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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。

<p>In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as &lsquo / mean-unbiased&rsquo / and &lsquo / medianunbiased&rsquo / estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1).</p> <p><br /> However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to&nbsp / compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the &lsquo / medianunbiased&rsquo / estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed / the &lsquo / most-probably-unbiased&rsquo / estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed / (2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model / (3) the exact variance and MSE of LS estimator is determined / (4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort / (5) an exact method of evaluating the density of the three estimators is described / (6) their exact bias, mean, variance and MSE are determined and analysed / and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed.</p> <p><br /> The discussion and results show that the estimators are still biased in the usual sense: &lsquo / in expectation&rsquo / . However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation.</p>

<p>In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as &lsquo / mean-unbiased&rsquo / and &lsquo / medianunbiased&rsquo / estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1).</p> <p><br /> However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to&nbsp / compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the &lsquo / medianunbiased&rsquo / estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed / the &lsquo / most-probably-unbiased&rsquo / estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed / (2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model / (3) the exact variance and MSE of LS estimator is determined / (4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort / (5) an exact method of evaluating the density of the three estimators is described / (6) their exact bias, mean, variance and MSE are determined and analysed / and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed.</p> <p><br /> The discussion and results show that the estimators are still biased in the usual sense: &lsquo / in expectation&rsquo / . However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation.</p>

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.

Submitted by Yuri Barboza Cocchiarale (yuriufrj1410@hotmail.com) on 2017-07-18T13:48:06Z No. of bitstreams: 1 Dissertação FGV - Yuri Barboza 2017.pdf: 7367125 bytes, checksum: f7c2e1f50effbdca635ca98fe61d1862 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2017-07-21T14:50:15Z (GMT) No. of bitstreams: 1 Dissertação FGV - Yuri Barboza 2017.pdf: 7367125 bytes, checksum: f7c2e1f50effbdca635ca98fe61d1862 (MD5) / Made available in DSpace on 2017-07-27T12:28:16Z (GMT). No. of bitstreams: 1 Dissertação FGV - Yuri Barboza 2017.pdf: 7367125 bytes, checksum: f7c2e1f50effbdca635ca98fe61d1862 (MD5) Previous issue date: 2017-05-31 / The aim of this study is to show that the creation of the Law no. 12,858 / 2013 has an irrelevant effect in the short term, regarding issues related to health and education problems. By adopting some assumptions capable of modeling the obtained database and estimating oil production using the SARIMA, Holt-Winters and Kalman Filter models, combined with the price forecast, the portrayed results can consistently reflect the impacts brought by this law. The problem becomes even bigger in a long-term horizon, in which the migration of revenue from royalties will overwhelmingly affect the entities who benefit from it. / Este trabalho tem como objetivo mostrar que a criação da Lei n° 12.858/2013 possui um efeito irrelevante no curto prazo, no que tange as questões ligadas aos problemas da saúde e educação. Adotando algumas premissas capazes de modelar o banco de dados obtido e estimando a produção do petróleo utilizando os modelos SARIMA, Holt-Winters e Filtro de Kalman, combinadas com a previsão dos preços, os resultados apresentados conseguem refletir de forma consistente os impactos trazidos por esta lei. O problema ainda se torna maior em um horizonte de longo prazo, onde a migração da receita provida dos royalties afetará de forma devastadora os entes que se beneficiam dela.

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)

Made available in DSpace on 2014-12-17T14:08:53Z (GMT). No. of bitstreams: 1 FranciscaFNS_DISSERT.pdf: 1424383 bytes, checksum: 6d399b5a60f42e3c2b87657eb17e44e0 (MD5) Previous issue date: 2013-02-05 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Atualmente, ? de grande interesse o estudo de m?todos de previs?o de S?ries Temporais, ou seja, conseguir identificar e predizer algumas caracter?sticas do processo num ponto futuro. Na engenharia de petr?leo uma das atividades essenciais ? a estimativa de produ??o de ?leo existente nas reservas petrol?feras de reservat?rios maduros. O c?lculo dessas reservas ? crucial para a determina??o da viabilidade econ?mica de sua explota??o. Para tanto, a ind?stria do petr?leo faz uso de t?cnicas convencionais de modelagem de reservat?rios como simula??o num?rica matem?tica para previs?o da produ??o de petr?leo. Diante deste fato, o objetivo fundamental deste trabalho ? propor uma metodologia de An?lise de S?ries Temporais baseada nos tradicionais modelos estat?sticos de Box & Jenkins, que em conjunto com a t?cnica inteligente de Redes Neurais Artificiais (RNA s), possibilite a constru??o de um modelo h?brido de predi??o de dados de produ??o de petr?leo, tomando por base a capacidade que a rede tem em aprender com a experi?ncia e partir para generaliza??o baseada no seu conhecimento pr?vio. Para tanto, a Rede Neural ser? treinada com a finalidade de estimar e corrigir os erros associados ao modelo estat?stico de S?rie Temporal, de forma a aproximar a s?rie estimada ? s?rie de dados original. Os dados da S?rie Temporal em estudo referem-se ? curva de vaz?o de petr?leo de um reservat?rio localizado em um campo da regi?o nordeste do Brasil. A s?rie em estudo foi obtida no per?odo 31de julho do ano 1998 ate 31 de dezembro de 2007, com os dados (vaz?o) sendo obtidos com intervalos mensais, totalizando 127 meses de informa??es. O algoritmo de predi??o proposto pela Rede Neural receber? como entrada os erros gerados pelo modelo estat?stico de s?rie e fornecer? como sa?da uma estimativa do erro no tempo n+h onde h representa o horizonte de predi??o. Os erros estimados pela Rede Neural ser?o adicionados ao Modelo de S?rie Temporal com a finalidade de corrigi-lo. Por fim, ser? feito um estudo comparativo da performance preditiva do modelo de Box & Jenkins cl?ssico e o modelo de Box & Jenkins corrigido pela Rede Neural. A arquitetura recorrente em estudo neste trabalho dever? ser capaz de prover estimativas confi?veis, tanto para um horizonte de predi??o de passos simples quanto para um horizonte de m?ltiplos passos. O software utilizado para realiza??o do ajuste do modelo estat?stico de S?rie Temporal foi o R Project for Statistical Computing - vers?o 2.14.1. Para fazer as implementa??es necess?rias da Rede Neural, a ferramenta computacional utilizada foi o software Matlab Vers?o 7.0.2 (R2011a)

Magister Scientiae - MSc / In recent years, two estimators have been proposed to correct the bias exhibited by the leastsquares (LS) estimator of the lagged dependent variable (LDV) coefficient in dynamic regression models when the sample is finite. They have been termed as &lsquo;mean-unbiased&rsquo; and &lsquo;medianunbiased&rsquo; estimators. Relative to other similar procedures in the literature, the two locationbased estimators have the advantage that they offer an exact and uniform methodology for LS estimation of the LDV coefficient in a first order autoregressive model with or without exogenous regressors i.e. ARX(1). However, no attempt has been made to accurately establish and/or compare the statistical properties among these estimators, or relative to those of the LS estimator when the LDV coefficient is restricted to realistic values. Neither has there been an attempt to&nbsp; compare their performance in terms of their mean squared error (MSE) when various forms of the exogenous regressors are considered. Furthermore, only implicit confidence intervals have been given for the &lsquo;medianunbiased&rsquo; estimator. Explicit confidence bounds that are directly usable for inference are not available for either estimator. In this study a new estimator of the LDV coefficient is proposed; the &lsquo;most-probably-unbiased&rsquo; estimator. Its performance properties vis-a-vis the existing estimators are determined and compared when the parameter space of the LDV coefficient is restricted. In addition, the following new results are established: (1) an explicit computable form for the density of the LS estimator is derived for the first time and an efficient method for its numerical evaluation is proposed; (2) the exact bias, mean, median and mode of the distribution of the LS estimator are determined in three specifications of the ARX(1) model; (3) the exact variance and MSE of LS estimator is determined; (4) the standard error associated with the determination of same quantities when simulation rather than numerical integration method is used are established and the methods are compared in terms of computational time and effort; (5) an exact method of evaluating the density of the three estimators is described; (6) their exact bias, mean, variance and MSE are determined and analysed; and finally, (7) a method of obtaining the explicit exact confidence intervals from the distribution functions of the estimators is proposed. The discussion and results show that the estimators are still biased in the usual sense: &lsquo;in expectation&rsquo;. However the bias is substantially reduced compared to that of the LS estimator. The findings are important in the specification of time-series regression models, point and interval estimation, decision theory, and simulation. / South Africa