Using monthly returns to model conditional heteroscedasticity

This empirical study examines the extent of non-linearity in a multivariate model of monthly financial series. To capture the conditional heteroscedasticity in the series, both the GARCH(1,1) and GARCH(1,1)-in-mean models are employed. The conditional errors are assumed to follow the normal and Student-t distributions. The non-linearity in the residuals of a standard OLS regression are also assessed. It is found that the OLS residuals as well as conditional errors of the GARCH models exhibit strong non-linearity. Under the Student density, the extent of non-linearity in the GARCH conditional errors was generally similar to those of the standard OLS. The GARCH-in-mean regression generated the worse out-of-sample forecasts.

Autoregressive conditional kurtosis

This article proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student’s t-density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising U.S. and U.K. stocks and bonds, and significant evidence in favor of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are proposed, and we show that the response of kurtosis to good and bad news is not significantly asymmetric.

The Impact of European Macroeconomic News Announcements on CIVETS Stock Markets

The purpose of this research is to investigate how CIVETS (Colombia, Indonesia, Vietnam, Egypt, Turkey and South Africa) stock markets are integrated with Europe as measured by the impact of euro area (EA) scheduled macroeconomic news announcements, which are related to macroeconomic indicators that are commonly used to indicate the direction of the economy. Macroeconomic announcements used in this study can be divided into four categories; (1) prices, (2) real economy, (3) money supply and (4) business climate and consumer confidence. The data set consists of daily market data from CIVETS and scheduled macroeconomic announcements from the EA for the years 2007-2012. The econometric model used in this research is Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). Empirical results show diverse impacts of macroeconomic news releases and surprises for different categories of news supporting the perception of heterogeneity among CIVETS. The analyses revealed that in general EA macroeconomic news releases and surprises affect stock market volatility in CIVETS and only in some cases asset pricing. In conclusion, all CIVETS stock markets reacted to the incoming EA macroeconomic news suggesting market integration to some extent. Thus, EA should be considered as a possible risk factor when investing in CIVETS.

A note on estimating market–based minimum capital risk requirements: a multivariate GARCH approach

Internal risk management models of the kind popularized by J. P. Morgan are now used widely by the world’s most sophisticated financial institutions as a means of measuring risk. Using the returns on three of the most popular futures contracts on the London International Financial Futures Exchange, in this paper we investigate the possibility of using multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models for the calculation of minimum capital risk requirements (MCRRs). We propose a method for the estimation of the value at risk of a portfolio based on a multivariate GARCH model. We find that the consideration of the correlation between the contracts can lead to more accurate, and therefore more appropriate, MCRRs compared with the values obtained from a univariate approach to the problem.

Dynamic correlations between REIT sub-sectors and the implications for diversification

The issue of whether Real Estate Investment Trusts (REITs) should pursue a focused or diversified investment strategy remains an ongoing debate within both the academic and industry communities. This article considers the relationship between REITs focused on different property sectors in a Generalized Autoregressive Conditional Heteroscedasticity-Dynamic Control Correlation (GARCH-DCC) framework. The daily conditional correlations reveal that since 1990 there has been a marked upward trend in the coefficients between US REIT sub-sectors. The findings imply that REITs are behaving in a far more homogeneous manner than in the past. Furthermore, the argument that REITs should be focused in order that investors can make the diversification decision is reduced.

The influence of ARIMA-GARCH parameters in feed forward neural networks prediction

The objective of this article is to find out the influence of the parameters of the ARIMA-GARCH models in the prediction of artificial neural networks (ANN) of the feed forward type, trained with the Levenberg-Marquardt algorithm, through Monte Carlo simulations. The paper presents a study of the relationship between ANN performance and ARIMA-GARCH model parameters, i.e. the fact that depending on the stationarity and other parameters of the time series, the ANN structure should be selected differently. Neural networks have been widely used to predict time series and their capacity for dealing with non-linearities is a normally outstanding advantage. However, the values of the parameters of the models of generalized autoregressive conditional heteroscedasticity have an influence on ANN prediction performance. The combination of the values of the GARCH parameters with the ARIMA autoregressive terms also implies in ANN performance variation. Combining the parameters of the ARIMA-GARCH models and changing the ANN`s topologies, we used the Theil inequality coefficient to measure the prediction of the feed forward ANN.

Previsão de volatilidade no Brasil: RiskMetrics, GARCH, volatilidade implícita ou uma combinação desses modelos?: um estudo empírico

O trabalho testa o poder de previsão da volatilidade futura, de cinco modelos : um modelo ingênuo, do tipo martingale, o modelo sugerido pelo JPMorgan em seu RiskMetrics™, o modelo GARCH-Generalized Autoregressive Conditional Heteroscedasticity, o modelo da volatilidade implícita e combinações de Risk:MetricsTM com volatilidade implícita e de GARCH com volatilidade implícita. A série estudada é a volatilidade para vinte e cinco dias, dos retornos diários do contrato futuro de Ibovespa, negociado na BM&F - Bolsa de Mercadorias e Futuros. Particularidades brasileiras são introduzidas na. estimação dos parâmetros do modelo GARCH. O poder de previsão é testado com medidas estatísticas, envolvendo equações de perdas (loss functions) simétricas e assimétricas, e com uma medida econômica, dada pelo lucro obtido a partir da simulação da realização de operações hedgeadas, sugeridas pelas previsões de volatilidade. Tanto com base nas medidas estatísticas como na medida econômica, o modelo GARCH emerge como o de melhor desempenho. Com base nas medidas estatísticas, esse modelo é particularmente melhor em período de mais alta volatilidade. Com base na medida econômica, contudo, o lucro obtido não é estatisticamente diferente de zero, indicando eficiência do mercado de opções de compra do contrato futuro de Ibovespa, negociado na mesmaBM&F.

Cálculo do Value at Risk (VaR) para o Ibovespa, pós crise de 2008, por meio dos modelos de heterocedasticidade condicional (GARCH) e de volatilidade estocástica (Local Scale Model - LSM)

O objetivo deste estudo é propor a implementação de um modelo estatístico para cálculo da volatilidade, não difundido na literatura brasileira, o modelo de escala local (LSM), apresentando suas vantagens e desvantagens em relação aos modelos habitualmente utilizados para mensuração de risco. Para estimação dos parâmetros serão usadas as cotações diárias do Ibovespa, no período de janeiro de 2009 a dezembro de 2014, e para a aferição da acurácia empírica dos modelos serão realizados testes fora da amostra, comparando os VaR obtidos para o período de janeiro a dezembro de 2014. Foram introduzidas variáveis explicativas na tentativa de aprimorar os modelos e optou-se pelo correspondente americano do Ibovespa, o índice Dow Jones, por ter apresentado propriedades como: alta correlação, causalidade no sentido de Granger, e razão de log-verossimilhança significativa. Uma das inovações do modelo de escala local é não utilizar diretamente a variância, mas sim a sua recíproca, chamada de “precisão” da série, que segue uma espécie de passeio aleatório multiplicativo. O LSM captou todos os fatos estilizados das séries financeiras, e os resultados foram favoráveis a sua utilização, logo, o modelo torna-se uma alternativa de especificação eficiente e parcimoniosa para estimar e prever volatilidade, na medida em que possui apenas um parâmetro a ser estimado, o que representa uma mudança de paradigma em relação aos modelos de heterocedasticidade condicional.

Computational tools for comparing asymmetric GARCH models via Bayes factors

In this paper we use Markov chain Monte Carlo (MCMC) methods in order to estimate and compare GARCH models from a Bayesian perspective. We allow for possibly heavy tailed and asymmetric distributions in the error term. We use a general method proposed in the literature to introduce skewness into a continuous unimodal and symmetric distribution. For each model we compute an approximation to the marginal likelihood, based on the MCMC output. From these approximations we compute Bayes factors and posterior model probabilities. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

Integração espacial e eficiência do hedge no mercado sul-americano de soja: comparações entre Brasil e Argentina

Este trabalho tem por objetivo analisar o potencial de desenvolvimento do contrato futuro de soja no Brasil, por meio da atração de hedgers brasileiros e argentinos. Para tanto, faz-se necessário conhecer os padrões das conexões dos preços entre as regiões analisadas. Nesse sentido, o Capítulo 2 investigou a integração espacial do mercado físico de soja no Brasil (região de Sorriso, no Mato Grosso) e na Argentina (região de Rosário, na província de Santa Fé) e comparou ao grau de integração com os Estados Unidos. Foram empregados modelos autorregressivos com threshold (TAR e M-TAR) e modelos vetoriais de correção de erros, lineares e com threshold (VECM e TVECM), visando captar os efeitos dos custos de transação sobre a integração espacial entre essas regiões. Os resultados apontaram que o mercado de soja brasileiro, argentino e norte-americano são integrados, mesmo considerando-se os efeitos dos custos de transação sobre as decisões de arbitragem espacial. Consequentemente, os preços da soja no mercado internacional tendem a refletir o comportamento dos principais países produtores. Apesar disso, o tempo de transmissão de choques de preços mostrou-se, em geral, menor entre Brasil e Argentina, refletindo a proximidade geográfica. Apontou-se também o comportamento assimétrico da transmissão desses choques, uma vez que choques positivos sobre a relação de longo prazo tendem a ser mais persistentes que os negativos. Se o contrato futuro reflete o comportamento de preços de um único mercado físico integrado, deve-se então esperar que o risco de base seja menor para este mercado e, portanto, que a eficiência do hedge seja maior. No Capítulo 3, o objetivo se constituiu em verificar se há maior eficiência no hedge realizado com os contratos com vencimento em março na CME em relação à BM&FBOVESPA, considerando-se as relações de longo prazo entre os preços à vista e futuros, bem como a dinâmica na estrutura de covariâncias condicionais, por meio de modelos de correção de erros (VECM) e modelos de heterocedasticidade condicional generalizados com correlação condicional dinâmica (DCC-GARCH). Os resultados mostraram que, em geral, a introdução da dinâmica nos segundos momentos das distribuições dos erros tende a aumentar a eficiência da estratégia de hedge. Além disso, foi observado que os produtores de Sorriso tendem a obter melhores condições de hedge na CME, embora haja redução da variância ao se operar na BM&FBOVESPA. Por outro lado, a eficiência do hedge para os produtores de Rosário foi significativamente maior na BM&FBOVESPA do que na CME, o que indica o mercado potencial de hedgers argentinos para negociar o contrato futuro de soja local no Brasil.

Pricing-to-market and the volatility of UK export prices

This empirical study examines the Pricing-To-Market (PTM) behaviour of 20 UK export sectors. Using both Exponential General Autoregressive Conditional Heteroscedasticity (EGARCH) and Threshold GARCH (TGARCH) estimation methods, we find evidence of PTM that is accompanied by strong conditional volatility and weak asymmetry effects. The PTM estimates suggest that when the currency of exporters appreciates in the current period, exporters pass-on between 31% and 94% of the Foreign Exchange (FX) rate increase to importers. However, both export price changes and producers' prices are sluggish, perhaps being driven by coordination failure and menu driven costs, amongst others. Furthermore, export prices contain strong time varying effects which impact on PTM strategy. Exporters do not typically appear to put much more weight on negative news of (say) an FX rate appreciation compared to positive news of an FX rate depreciation. Much depends on the export sector. © 2010 Taylor & Francis.

Split-ARCH

2000 Mathematics Subject Classification: 62M10

INFLACIÓN E INCERTIDUMBRE INFLACIONARIA: EVIDENCIA PARA COSTA RICA

En este documento se estima una medida de la incertidumbre inflacionaria. Un modelo de inflación señala incertidumbre cuando los errores de pronóstico son heteroscedásticos. Por medio de la especificación de una ecuación GARCH (Generalized Autoregressive Conditional Heteroscedasticity), para la varianza del término de error de un modelo de inflación, es posible estimar una proxy de incertidumbre inflacionaria. La estimación simultánea del modelo de inflación y de la ecuación GARCH, produce un nuevo modelo de inflación en el cual los errores de pronóstico son homocedásticos. Existe consenso en la literatura económica en que hay una correlación positiva entre incertidumbre inflacionaria y la magnitud de la tasa de inflación, lo cual, como lo señaló Friedman (1977), representa uno de los costos asociados con la persistencia inflacionaria. Esto es porque tal incertidumbre dificulta la toma de decisiones óptimas por parte de los agentes económicos.La evidencia empírica, para el periodo 1954:01-2002:08, apoya la hipótesis de que para el caso de Costa Rica mientras mayor es la inflación mayor es la incertidumbre respecto a esta variable. En los últimos siete años (1997-2002) la incertidumbre presenta la variación media más baja de todo el periodo. Además, se identifica un efecto asimétrico de la inflación sobre la incertidumbre inflacionaria, es decir, la incertidumbre inflacionaria tiende a incrementarse más para el siguiente periodo cuando la inflación pronosticada está por debajo de la inflación actual, que cuando la inflación pronosticada está por arriba de la tasa observada de inflación. Estos resultados tienen una clara implicación para la política monetaria. Para minimizar la dificultad que la inflación causa en la toma óptima de decisiones de los agentes económicos es necesario perseguir no solamente un nivel bajo de inflación sino que también sea estable.AbstractThis paper estimates a measure of inflationary uncertainty. An inflation model signals uncertainty when the forecast errors are heteroskedastic. By the specification of a GARCH (Generalized Autoregressive Conditional Heteroscedasticity) equation, for the variance of the error term of the inflation model, it is possible to estimate a proxy for inflationary uncertainty. By the simultaneous estimation of the inflation model and the GARCH equation, a new inflation model is obtained in which the forecast errors are homocedastic. Most economists agree that there is a positive correlation between inflationary uncertainty and the magnitude of the inflation rate, which, as was pointed out by Friedman (1977), represents one of costs associated with the persistence of inflation. This is because such uncertainty clouds the decision-making process of consumers and investors.The empirical evidence for the period 1954:01-2002:08 confirms that in the case of Costa Rica inflationary uncertainty increases as inflation rises. In the last seven years(1997-2002) the uncertainty present the mean variation most small of the period. In addition, inflation has an asymmetric effect on inflationary uncertainty. That is, when the inflation forecast is below the actual inflation, inflationary uncertainty increases for the next period. The opposite happens when the inflation forecast is above the observed rate of inflation. Besides, the absolute value of the change on uncertainty is greater in the first case than the second. These results have a clear implication for monetary policy. To minimize the disruptions that inflation causes to the economic decision-making process, it is necessary to pursue, not only a low level of inflation, but a stable one as well.

Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.