This paper serves to address the effect of time on the sales of clothing retail, from 2010 to May 2019. The data was retrieved from the US Census, where N=113 observations were used, which were plotted to observe their trends. Once outliers and transformations were performed, the best model was fit, and diagnostic review occurred. Inspections for seasonality and forecasting was also conducted. The final model came out to be an ARIMA (2,0,1). Slight seasonality was present, but not enough to drastically influence the trends. Our results serve to highlight the economic growth of clothing retail sales for the past 8 years, cementing the significance of the production economy's stability. The quarterly GDP data was collected in order to find out the relationship with the differenced clothing data. Some observations of GDP data were affected by the clothing data before removing the seasonality. After removing the seasonality, the clothing expense is white noise and not predictable from the historical GDP.

The U.S. furniture industry has faced the challenge from increasing imports of furniture from foreign countries over the last decades. In the first part of this thesis, the import pattern of wooden bedroom furniture and the antidumping investigation against China were summarized, and furthermore, intervention analysis was employed to assess its impacts on the import value and unit price of China. The results revealed that the impact on import values was temporary but there was no significant impact on unit prices. The traditional suppliers have been substituted by the newly developing countries such as China and Vietnam. In the second part of this thesis, to explain the market structure change, a dynamic AIDS model was used to analyze the consumer behavior and evaluate the impacts of antidumping investigation on the major competitors in the second part. The results indicated that most imported wooden bedroom furniture can be substituted between suppliers and trade diversion occurred from China to Vietnam, Indonesia, and Brazil.

No description available.

<p>The study of Internet traffic behavior in a real IP network is the subject of this thesis. Traffic Matrix of a telecommunication network represents the exchanged traffic volume between the source and destination nodes in the network and is a critical input for network studies. However, in most cases, traffic matrices are not readily available. Existing network management protocols such as the ‘Simple Network Management Protocol’ (SNMP) have been used to gather other observable measures, such as link load observations. The first part of this thesis reviews famous methods and approaches that try to infer and estimate the source-destination traffic matrix from the observable link loads.</p> <p>Another important subject in networks is to predict bandwidth requirements in the future. The second part of this thesis reviews some existing methods and approaches of traffic prediction. Recently a traffic prediction method which uses multiple Time-Series analysis, each operating on a different time-scale, has been proposed. This method uses multiple ‘AutoRegressive Integrated Moving Average’ (ARIMA) filters to predict the future bandwidth requirements. Each ARIMA filter operates on a different time scale, i.e., quarter-hour, hour, day, and week. The proposed method associates a weight with each ARIMA filter, and adjusts the weights according to which filter is currently the most accurate predictor. A review of this newly proposed method is presented. Extensive experimental results have been gathered to test the robustness of the method. The filter coefficients of each ARIMA filter have been varied, and the accuracy of the predicted traffic has been measured. Extensive experimental measurements indicate that the model is very robust, and that large changes to each filter's coefficients have only a small effect on the accuracy. In all cases we evaluated, the method is very robust, predicting short-term future traffic demands with typically ≈95% success rates.</p> / Master of Applied Science (MASc)

A time series process can be influenced by an interruptive event which starts at a certain time point and so a structural break in either mean or variance may occur before and after the event time. However, the traditional statistical tests of two independent samples, such as the t-test for a mean difference and the F-test for a variance difference, cannot be directly used for detecting the structural breaks because it is almost certainly impossible that two random samples exist in a time series. As alternative methods, the likelihood ratio (LR) test for a mean change and the cumulative sum (CUSUM) of squares test for a variance change have been widely employed in literature. Another point of interest is temporal aggregation in a time series. Most published time series data are temporally aggregated from the original observations of a small time unit to the cumulative records of a large time unit. However, it is known that temporal aggregation has substantial effects on process properties because it transforms a high frequency nonaggregate process into a low frequency aggregate process. In this research, we investigate the effects of temporal aggregation on the LR test and the CUSUM test, through the ARIMA model transformation. First, we derive the proper transformation of ARIMA model orders and parameters when a time series is temporally aggregated. For the LR test for a mean change, its test statistic is associated with model parameters and errors. The parameters and errors in the statistic should be changed when an AR(p) process transforms upon the mth order temporal aggregation to an ARMA(P,Q) process. Using the property, we propose a modified LR test when a time series is aggregated. Through Monte Carlo simulations and empirical examples, we show that the aggregation leads the null distribution of the modified LR test statistic being shifted to the left. Hence, the test power increases as the order of aggregation increases. For the CUSUM test for a variance change, we show that two aggregation terms will appear in the test statistic and have negative effects on test results when an ARIMA(p,d,q) process transforms upon the mth order temporal aggregation to an ARIMA(P,d,Q) process. Then, we propose a modified CUSUM test to control the terms which are interpreted as the aggregation effects. Through Monte Carlo simulations and empirical examples, the modified CUSUM test shows better performance and higher test powers to detect a variance change in an aggregated time series than the original CUSUM test. / Statistics

The deregulation of the Electricity Sector in US has led to a tremendous increase in the inter-regional wholesale electricity trade between neighboring utilities or regions. For instance, the generation deficit regions may choose to import power from surplus regions; thus the wholesale electricity market prices in the regions are also affected by the dynamics of its electricity trade with other regions. Valuable insights into such imports/exports ahead of time have become crucial market intelligence for the various academicians and the market players associated with the industry. In this thesis, the task of short-term forecasting of the power flows over three major transmission interties of the Pacific Northwest region, namely the Pacific AC Intertie, the Pacific DC Intertie and the Northern Intertie, is successfully accomplished. The Pacific AC and the Pacific DC interties connect the Pacific Northwest region of US with the state of California. The Northern Intertie is the only intertie connecting the British Columbia region in Canada with the Pacific Northwest US. Box-Jenkins ARIMA (Auto Regressive Integrated Moving Average) and Transfer function methodologies are used as the statistical tools to identify the forecasting models in this thesis. The data requirement for all of the models is restricted to publicly available data. / Master of Science

En damm används i huvudsak för att magasinera vatten i energiutvinningssyfte. Dammen rör sig fram och tillbaka i ett säsongsmönster mestadels beroende på skillnader i utomhustemperatur och vattentemperaturen i magasinet. Det nordiska klimatet innebär risk för isläggning i magasinet, för vilken lasten är relativt outforskad. Denna rapport syftar till ett med multipla linjära regressionsmodeller samt dynamiska regressionsmodeller avgöra vilka variabler som förklarar en specifik svensk dammkonstruktions rörelse. Dammens rörelse mäts genom att mäta dammens förflyttning kontra berggrunden med data från dammens inverterade pendlar. Av särskilt intresse är att avgöra islastens påverkan på rörelsen. Resultaten visar att multipla linjära regressions-modeller inte fullständigt lyckas modellera dammens rörelse, då de har problem med autokorrelerade residualer. Detta hanteras med hjälp av autoregressiva regressionsmodeller där de initiala förklarande variablerna inkluderas, kallat dynamisk regression. Denna rapports resultat visar att de autoregressiva parametrarna fungerar mycket väl för att förklara pendlarna, men att även tid, temperatur, det hydrostatiska trycket samt istjocklek är användbara förklarande variabler. Istjockleken visar signifikant påverkan på 5 % signifikansnivå på två av de undersökta pendlarna, vilket är ett noterbart resultat. Författarna menar att rapportens resultat indikerar att det finns anledning att fortsätta forska kring islastens påverkan på dammkonstruktioner. / A dam is a structure mainly used for storing water and generating electricity. The structure of a dam moves in a season-based pattern, mainly because of the difference in temperature between the air on outside of the dam and the water on the inside. Due to the Nordic climate, occurrences of icing on the water in the basin is fairly frequent. The effects of ice on the structural load of the dam are relatively unexplored and are the subject to this bachelor’s thesis. The goal of this project is to evaluate which predictors are significant to the movement of the dam with multiple linear regression models and dynamic regressions. The movement is measured by inverted pendulums that register the dam’s movement compared to the foundation. It is of particular interest to determine if the ice load influences the movement of the dam. The multiple regression models used to explain the dam’s movement were all discarded due to autocorrelation in the residuals. This falsifies the models, since autocorrelation means that they don’t meet the needed assumptions. To counteract the autocorrelation, dynamic models with autoregressive terms were fitted. These models showed no problem with autocorrelation. The result from the dynamic models were successful and managed to significantly explain the movement of the dam. The autoregressive terms proved to be efficient explanatory variables. The dynamic regression models also show that the time, temperature, hydrostatic pressure and ice thickness variables are also useful explanatory variables. The ice thickness shows a significant effect at the 5 % significance level on two of the investigated pendulums. The report's results indicate that there is reason to continue research on the ice load impact on dam constructions.

Time series model have been used in many areas of knowledge and have become a current necessity for companies to survive in a globalized and competitive market, as well as climatic factors that have always been a concern because of the different ways they interfere in human life. In this context, this work aims to present a comparison among the performances by the following models of time series: ARIMA, ARMAX and Exponential Smoothing, adjusted to air relative humidity (UR) and also to verify the volatility present in the series through non-linear models ARCH/GARCH, adjusted to residues of the ARIMA and ARMAX models. The data were collected from INMET from October, 1st to January, 22nd, 2014. In the comparison of the results and the selection of the best model, the criteria MAPE, EQM, MAD and SSE were used. The results showed that the model ARMAX(3,0), with the inclusion of exogenous variables produced better forecast results, compared to the other models SARMA(3,0)(1,1)12 and the Holt-Winters multiplicative. In the volatility study of the series via non-linear ARCH(1), adjusted to the quadrants of SARMA(3,0)(1,1)12 and ARMAX(3,0) residues, it was observed that the volatility does not tend to influence the future long-term observations. It was then concluded that the classes of models used and compared in this study, for data of a climatologic variable, showed a good performance and adjustment. We highlight the broad usage possibility in the techniques of temporal series when it is necessary to make forecasts and also to describe a temporal process, being able to be used as an efficient support tool in decision making. / Modelos de séries temporais vêm sendo empregados em diversas áreas do conhecimento e têm surgido como necessidade atual para empresas sobreviverem em um mercado globalizado e competitivo, bem como fatores climáticos sempre foram motivo de preocupação pelas diferentes formas que interferem na vida humana. Nesse contexto, o presente trabalho tem por objetivo apresentar uma comparação do desempenho das classes de modelos de séries temporais ARIMA, ARMAX e Alisamento Exponencial, ajustados a dados de umidade relativa do ar (UR) e verificar a volatilidade presente na série por meio de modelos não-lineares ARCH/GARCH ajustados aos resíduos dos modelos ARIMA e ARMAX. Os dados foram coletados junto ao INMET no período de 01 de outubro de 2001 a 22 de janeiro de 2014. Na comparação dos resultados e na seleção do melhor modelo foram utilizados os critérios MAPE, EQM, MAD e SSE. Os resultados mostraram que o modelo ARMAX(3,0) com a inclusão de variáveis exógenas produziu melhores resultados de previsão em relação aos seus concorrentes SARMA(3,0)(1,1)12 e o Holt-Winters multiplicativo. No estudo da volatilidade da série via modelo não-linear ARCH(1), ajustado aos quadrados dos resíduos dos modelos SARMA(3,0)(1,1)12 e ARMAX(3,0), observou-se que a volatilidade não tende a influenciar as observações futuras em longo prazo. Conclui-se que as classes de modelos utilizadas e comparadas neste estudo, para dados de uma variável climatológica, demonstraram bom desempenho e ajuste. Destaca-se a ampla possibilidade de utilização das técnicas de séries temporais quando se deseja fazer previsões e descrever um processo temporal, podendo ser utilizadas como ferramenta eficiente de apoio nas tomadas de decisão.

[pt] Nesta dissertação, estratégias de modelagem são apresentadas envolvendo modelos de séries temporais lineares e não lineares para modelar a série do preço spot no mercado elétrico brasileiro. Foram usados, dentre os lineares, os modelos ARIMA(p,d,q) proposto por Box, Jenkins e Reinsel (1994) e os modelos de regressão dinâmica. Dentre os não lineares, o modelo escolhido foi o STAR desenvolvido, inicialmente, por Chan e Tong (1986) e, posteriormente, por Teräsvista (1994). Para este modelo, testes do tipo Multiplicador de Lagrange foram usados para testar linearidade, bem como para avaliar os modelos estimados. Além disso, foi também utilizada uma proposta para os valores iniciais do algoritmo de otimização, desenvolvido por Franses e Dijk (2000). Estimativas do filtro de Kalman suavizado foram usadas para substituir os valores da série de preço durante o racionamento de energia ocorrido no Brasil. / [en] In this dissertation, modeling strategies are presented involving linear and non-linear time series models to model the spot price of Brazil s electrical energy market. It has been used, among the linear models, the modeling approach of Box, Jenkins and Reinsel (1994) i.e., ARIMA(p,d,q) models, and dynamic regression. Among the non-linear ones, the chosen model was the STAR developed, initially, by Chan and Tong (1986) and, later, by Teräsvirta (1994). For this model, the Lagrange Multipliers test, to measure the degree of non linearity of the series , as well as to evaluate the estimated model was used. Moreover, it was also used a proposal for the initial values of the optimization algorithm, developed by Franses and Dijk (2000). The smoothed Kalman filter estimates were used in order to provide values for the spot price series during the energy shortage period.

This thesis is focused on mathematical modelling of exchange rate CZK/USD in 1991 - 2014. Time series was divided into 5 parts. First Box-Jenkins methodology models were examined, especially ARIMA model. Unfortunately, the model could not be used because none of the time series showed correlation. The time series is considered as a white noise. The data appear to be completely random and unpredictable. The time series have not constant variance neither normal distribution and therefore GARCH volatility model was used as the second model. It is better not to divide time series when using model of volatility. Volatility model contributes to more accurate prediction than the standard deviation. Results were calculated in RStudio software and MS Excel.