Dissertation thesis creates a complex and modern scheme for stochastic modeling of demographic processes, which is universally applicable to any population in the world. All calculations are described in detail on the data of the Czech Republic. Throughout the work the attention is drawn to the issues, that every analyst must necessarily take into account in order to obtain correct results. Data comes mostly from the Czech Statistical Office database. However, some data matrices had to be calculated for the purposes of the thesis. Particular demographic processes (mortality, fertility and migration) are modeled using selected modern approaches (ARIMA models, Lee-Carter method) and based on the constructed models these processes are forecasted to the future. Using partially projected results a comprehensive demographic projection of the population of the Czech Republic is created up to the year 2050. However, not on the basis of the current state and expert expectations of the future development, but based on sophistically projected demographic events, which are explained using the trends and main components of their previous development. This demographic projection is created in three scenarios (marked SC1, SC2 and SC3), which are made from selected optimal models, presented in particular sections of the work. One part of the thesis is also the backward retropolation of age-specific number of net migrants by sex in the Czech Republic since 1948. On its basis the analysis and prediction of the migration can be done. The thesis is a synthesis of the projections of demographic processess of mortality, fertility, and migration. Final results are confronted with three scenarios of population projections of the Czech Republic created by the Czech Statistical Office and five scenarios of population projections by Eurostat. The purely statistical approach of demographic forecasting in comparison with deterministic models and expert expectations has its positives and negatives. Therefore, the different results due to various methodological approaches are discussed and compared in the conclusion of the thesis.

The main objective of the thesis was to investigate the feasibility of accurately and precisely fore- casting the number of both national and provincial bene ciaries of social security grants in South Africa, using simple autoregressive integrated moving average (ARIMA) models. The series of the monthly number of bene ciaries of the old age, child support, foster care and disability grants from April 2004 to March 2010 were used to achieve the objectives of the thesis. The conclusions from analysing the series were that: (1) ARIMA models for forecasting are province and grant-type spe- ci c; (2) for some grants, national forecasts obtained by aggregating provincial ARIMA forecasts are more accurate and precise than those obtained by ARIMA modelling national series; and (3) for some grants, forecasts obtained by modelling the latest half of the series were more accurate and precise than those obtained from modelling the full series. / Mathematical Sciences / M.Sc. (Statistics)

Submitted by Simone Jager (si_jager@hotmail.com) on 2014-02-10T15:30:57Z No. of bitstreams: 1 Simone Jager 2014.pdf: 764649 bytes, checksum: 100e29a7572ff1d6c57a770ace28e1bf (MD5) / Approved for entry into archive by Vitor Souza (vitor.souza@fgv.br) on 2014-02-24T21:08:40Z (GMT) No. of bitstreams: 1 Simone Jager 2014.pdf: 764649 bytes, checksum: 100e29a7572ff1d6c57a770ace28e1bf (MD5) / Made available in DSpace on 2014-05-20T13:15:26Z (GMT). No. of bitstreams: 1 Simone Jager 2014.pdf: 764649 bytes, checksum: 100e29a7572ff1d6c57a770ace28e1bf (MD5) Previous issue date: 2014-01-23 / This paper compares time series models to forecast short-term Brazilian inflation measured by Consumer Price Index (IPCA). Were considered SARIMA Box-Jenkins models and structural models in state space, as estimated by the Kalman filter. For estimation of the models, the series of IPCA monthly basis from March 2003 to March 2012 was used. The SARIMA models were estimated in EVIEWS and structural models in STAMP. For the validation of the models out of sample forecasts were considered one step ahead for the period April 2012 to March 2013, based on the main criteria for assessing predictive ability proposed in the literature. The conclusion of the study is that, although the structural model allows, to decompose the series into components with direct interpretation and study them separately, while incorporating explanatory variables in a simple way, the performance of the SARIMA model to predict Brazilian inflation was higher in the period and horizon considered. Another important positive aspect is that the implementation of a SARIMA model is ready, and predictions from it are obtained in a simple and direct way. / Este trabalho compara modelos de séries temporais para a projeção de curto prazo da inflação brasileira, medida pelo Índice de Preços ao Consumidor Amplo (IPCA). Foram considerados modelos SARIMA de Box e Jenkins e modelos estruturais em espaço de estados, estimados pelo filtro de Kalman. Para a estimação dos modelos, foi utilizada a série do IPCA na base mensal, de março de 2003 a março de 2012. Os modelos SARIMA foram estimados no EVIEWS e os modelos estruturais no STAMP. Para a validação dos modelos para fora da amostra, foram consideradas as previsões 1 passo à frente para o período de abril de 2012 a março de 2013, tomando como base os principais critérios de avaliação de capacidade preditiva propostos na literatura. A conclusão do trabalho é que, embora o modelo estrutural permita, decompor a série em componentes com interpretação direta e estudá-las separadamente, além de incorporar variáveis explicativas de forma simples, o desempenho do modelo SARIMA para prever a inflação brasileira foi superior, no período e horizonte considerados. Outro importante aspecto positivo é que a implementação de um modelo SARIMA é imediata, e previsões a partir dele são obtidas de forma simples e direta.

The main objective of the thesis was to investigate the feasibility of accurately and precisely fore- casting the number of both national and provincial bene ciaries of social security grants in South Africa, using simple autoregressive integrated moving average (ARIMA) models. The series of the monthly number of bene ciaries of the old age, child support, foster care and disability grants from April 2004 to March 2010 were used to achieve the objectives of the thesis. The conclusions from analysing the series were that: (1) ARIMA models for forecasting are province and grant-type spe- ci c; (2) for some grants, national forecasts obtained by aggregating provincial ARIMA forecasts are more accurate and precise than those obtained by ARIMA modelling national series; and (3) for some grants, forecasts obtained by modelling the latest half of the series were more accurate and precise than those obtained from modelling the full series. / Mathematical Sciences / M.Sc. (Statistics)