Forecasting accuracy and estimation uncertainty using VAR models with short- and long-term economic restrictions: a Monte-Carlo study

Using vector autoregressive (VAR) models and Monte-Carlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The ��rst reduces parameter space by imposing long-term restrictions on the behavior of economic variables as discussed by the literature on cointegration, and the second reduces parameter space by imposing short-term restrictions as discussed by the literature on serial-correlation common features (SCCF). Our simulations cover three important issues on model building, estimation, and forecasting. First, we examine the performance of standard and modi��ed information criteria in choosing lag length for cointegrated VARs with SCCF restrictions. Second, we provide a comparison of forecasting accuracy of ��tted VARs when only cointegration restrictions are imposed and when cointegration and SCCF restrictions are jointly imposed. Third, we propose a new estimation algorithm where short- and long-term restrictions interact to estimate the cointegrating and the cofeature spaces respectively. We have three basic results. First, ignoring SCCF restrictions has a high cost in terms of model selection, because standard information criteria chooses too frequently inconsistent models, with too small a lag length. Criteria selecting lag and rank simultaneously have a superior performance in this case. Second, this translates into a superior forecasting performance of the restricted VECM over the VECM, with important improvements in forecasting accuracy ��reaching more than 100% in extreme cases. Third, the new algorithm proposed here fares very well in terms of parameter estimation, even when we consider the estimation of long-term parameters, opening up the discussion of joint estimation of short- and long-term parameters in VAR models.

Analisando o risco de uma carteira de cr��dito via simula����es de Monte Carlo

Neste trabalho, analisamos utiliza����o da metodologia CreditRLsk+ do Credit Suisse sua adequa����o ao mercado brasileiro, com objetivo de calcular risco de uma carteira de cr��dito. Certas hip��teses assumidas na formula����o do modelo CreditRisk+ n��o valem para o mercado brasileiro, caracterizado, por exemplo, por uma elevada probabilidade de defcnilt. Desenvolvemos, ent��o, uma metodologia para c��lculo da distribui����o de perdas atrav��s do m��todo de Simula����o de Monte Cario, alterando algumas hip��teses originais do modelo com objetivo de adapt��-lo ao nosso mercado. utiliza����o de simula����es tamb��m oferece resultados mais precisos em situa����es onde as carteiras possuem uma pequena popula����o de contratos, al��m de eliminar poss��veis problemas de converg��ncia do m��todo anal��tico, mesmo considerando as hip��teses do modelo original. Verifica-se ainda que tempo computacional pode ser menor que da metodologia original, principalmente em carteiras com elevado n��mero de devedores de perfis distintos com aloca����es em diversos setores da economia. Tendo em vista as restri����es acima, acreditamos que metodologia proposta seja uma alternativa para forma anal��tica do modelo CreditRisk+. Apresentamos exemplos de utiliza����o resultados providos por estas simula����es. ponto central deste trabalho real��ar import��ncia da utiliza����o de metodologias alternativas de medi����o de risco de cr��dito que incorporem as particularidades do mercado brasileiro.

Uma an��lise comparativa entre a metodologia anal��tica e a metodologia de simula����o Monte Carlo para o c��lculo do value at risk

O presente trabalho tem por objetivo descrever, avaliar comparar as metodologias anal��tica da simula����o Monte Cario para c��lculo do Value at Risk (Valor em Risco) de institui����es financeiras de empresas. Para comparar as vantagens desvantagens de cada metodologia, efetuaremos compara����es alg��bricas realizamos diversos testes emp��ricos com institui����es hipot��ticas que apresentassem diferentes n��veis de alavancagem de composi����o em seus balan��os, que operassem em diferentes mercados (consideramos os mercados de a����es, de op����es de compra de t��tulos de renda fixa prefixados).

A simula����o de Monte Carlo como instrumento de an��lise de riscos e sele����o de projetos

Trata da aplicabilidade da Simula����o de Monte Carlo para a an��lise de riscos e, conseq��entemente, o apoio �� decis��o de investir ou n��o em um projeto. S��o abordados m��todos de an��lise de riscos e sele����o de projetos, bem como a natureza, vantagens e limita����es da Simula����o de Monte Car��o. Por fim este instrumento tem sua viabilidade analisada sob a luz do processo de an��lise de riscos de uma empresa brasileira.

The importance of common cyclical features in VAR analysis: a Monte-Carlo study

Despite the commonly held belief that aggregate data display short-run comovement, there has been little discussion about the econometric consequences of this feature of the data. We use exhaustive Monte-Carlo simulations to investigate the importance of restrictions implied by common-cyclical features for estimates and forecasts based on vector autoregressive models. First, we show that the ��best�� empirical model developed without common cycle restrictions need not nest the ��best�� model developed with those restrictions. This is due to possible differences in the lag-lengths chosen by model selection criteria for the two alternative models. Second, we show that the costs of ignoring common cyclical features in vector autoregressive modelling can be high, both in terms of forecast accuracy and efficient estimation of variance decomposition coefficients. Third, we find that the Hannan-Quinn criterion performs best among model selection criteria in simultaneously selecting the lag-length and rank of vector autoregressions.

The importance of Common-Cyclical Features in VAR analysis: a Monte-Carlo study (Preliminary Version)

Despite the belief, supported byrecentapplied research, thataggregate datadisplay short-run comovement, there has been little discussion about the econometric consequences ofthese data ���features.��� W e use exhaustive M onte-Carlo simulations toinvestigate theimportance ofrestrictions implied by common-cyclicalfeatures for estimates and forecasts based on vectorautoregressive and errorcorrection models. First, weshowthatthe���best��� empiricalmodeldevelopedwithoutcommoncycles restrictions neednotnestthe���best��� modeldevelopedwiththoserestrictions, duetothe use ofinformation criteria forchoosingthe lagorderofthe twoalternative models. Second, weshowthatthecosts ofignoringcommon-cyclicalfeatures inV A R analysis may be high in terms offorecastingaccuracy and e��ciency ofestimates ofvariance decomposition coe��cients. A lthough these costs are more pronounced when the lag orderofV A R modelsareknown, theyarealsonon-trivialwhenitis selectedusingthe conventionaltoolsavailabletoappliedresearchers. T hird, we���ndthatifthedatahave common-cyclicalfeatures andtheresearcherwants touseaninformationcriterium to selectthelaglength, theH annan-Q uinn criterium is themostappropriate, sincethe A kaike and theSchwarz criteriahave atendency toover- and under-predictthe lag lengthrespectivelyinoursimulations.

Estimation of DSGE Models: A Monte Carlo Analysis

Neste trabalho investigamos as propriedades em pequena amostra e a robustez das estimativas dos par��metros de modelos DSGE. Tomamos o modelo de Smets and Wouters (2007) como base e avaliamos a performance de dois procedimentos de estima����o: M��todo dos Momentos Simulados (MMS) e M��xima Verossimilhan��a (MV). Examinamos a distribui����o emp��rica das estimativas dos par��metros e sua implica����o para as an��lises de impulso-resposta e decomposi����o de vari��ncia nos casos de especifica����o correta e m�� especifica����o. Nossos resultados apontam para um desempenho ruim de MMS e alguns padr��es de vi��s nas an��lises de impulso-resposta e decomposi����o de vari��ncia com estimativas de MV nos casos de m�� especifica����o considerados.

Elabora����o de um modelo de valora����o quantitativa das garantias para o setor de saneamento com utiliza����o de Simula����o de Monte Carlo: o caso PPP de Esgoto para a Regi��o Metropolitana do Recife e Munic��pio de Goi��nia

A situa����o do saneamento no Brasil �� alarmante. Os servi��os de ��gua e esgotamento sanit��rio s��o prestados adequadamente somente para 59,4% e 39,7%, respectivamente, da popula����o brasileira. Para mudar este quadro, estima-se que sejam necess��rios R$ 304 bilh��es em investimentos. Parte desse volume ter�� que vir da iniciativa privada e a estrutura����o de parcerias p��blico privadas �� uma das formas de atingir este objetivo. Nestes projetos �� comum o setor p��blico oferecer garantias ao parceiro privado para assegurar a viabilidade do empreendimento. O presente trabalho apresenta um modelo para valora����o destas garantias, utilizando como estudos de caso as PPP de esgoto da regi��o metropolitana de Recife e do Munic��pio de Goiana. O resultado obtido mostrou a import��ncia desta valora����o, uma vez que dependendo do n��vel de garantia oferecida o valor presente dos desembolsos previstos para o setor p��blico variou de zero a at�� R$ 204 milh��es.

Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.

Estima����o de regress��es aditivas via backfitting e integra����o marginal: performance em pequenas amostras

Nesta disserta����o realizou-se um experimento de Monte Carlo para re- velar algumas caracter��sticas das distribui����es em amostras finitas dos estimadores Backfitting (B) e de Integra����o Marginal(MI) para uma regress��o aditiva bivariada. Est��-se particularmente interessado em fornecer alguma evid��ncia de como os diferentes m��todos de sele����o da janela hn, tais co- mo os m��todos plug-in, impactam as propriedades em pequenas amostras dos estimadores. Est��-se interessado, tamb��m, em fornecer evid��ncia do comportamento de diferentes estimadores de hn relativamente a seq����ncia ��tima de hn que minimiza uma fun����o perda escolhida. O impacto de ignorar a depend��ncia entre os regressores na estima����o da janela �� tam- b��m investigado. Esta �� uma pr��tica comum e deve ter impacto sobre o desempenho dos estimadores. Al��m disso, n��o h�� nenhuma rotina atual- mente dispon��vel nos pacotes estat��sticos/econom��tricos para a estima����o de regress��es aditivas via os m��todos de Backfitting e Integra����o Marginal. �� um dos objetivos a cria����o de rotinas em Gauss para a implementa����o pr��tica destes estimadores. Por fim, diferentemente do que ocorre atual- mente, quando a utiliza����o dos estimadores-B e MI �� feita de maneira completamente ad-hoc, h�� o objetivo de fornecer a usu��rios informa����o que permita uma escolha mais objetiva de qual estimador usar quando se est�� trabalhando com uma amostra finita.

A study on time-varying quantile and its applications

This Thesis is the result of my Master Degree studies at the Graduate School of Economics, Get��lio Vargas Foundation, from January 2004 to August 2006. am indebted to my Thesis Advisor, Professor Luiz Renato Lima, who introduced me to the Econometrics' world. In this Thesis, we study time-varying quantile process and we develop two applications, which are presented here as Part and Part II. Each of these parts was transformed in paper. Both papers were submitted. Part shows that asymmetric persistence induces ARCH effects, but the LMARCH test has power against it. On the other hand, the test for asymmetric dynamics proposed by Koenker and Xiao (2004) has correct size under the presence of ARCH errors. These results suggest that the LM-ARCH and the Koenker-Xiao tests may be used in applied research as complementary tools. In the Part II, we compare four different Value-at-Risk (VaR) methodologies through Monte Cario experiments. Our results indicate that the method based on quantile regression with ARCH effect dominates other methods that require distributional assumption. In particular, we show that the non-robust method ologies have higher probability to predict VaRs with too many violations. We illustrate our findings with an empirical exercise in which we estimate VaR for returns of S��o Paulo stock exchange index, IBOVESPA, during periods of market turmoil. Our results indicate that the robust method based on quantile regression presents the least number of violations.

Testing unit root based on partially adaptive estimation

This paper proposes unit tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adptive estimation using nonparametric methods. The limiting distribution of the proposed test is a combination of standard normal and the traditional Dickey-Fuller (DF) distribution, including the traditional ADF test as a special case when using Gaussian density. Taking into a account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, wich includes te normal distribution as a limiting case. Monte Carlo Experiments indicate that, in the presence of heavy tail distributions or innovations that are contaminated by outliers, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit roots is not found in real exchange rate and nominal interest rate even haevy-tail is taken into a account.

Comparing value-at-risk methodologies

In this paper, we compare four different Value-at-Risk (V aR) methodologies through Monte Carlo experiments. Our results indicate that the method based on quantile regression with ARCH effect dominates other methods that require distributional assumption. In particular, we show that the non-robust methodologies have higher probability to predict V aRs with too many violations. We illustrate our findings with an empirical exercise in which we estimate V aR for returns of S��ao Paulo stock exchange index, IBOVESPA, during periods of market turmoil. Our results indicate that the robust method based on quantile regression presents the least number of violations.

Avalia����o de m��todos num��ricos para precifica����o de derivativos: aplica����o ao mercado brasileiro

Os objetivos deste trabalho foram (i) rever m��todos num��ricos para precifica����o de derivativos; e (ii) comparar os m��todos assumindo que os pre��os de mercado refletem ��queles obtidos pela f��rmula de Black Scholes para precifica����o de op����es do tipo europ��ia. Aplicamos estes m��todos para precificar op����es de compra da a����es Telebr��s. Os crit��rios de acur��cia e de custo computacional foram utilizados para comparar os seguintes modelos binomial, Monte Carlo, e diferen��as finitas. Os resultados indicam que o modelo binomial possui boa acur��cia e custo baixo, seguido pelo Monte Carlo e diferen��as finitas. Entretanto, o m��todo Monte Carlo poderia ser usado quando o derivativo depende de mais de dois ativos-objetos. �� recomend��vel usar o m��todo de diferen��as finitas quando se obt��m uma equa����o diferencial parcial cuja solu����o �� o valor do derivativo.

Convex combinations of long memory estimates from different sampling rates

Convex combinations of long memory estimates using the same data observed at different sampling rates can decrease the standard deviation of the estimates, at the cost of inducing a slight bias. The convex combination of such estimates requires a preliminary correction for the bias observed at lower sampling rates, reported by Souza and Smith (2002). Through Monte Carlo simulations, we investigate the bias and the standard deviation of the combined estimates, as well as the root mean squared error (RMSE), which takes both into account. While comparing the results of standard methods and their combined versions, the latter achieve lower RMSE, for the two semi-parametric estimators under study (by about 30% on average for ARFIMA(0,d,0) series).