The trend seasonal demand pattern is encountered when both trend and seasonal influences are interactive. The problem of this research is to project the seasonal market sales using ice cream and fresh milk in Taiwan as examples. In order to improve the accuracy of forecast, two different methods are validated and the best forecasting method is selected based on the minimum Mean Square Error. In this study, we present two forecasting models used for evaluation to predict seasonal market sales of ice cream, fresh milk, and air conditioner in Taiwan. It includes Winters multiplicative seasonal trend model and the Decomposition method. Two different methods are validated and the best forecasting method is selected based on the minimum Mean Square Error. After the validation process, Winters multiplicative seasonal trend model is selected based on the minimum MSE, and the monthly sales forecast for the year of 2011 is conducted using the data(60 months). Number Cruncher Statistical System (NCSS) is used for analyzing the data which proves useful and powerful. In summary, the results demonstrate that Winters multiplicative seasonal trend model has the smallest mean square error in this case. Therefore, we conclude that both Winters multiplicative seasonal trend model and the Decomposition model are well fitted for forecasting the seasonal market sales. Yet, Winters multiplicative seasonal trend model is the better method to be used in this study since it generates the smallest mean square error (MSE) during the period of validation.

I denna rapport presenteras ett tillvägagångssätt för att hitta och datera brytpunkter i tidsserier. En brytpunkt definieras av det datum då det skett en stor nivåförändring i tidsserien. Det presenteras även en strategi för att skatta effekten av daterade brytpunkter. Genom att analysera tidsserier över AFA Försäkrings ärendeinflöde visar det sig att brytpunkter i tidsserien sammanfaller med exogena händelser som kan ha orsakat dessa brytpunkter, till exempel villkors- eller lagförändringar inom försäkringsbranschen. Rapporten visar att det genom ett metodiskt angreppssätt går att skatta effekten av en exogen händelse. Dessa skattade effekter kan användas vid framtida prognoser då en liknande förändring förväntas inträffa. Dessutom skapas prognoser över ärendeinflödet två år framåt med olika tidsseriemodeller.

零售業是美國最大的產業之一，近年來科技進步以及網路購物擁有價格優勢、交易方便等優點，未來電子商務將成為主流的銷售形式之一，一般實體零售業者如何因應這股潮流是一大課題。 　　與本研究有關之美國服飾零售業，實體店家還是占市場的多數，因此，為了提升服飾零售實體店家的競爭優勢，我們預測來店人數，一方面調整人力資源的分配與進貨量，提供顧客優良的服務品質，另一方面視情況提出促銷方案吸引顧客上門，進而提升營運效率。 　　每年從感恩節到聖誕節這一個月的時間，是關乎全美零售業生存與否的重要時刻，這段時間的銷售額約占全年銷售總額的1/5，也就表示來店人數在這段期間會維持在一定的數值以上甚至達到全年巔峰，而如何不受影響達到精準預測？本研究欲找出指數平滑法中適合的模型精準預測來店人數的資料。 　　本研究旨在探討指數平滑法與延伸之狀態空間模型，指數平滑法屬於時間序列(Time series)的預測方法，是應用相當廣的一種預測方法，一般由趨勢(Trend)以及季節性(Seasonality)組合而成，而將指數平滑模型加入誤差項以後的狀態空間模型，過去一直沒有一個隨機模型做為架構納入概似估計與預測區間等，近幾年才發展出模型之最佳化準則來估計參數，而本研究想探討哪一個狀態空間模型適用於預測來店人數資料以及狀態空間模型之最佳化準則是否能使預測結果更準確。 　　本研究之資料為美國時尚精品服飾店2007年營業時間內每小時來店人數，而實證分析後發現Holt-Winters季節性加法模型ETS(A,A,A)蠻適合用來預測來店人數，此外ETS(A,A,A)模型之最佳化準則以AMSE準則與MLE準則表現最佳， MAE準則表現最差。

Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity

[ES] De acuerdo con las regulaciones europeas y muchos estudios científicos, es necesario monitorear y analizar las condiciones microclimáticas en museos o edificios, para preservar las obras de arte en ellos. Con el objetivo de ofrecer herramientas para el monitoreo de las condiciones climáticas en este tipo de edificios, en esta tesis doctoral se propone una nueva metodología estadística para clasificar series temporales de parámetros climáticos como la temperatura y humedad relativa. La metodología consiste en aplicar un método de clasificación usando variables que se computan a partir de las series de tiempos. Los dos primeros métodos de clasificación son versiones conocidas de métodos sparse PLS que no se habían aplicado a datos correlacionados en el tiempo. El tercer método es una nueva propuesta que usa dos algoritmos conocidos. Los métodos de clasificación se basan en diferentes versiones de un método sparse de análisis discriminante de mínimos cuadra- dos parciales PLS (sPLS-DA, SPLSDA y sPLS) y análisis discriminante lineal (LDA). Las variables que los métodos de clasificación usan como input, corresponden a parámetros estimados a partir de distintos modelos, métodos y funciones del área de las series de tiempo, por ejemplo, modelo ARIMA estacional, modelo ARIMA- TGARCH estacional, método estacional Holt-Winters, función de densidad espectral, función de autocorrelación (ACF), función de autocorrelación parcial (PACF), rango móvil (MR), entre otras funciones. También fueron utilizadas algunas variables que se utilizan en el campo de la astronomía para clasificar estrellas. En los casos que a priori no hubo información de los clusters de las series de tiempos, las dos primeras componentes de un análisis de componentes principales (PCA) fueron utilizadas por el algoritmo k- means para identificar posibles clusters de las series de tiempo. Adicionalmente, los resultados del método sPLS-DA fueron comparados con los del algoritmo random forest. Tres bases de datos de series de tiempos de humedad relativa o de temperatura fueron analizadas. Los clusters de las series de tiempos se analizaron de acuerdo a diferentes zonas o diferentes niveles de alturas donde fueron instalados sensores para el monitoreo de las condiciones climáticas en los 3 edificios.El algoritmo random forest y las diferentes versiones del método sparse PLS fueron útiles para identificar las variables más importantes en la clasificación de las series de tiempos. Los resultados de sPLS-DA y random forest fueron muy similares cuando se usaron como variables de entrada las calculadas a partir del método Holt-Winters o a partir de funciones aplicadas a las series de tiempo. Aunque los resultados del método random forest fueron levemente mejores que los encontrados por sPLS-DA en cuanto a las tasas de error de clasificación, los resultados de sPLS- DA fueron más fáciles de interpretar. Cuando las diferentes versiones del método sparse PLS utilizaron variables resultantes del método Holt-Winters, los clusters de las series de tiempo fueron mejor discriminados. Entre las diferentes versiones del método sparse PLS, la versión sPLS con LDA obtuvo la mejor discriminación de las series de tiempo, con un menor valor de la tasa de error de clasificación, y utilizando el menor o segundo menor número de variables.En esta tesis doctoral se propone usar una versión sparse de PLS (sPLS-DA, o sPLS con LDA) con variables calculadas a partir de series de tiempo para la clasificación de éstas. Al aplicar la metodología a las distintas bases de datos estudiadas, se encontraron modelos parsimoniosos, con pocas variables, y se obtuvo una discriminación satisfactoria de los diferentes clusters de las series de tiempo con fácil interpretación. La metodología propuesta puede ser útil para caracterizar las distintas zonas o alturas en museos o edificios históricos de acuerdo con sus condiciones climáticas, con el objetivo de prevenir problemas de conservación con las obras de arte. / [CA] D'acord amb les regulacions europees i molts estudis científics, és necessari monitorar i analitzar les condiciones microclimàtiques en museus i en edificis similars, per a preservar les obres d'art que s'exposen en ells. Amb l'objectiu d'oferir eines per al monitoratge de les condicions climàtiques en aquesta mena d'edificis, en aquesta tesi es proposa una nova metodologia estadística per a classificar series temporals de paràmetres climàtics com la temperatura i humitat relativa.La metodologia consisteix a aplicar un mètode de classificació usant variables que es computen a partir de les sèries de temps. Els dos primers mètodes de classificació són versions conegudes de mètodes sparse PLS que no s'havien aplicat adades correlacionades en el temps. El tercer mètode és una nova proposta que usados algorismes coneguts. Els mètodes de classificació es basen en diferents versions d'un mètode sparse d'anàlisi discriminant de mínims quadrats parcials PLS (sPLS-DA, SPLSDA i sPLS) i anàlisi discriminant lineal (LDA). Les variables queels mètodes de classificació usen com a input, corresponen a paràmetres estimats a partir de diferents models, mètodes i funcions de l'àrea de les sèries de temps, per exemple, model ARIMA estacional, model ARIMA-TGARCH estacional, mètode estacional Holt-Winters, funció de densitat espectral, funció d'autocorrelació (ACF), funció d'autocorrelació parcial (PACF), rang mòbil (MR), entre altres funcions. També van ser utilitzades algunes variables que s'utilitzen en el camp de l'astronomia per a classificar estreles. En els casos que a priori no va haver-hi información dels clústers de les sèries de temps, les dues primeres components d'una anàlisi de components principals (PCA) van ser utilitzades per l'algorisme k-means per a identificar possibles clústers de les sèries de temps. Addicionalment, els resultats del mètode sPLS-DA van ser comparats amb els de l'algorisme random forest.Tres bases de dades de sèries de temps d'humitat relativa o de temperatura varen ser analitzades. Els clústers de les sèries de temps es van analitzar d'acord a diferents zones o diferents nivells d'altures on van ser instal·lats sensors per al monitoratge de les condicions climàtiques en els edificis.L'algorisme random forest i les diferents versions del mètode sparse PLS van ser útils per a identificar les variables més importants en la classificació de les series de temps. Els resultats de sPLS-DA i random forest van ser molt similars quan es van usar com a variables d'entrada les calculades a partir del mètode Holt-winters o a partir de funcions aplicades a les sèries de temps. Encara que els resultats del mètode random forest van ser lleument millors que els trobats per sPLS-DA quant a les taxes d'error de classificació, els resultats de sPLS-DA van ser més fàcils d'interpretar.Quan les diferents versions del mètode sparse PLS van utilitzar variables resultants del mètode Holt-Winters, els clústers de les sèries de temps van ser més ben discriminats. Entre les diferents versions del mètode sparse PLS, la versió sPLS amb LDA va obtindre la millor discriminació de les sèries de temps, amb un menor valor de la taxa d'error de classificació, i utilitzant el menor o segon menor nombre de variables.En aquesta tesi proposem usar una versió sparse de PLS (sPLS-DA, o sPLS amb LDA) amb variables calculades a partir de sèries de temps per a classificar series de temps. En aplicar la metodologia a les diferents bases de dades estudiades, es van trobar models parsimoniosos, amb poques variables, i varem obtindre una discriminació satisfactòria dels diferents clústers de les sèries de temps amb fácil interpretació. La metodologia proposada pot ser útil per a caracteritzar les diferents zones o altures en museus o edificis similars d'acord amb les seues condicions climàtiques, amb l'objectiu de previndre problemes amb les obres d'art. / [EN] According to different European Standards and several studies, it is necessary to monitor and analyze the microclimatic conditions in museums and similar buildings, with the goal of preserving artworks. With the aim of offering tools to monitor the climatic conditions, a new statistical methodology for classifying time series of different climatic parameters, such as relative humidity and temperature, is pro- posed in this dissertation.The methodology consists of applying a classification method using variables that are computed from time series. The two first classification methods are ver- sions of known sparse methods which have not been applied to time dependent data. The third method is a new proposal that uses two known algorithms. These classification methods are based on different versions of sparse partial least squares discriminant analysis PLS (sPLS-DA, SPLSDA, and sPLS) and Linear Discriminant Analysis (LDA). The variables that are computed from time series, correspond to parameter estimates from functions, methods, or models commonly found in the area of time series, e.g., seasonal ARIMA model, seasonal ARIMA-TGARCH model, seasonal Holt-Winters method, spectral density function, autocorrelation function (ACF), partial autocorrelation function (PACF), moving range (MR), among others functions. Also, some variables employed in the field of astronomy (for classifying stars) were proposed.The methodology proposed consists of two parts. Firstly, different variables are computed applying the methods, models or functions mentioned above, to time series. Next, once the variables are calculated, they are used as input for a classification method like sPLS-DA, SPLSDA, or SPLS with LDA (new proposal). When there was no information about the clusters of the different time series, the first two components from principal component analysis (PCA) were used as input for k-means method for identifying possible clusters of time series. In addition, results from random forest algorithm were compared with results from sPLS-DA.This study analyzed three sets of time series of relative humidity or temperate, recorded in different buildings (Valencia's Cathedral, the archaeological site of L'Almoina, and the baroque church of Saint Thomas and Saint Philip Neri) in Valencia, Spain. The clusters of the time series were analyzed according to different zones or different levels of the sensor heights, for monitoring the climatic conditions in these buildings.Random forest algorithm and different versions of sparse PLS helped identifying the main variables for classifying the time series. When comparing the results from sPLS-DA and random forest, they were very similar for variables from seasonal Holt-Winters method and functions which were applied to the time series. The results from sPLS-DA were easier to interpret than results from random forest. When the different versions of sparse PLS used variables from seasonal Holt- Winters method as input, the clusters of the time series were identified effectively.The variables from seasonal Holt-Winters helped to obtain the best, or the second best results, according to the classification error rate. Among the different versions of sparse PLS proposed, sPLS with LDA helped to classify time series using a fewer number of variables with the lowest classification error rate.We propose using a version of sparse PLS (sPLS-DA, or sPLS with LDA) with variables computed from time series for classifying time series. For the different data sets studied, the methodology helped to produce parsimonious models with few variables, it achieved satisfactory discrimination of the different clusters of the time series which are easily interpreted. This methodology can be useful for characterizing and monitoring micro-climatic conditions in museums, or similar buildings, for preventing problems with artwork. / I gratefully acknowledge the financial support of Pontificia Universidad Javeriana Cali – PUJ and Instituto Colombiano de Crédito Educativo y Estudios Técnicos en el Exterior – ICETEX who awarded me the scholarships ’Convenio de Capacitación para Docentes O. J. 086/17’ and ’Programa Crédito Pasaporte a la Ciencia ID 3595089 foco-reto salud’ respectively. The scholarships were essential for obtaining the Ph.D. Also, I gratefully acknowledge the financial support of the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 814624. / Ramírez Buelvas, SM. (2022). A Statistical Methodology for Classifying Time Series in the Context of Climatic Data [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/181123

[pt] O objetivo do presente trabalho é o desenvolvimento de um algoritmo estatístico de previsão da potência transmitida pela usina geradora termelétrica de Linhares, localizada no Espírito Santo, medida no ponto de entrada da rede da concessionária regional, a ser integrado em plataforma composta por sistema supervisório em tempo real em ambiente MS Windows. Para tal foram comparadas as metodologias de Modelos Arima(p,d,q), regressão usando polinômios ortogonais e técnicas de amortecimento exponencial para identificar a mais adequada para a realização de previsões 5 passos-à-frente. Os dados utilizados são provenientes de observações registradas a cada 5 minutos, contudo, o alvo é produzir estas previsões para observações registradas a cada 5 segundos. Os resíduos estimados do modelo ajustado foram analisados via gráficos de controle para checar a estabilidade do processo. As previsões produzidas serão usadas para subsidiar decisões dos operadores da usina, em tempo real, de forma a evitar a ultrapassagem do limite de 200.000 kW por mais de quinze minutos. / [en] The objective of this study is to develop a statistical algorithm to predict the power transmitted by a thermoelectric power plant in Linhares, located at Espírito Santo state, measured at the entrance of the utility regional grid, which will be integrated to a platform formed by a real time supervisor system developed in MS Windows. To this end we compared Arima (p,d,q), Regression using Orthogonal Polynomials and Exponential Smoothing techniques to identify the best suited approach to make predictions five steps ahead. The data used are observations recorded every 5 minutes, however, the target is to produce these forecasts for observations recorded in every five seconds. The estimated residuals of the fitted model were analysed via control charts to check on the stability of the process. The forecasts produced by this model will be used to help not to exceed the 200.000 kW energy generation upper bound for more than fifteen minutes.

[pt] As partículas finas (PM2.5) são um dos principais poluentes atmosféricos associados a problemas de saúde. Estas partículas penetram no sistema respiratório, carreando desde metais traços a substâncias orgânicas. Apesar disso, a legislação ambiental brasileira ainda não tem estabelecido padrões para este poluente. Entretanto, Agencia Ambiental dos Estados Unidos (US.EPA) já tem adotado limites para exposições de curto (25 (micro)g m-3/diário) e longo (15 (micro)g m-3/anual) prazo. Esta tese teve quatro principais objetivos: (1) investigar a relação das condições meteorológicas, sazonalidade e bacias aéreas sobre as concentrações de PM2.5 na atmosfera; (2) avaliar modelos de previsão de qualidade do ar inovadores para estimar concentração de PM2.5 em locais com diferentes fontes de emissão; (3) validar método de extração e determinação pseudototal de metais traços presentes no material particulado, com espectrômetro de emissão ótica por plasma indutivamente acoplado (ICP-OES) de acordo com critérios estabelecidos pelo INMETRO; (4) quantificar carbono orgânico e metais traços presentes no material particulado fino para entender melhor como a atmosfera do estado do Rio de Janeiro tem sido afetada, devido aos vários tipos de emissão e condições meteorológicas. Amostradores de grandes volumes coletaram todas as amostras de PM2.5. Estes amostradores foram operados por 24 h, a cada seis dias, em locais com diferentes fontes de emissão (industrial, veicular, poeira do solo, etc.), no estado do Rio de Janeiro. As amostras foram coletadas pelo Instituto Estadual do Ambiente (INEA), no período de janeiro/11 até dezembro/13. Variáveis meteorológicas próximas (d(menor que)2 km) aos pontos de monitoramento de PM2.5 também foram obtidas na mesma frequência e período de amostragem. Em relação a este estudo, quatro resultados podem ser destacados. O primeiro, as concentrações médias diárias de PM2.5 variaram de 1-65 (micro)g m-3, ultrapassando em alguns pontos os limites adotados pela US.EPA. Estes resultados mostraram que concentrações de PM2.5 no RJ não é influenciada, em expressão, pela sazonalidade. Além disso, foi observado que as bacias aéreas definidas no Rio de Janeiro não têm sido confirmadas, e os locais mostraram uma semelhança de comportamento em função da sua fonte de emissão. O segundo, a aplicação do modelo Holt-Winters para previsão de PM2.5 simulou melhor a zona industrial, com RMSE (raiz do erro quadrático médio) entre 5,8-14,9 (micro)g m-3. Em contrapartida, a rede neural artificial associada a variáveis meteorológicas estimou melhor os resultados das zonas urbanas e rurais, com RMSE entre 4,2-9,3 (micro)g m-3. O terceiro, o método de extração e determinação pseudototal de metais por ICP-OES atendeu aos critérios de validação estabelecidos pelo INMETRO. Além disso, mostrou-se ser equivalente ao método US.EPA IO-3.1. Finalmente, as concentrações de carbono orgânico solúvel em água variaram de 0,8-4,9 (micro)g m-3. Os principais metais determinados foram: Na (5,8-13,6 (micro)g m-3), Al (1,6-6,7 (micro)g m-3) e Zn (1,9-6,6 (micro)g m-3). Foi verificado também que os fenômenos meteorológicos de superfície aumentam em 30 por cento a explicação da variância do modelo receptor (PCA), quando adicionados aos dados das substâncias químicas analisadas do PM2.5. Contudo, é crucial a aplicação de ferramentas quimiométricas para ajudar na caracterização e estimava das concentrações de poluentes atmosféricos. / [en] Fine particulate matters (PM2.5) are one of the primary air pollutants associated with health problems. These particles penetrate in the respiratory system, loading from trace metals to organic compounds. Neverthelere4ss, the Brazilian environmental legislation has not yet established standards for this pollutant. However, the US Environmental Agency (US.EPA) has already adopted limits for short-term (25 (micro)g m-3/daily) and long-term (15 (micro)g m-3/annual) exposures. This thesis had four main objectives: (1) to investigate the relation of weather conditions, seasonality and air basins on PM2.5 concentrations in the atmosphere; (2) to evaluate innovative air quality forecast models to estimate PM2.5 concentration in sites with different emission sources; (3) to validate method to extract and pseudo total determinate trace metals present in the particulate matter by inductively coupled plasma optical emission spectrometer (ICP-OES) according to criteria established by INMETRO; (4) to quantify organic carbon and trace metals present in fine particulate matter to better understand how the Rio de Janeiro State (RJ) atmosphere has been affected due to the various types of emission and weather conditions. High volumes samplers PM2.5 collected all PM2.5 samples. These samplers were operated for 24 h, every six days, in places with different emission sources (industrial, vehicular, soil dust, et caetera), in the Rio de Janeiro State. The samples were collected by the State Environmental Institute (INEA) during the period from January/2011 still December/2013. Meteorological variables nearby (d(less than)2 km) to PM2.5 monitoring points were also obtained at the same frequency and sampling period. Regarding this study, four results can be highlighted. The first one, the PM2.5 dailly concentrations average ranged from 1-65 (micro)g m-3, exceeding in some sites the limits adopted by US.EPA. These results showed that PM2.5 concentrations in RJ is not influenced, in expression, by the seasonality. In addition, it was observed that the defined RJ air basins have not been confirmed, and the local showed a similar performance according to their emission sources. The second one, the application of the Holt-Winters model for PM2.5 forecast simulated best industrial zone, with RMSE (root mean square error) between 5.8 to 14.9 (micro)g m-3. On the others hand, the artificial neural network associated with meteorological variables estimated best results from urban and rural areas, with RMSE between 4.2 to 9.3 (micro)g m-3. The third one, the method to extract and determine pseudo total metals by ICP-OES followed the validation criteria established by INMETRO. Furthermore, it was shown to be equivalent to US.EPA IO-3.1 method. Finally, the water-soluble organic carbon concentrations ranged from 0.8 to 4.9 (micro)g m-3. The principal metals determined were: Na (5.8-13.6 (micro)g m-3), Al (1.6-6.7 (micro)g m-3) and Zn (1.9-6.6 (micro)g m-3). It was also found that the surface meteorological phenomena increase at 30 percent the explicated variance of the receiver model (PCA) when added to PM2.5 chemical analysis data. Therefore, it is crucial the application of chemometric tools to help in the characterization and estimated air pollutant concentrations.

This thesis examines how to design a mathematical inventory model for a ”Fast Moving Consumer Goods”-company (FMCG-company), which determines the optimal reorder point and order quantity such that the average inventory cost is minimized. The thesis was made in collaboration with a ”Software as a Service”- company which provided the data containing information about the products and inventory management of one of their customers, a FMCG-company. The thesis first considers a basic EOQ-model, with constant demand rate, that suggests a reorder time and order quantity for the products. Since constant demand rate might be an unrealistic assumption for a FMCG-company, the thesis also considers a (R,Q)-model, where the demand was based on a forecast made by using the Holt-Winters model on previous sales history. The solutions were found by investigating the singular points and comparing them to the critical point. The thesis shows that the EOQ-model gives useful results for the most indemand products, while the reorder times for the less popular products are instead impractically high. The (R,Q)-model showed more stable solutions for all products and therefore proves to be a better inventory model for FMCG-companies, as expected. Simulations of the (R,Q)-model showed various inventory cases, where some showed a mismatch between the inventory level and the demand. The cases shows how demand planning can be applied for different products for when to consider changing inventory strategy or discontinuing products and how the orders can be made optimally. / Detta examensarbete undersöker hur en matematisk lagermodell kan utformas för ett ”Fast Moving Consumer Goods”-företag (FMCG-företag), som bestämmer den optimala beställningspunkten och orderkvantiteten så att den genomsnittliga lagerkostnaden minimeras. Examensarbetet gjordes i samarbete med ett ”Software as a Service”-företag som tillhandahöll data innehållandes information om produkter och lagerhantering hos en av deras kunder, ett FMCG-företag. Avhandlingen behandlar först en grundläggande EOQ-modell, med konstant efterfrågan, som föreslår en återbeställningstid och orderkvantitet för produkterna. Eftersom att en konstant efterfågan kan anses vara ett orealistiskt antagande för ett FMCG-företag, tar avhandlingen även upp en (R,Q)-modell, där efterfrågan baserades på en prognos gjord med hjälp av Holt-Winters-modellen på tidigare försäljningshistorik. Lösningarna hittades genom att undersöka de singulära punkterna och jämföra dem med den kritiska punkten. Avhandlingen visar att EOQ-modellen ger användbara resultat för de mest efterfrågade produkterna medan beställningstiderna för de mindre populära produkter är ofta opraktiskt höga. (R,Q)-modellen visade mer stabila lösningar för alla produkter och visar sig därmed vara en bättre lagermodell för FMCGföretag, som förväntat. Simuleringar av (R,Q)-modellen visade olika fall, där vissa visade en obalans mellan lagernivån och efterfrågan. De olika fallen visar hur efterfrågeplanering kan tillämpas för olika produkter för när man ska överväga att ändra lagerstrategi eller avveckla produkter och hur beställningarna kan göras optimalt

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)

本論文運用Box-Jenkins 隨機時間序列模式與Winters 趨勢季節平滑模式，進行廿一 縣市液化石油氣需求預測，依模式之配合度、穩定度及預測能力予以評估上述兩種模 式之優缺點，并探討各模式於運用時之限制，以供企業界與學者運用此兩種模式之參 考。 本論文共壹冊，約為五萬餘字，分為八章，茲分述如下： 第一章：闡述研究之動機目的與方法。第二章；介紹Box-Jenkins 模型之理論與建立 方法。第三章：介紹指數平滑法之發展、種類及模式之建立方法。第四章：探討良好 預測模式所應具備之條件，以為評估之標準。第五章：運用Box-Jenkins 模式進行液 化石油氣需求模式之進立與預測。第六章：運用Winters 趨勢季節平滑模式從事液化 石油氣需求預測。第七章：比較前述兩章預測之結果。第八章：結論與建議。