestão da produção. Numa outra perspetiva, e sob o ponto de vista do consumidor, é possível identificar padrões de consumo e planear o consumo energético eficientemente, beneficiando de menores custos. O presente trabalho de estágio, a decorrer na empresa Whitesmith, terá como objetivo contribuir para o desenvolvimento da plataforma Unplugg, especificamente para a definição e elaboração de um modelo de previsão, clustering de séries temporais e deteção de change-points. A literatura aponta no sentido de que os modelos ARMA, ARIMA, SARIMA e Holt-Winters apresentam bom desempenho na previsão do consumo a curto e médio prazo. Para a previsão do consumo energético será, portanto, utilizada uma abordagem baseada em modelos de séries temporais uni-variados e multi-variados que permitem a previsão do consumo energético residencial. Serão comparados modelos, janelas de histórico e previsão, aplicação de filtros, transformações, utilização de diferentes tipos de histórico e, ainda, a utilização de variáveis exógenas de fatores ambientais. Adicionalmente serão efetuados clusterings de séries temporais para várias granularidades do consumo de séries temporais normalizadas e não-normalizadas para o efeito de previsão em bloco e da tipificação de padrões de consumo. Para tal, ao longo do primeiro semestre foi efetuada uma investigação extensiva sobre as temáticas relacionadas com o problema a solucionar, bem como a exploração das soluções HEM já implementadas. No segundo semestre foram analisados e caracterizados os dados provenientes de clientes reais, implementadas as soluções estudadas, efetuados testes e obtidos resultados com o objetivo da determinação da configuração adequada a uma previsão eficiente individual e em bloco e do desenvolvimento de uma adaptação dinâmica às rotinas dos consumidores residenciais. O resultado obtido deste trabalho foi uma configuração com base no modelo SARIMA cujo valor médio de MAPE é de cerca de 33.8%, 34.1% e 20.7%, para as granularidades horária, octahorária e diária, respetivamente, que está presentemente a ser posto em produção num sistema que irá analisar 10 000 habitações. O modelo desenvolvido neste trabalho será utilizado como validação para novas iterações com sucessivas melhorias do mesmo.