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on Econometric Time Series |
| By: | Geert Mesters (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam) |
| Abstract: | We study the forecasting of the yearly outcome of the Boat Race between Cambridge and Oxford. We compare the relative performance of different dynamic models for forty years of forecasting. Each model is defined by a binary density conditional on a latent signal that is specified as a dynamic stochastic process with fixed predictors. The out-of-sample predictive ability of the models is compared between each other by using a variety of loss functions and predictive ability tests. We find that the model with its latent signal specified as an autoregressive process cannot be outperformed by the other specifications. This model is able to correctly forecast 30 out of 40 outcomes of the Boat Race. |
| Keywords: | Binary time series; Predictive ability; Non-Gaussian state space model |
| JEL: | C32 C35 |
| Date: | 2012–10–23 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120110&r=ets |
| By: | Bannouh, K.; Martens, M.P.E.; Oomen, R.C.A.; Dijk, D.J.C. van |
| Abstract: | We introduce a Mixed-Frequency Factor Model (MFFM) to estimate vast dimensional covari- ance matrices of asset returns. The MFFM uses high-frequency (intraday) data to estimate factor (co)variances and idiosyncratic risk and low-frequency (daily) data to estimate the factor loadings. We propose the use of highly liquid assets such as exchange traded funds (ETFs) as factors. Prices for these contracts are observed essentially free of microstructure noise at high frequencies, allowing us to obtain precise estimates of the factor covariances. The factor loadings instead are estimated from daily data to avoid biases due to market microstructure effects such as the relative illiquidity of individual stocks and non-synchronicity between the returns on factors and stocks. Our theoretical, simulation and empirical results illustrate that the performance of the MFFM is excellent, both compared to conventional factor models based solely on low-frequency data and to popular realized covariance estimators based on high-frequency data. |
| Keywords: | dimensional covariance estimation;mixed-frequency factor models |
| Date: | 2012–10–23 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureri:1765037470&r=ets |
| By: | Sofia Anyfantaki; Antonis Demos (www.aueb.gr/users/demos) |
| Abstract: | Time-varying GARCH-M models are commonly employed in econometrics and financial economics. Yet the recursive nature of the conditional variance makes exact likelihood analysis of these models computationally infeasible. This paper outlines the issues and suggests to employ a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a simulated Bayesian solution in only O(T) computational operations, where T is the sample size. Furthermore, the theoretical dynamic properties of a time-varying-parameter EGARCH(1,1)-M are derived. We discuss them and apply the suggested Bayesian estimation to three major stock markets. |
| Keywords: | Dynamic heteroskedasticity, in mean models, time varying parameter, Markov chain Monte Carlo, simulated EM algorithm, Bayesian inference |
| JEL: | C13 C15 C63 |
| Date: | 2012–07–30 |
| URL: | http://d.repec.org/n?u=RePEc:aue:wpaper:1228&r=ets |
| By: | Rodríguez, Alejandro; Ruiz, Esther |
| Abstract: | In the context of linear state space models with known parameters, the Kalman filter (KF) generates best linear unbiased predictions of the underlying states together with their corresponding Prediction Mean Square Errors (PMSE). However, in practice, when the filter is run with the parameters substituted by consistent estimates, the corresponding PMSE do not take into account the parameter uncertainty. Consequently, they underestimate their true counterparts. In this paper, we propose two new bootstrap procedures to obtain PMSE of the unobserved states designed to incorporate this latter uncertainty. We show that the new bootstrap procedures have better finite sample properties than bootstrap alternatives and than procedures based on the asymptotic approximation of the parameter distribution. The proposed procedures are implemented for estimating the PMSE of several key unobservable US macroeconomic variables as the output gap, the Non-accelerating Inflation Rate of Unemployment (NAIRU), the long-run investment rate and the core inflation. We show that taking into account the parameter uncertainty may change their prediction intervals and, consequently, the conclusions about the utility of the NAIRU as a macroeconomic indicator for expansions and recessions. |
| Keywords: | NAIRU; Output gap; Parameter uncertainty; Prediction intervals; State space models; |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:carlos:info:hdl:10016/15743&r=ets |
| By: | Carnero, María Ángeles; Peña, Daniel; Ruiz, Esther |
| Abstract: | GARCH volatilities depend on the unconditional variance, which is a non-linear function of the parameters. Consequently, they can have larger biases than estimated parameters. Using robust methods to estimate both parameters and volatilities is shown to outperform Maximum Likelihood procedures. |
| Keywords: | Financial markets; Heteroscedasticity; QML estimator; Robustness; |
| JEL: | C22 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:carlos:info:hdl:10016/15744&r=ets |
| By: | Mustafa Hakan Eratalay |
| Abstract: | In this paper, we make two contributions to the MSV literature. First, we propose two new MSV models that account for leverage effects. Second, we compare the small sample performances of Quasi Maximum Likelihood (QML) and Monte Carlo Likelihood (MCL) methods through Monte Carlo studies for Constant Correlations MSV and Time Varying Correlations MSV and for the two MSV models with leverage we propose. We also provide the specific transformations necessary for the MCL estimation of the proposed MSV models with leverage. Our results confirm that the MCL estimator has better small sample performance compared to the QML estimator. In terms of parameter estimation, both estimators perform better when the series are highly correlated. In estimating the underlying volatilities and correlations, QML estimator’s performance comes closer to that of MCL estimator when the SV process has higher variance or when the correlations are time varying, while it is performing relatively worse in MSV models with leverage. Finally we include an empirical illustration by estimating an MSV model with leverage that we propose using a trivariate data from the major European stock markets. |
| Keywords: | Multivariate Stochastic Volatility, Estimation, Constant Correlations, Time Varying Correlations, Leverage |
| JEL: | C32 |
| Date: | 2012–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:eus:wpaper:ec0412&r=ets |
| By: | Omay, Tolga |
| Abstract: | The aim of this study is to search for a better optimization algorithm in applying unit root tests that inherit nonlinear models in the testing process. The algorithms analyzed include Broyden, Fletcher, Goldfarb and Shanno (BFGS), Gauss-Jordan, Simplex, Genetic, and Extensive Grid-Search. The simulation results indicate that the derivative free methods, such as Genetic and Simplex, have advantages over hill climbing methods, such as BFGS and Gauss-Jordan, in obtaining accurate critical values for the Leybourne, Newbold and Vougos (1996, 1998) (LNV) and Sollis (2004) unit root tests. Moreover, when parameters are estimated under the alternative hypothesis of the LNV type of unit root tests the derivative free methods lead to an unbiased and efficient estimator as opposed to those obtained from other algorithms. Finally, the empirical analyses show that the derivative free methods, hill climbing and simple grid search can be used interchangeably when testing for a unit root since all three optimization methods lead to the same empirical test results. |
| Keywords: | Nonlinear trend; Deterministic smooth transition; Structural change; Estimation methods |
| JEL: | C15 C22 C01 |
| Date: | 2012–10–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:42129&r=ets |
| By: | Bentes, Sonia R; Menezes, Rui |
| Abstract: | This paper examines the behavior of several implied volatility indexes in order to compare them with the volatility forecasts obtained from estimating a GARCH model. Though volatility has always been a prevailing subject of research it has become particularly relevant given the increasingly complexity and uncertainty of stock markets in these days. An important measure to assess the market expectations of the future volatility of the underlying asset is the implied volatility (IV) indexes. Generally, these indexes are calculated based on the prices of out-of-the money put and call options on the underlying asset. Sometimes called the “investor fear gauge”, the IV indexes are a measure of the implied volatility of the underlying index. This study focuses on the implied and GARCH forecasted volatility of some emerging countries and some developed countries. More specifically, it compares the predictive power of the IV indexes with the ones provided by standard volatility models such as the ARCH/GARCH (Autoregressive Conditional Heteroskedasticity Model/ Generalized Autoregressive Conditional Heteroskedasticity Model) type models. Finally, a debate of the results is also provided. |
| Keywords: | implied volatility; volatility forecasts; GARCH models; volatility indices |
| JEL: | F37 C32 C01 |
| Date: | 2012–10–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:42193&r=ets |
| By: | Camacho, Maximo; Pérez-Quirós, Gabriel |
| Abstract: | We examine the short-term performance of two alternative approaches of forecasting from dynamic factor models. The first approach extracts the seasonal component of the individual indicators before estimating the dynamic factor model, while the alternative uses the non seasonally adjusted data in a model that endogenously accounts for seasonal adjustment. Our Monte Carlo analysis reveals that the performance of the former is always comparable to or even better than that of the latter in all the simulated scenarios. Our results have important implications for the factor models literature because they show the that the common practice of using seasonally adjusted data in this type of models is very accurate in terms of forecasting ability. Using five coincident indicators, we illustrate this result for US data. |
| Keywords: | factor models; seasonal adjustment; short-term forecasting |
| JEL: | C22 E27 E32 |
| Date: | 2012–10 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9191&r=ets |