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162
Integer Factorization
, 2005
"... Many public key cryptosystems depend on the difficulty of factoring large integers. This thesis serves as a source for the history and development of integer factorization algorithms through time from trial division to the number field sieve. It is the first description of the number field sieve fro ..."
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Cited by 123 (8 self)
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Many public key cryptosystems depend on the difficulty of factoring large integers. This thesis serves as a source for the history and development of integer factorization algorithms through time from trial division to the number field sieve. It is the first description of the number field sieve from an algorithmic point of view making it available to computer scientists for implementation. I have implemented the general number field sieve from this description and it is made publicly available from the Internet. This means that a reference implementation is made available for future developers which also can be used as a framework where some of the sub
Macro factors in bond risk premia
 Review of Financial Studies
, 2009
"... Are there important cyclical fluctuations in bond market premiums and, if so, with what macroeconomic aggregates do these premiums vary? We use the methodology of dynamic factor analysis for large datasets to investigate possible empirical linkages between forecastable variation in excess bond retur ..."
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Cited by 61 (1 self)
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Are there important cyclical fluctuations in bond market premiums and, if so, with what macroeconomic aggregates do these premiums vary? We use the methodology of dynamic factor analysis for large datasets to investigate possible empirical linkages between forecastable variation in excess bond returns and macroeconomic fundamentals. We find that “real ” and “inflation ” factors have important forecasting power for future excess returns on U.S. government bonds, above and beyond the predictive power contained in forward rates and yield spreads. This behavior is ruled out by commonly employed affine term structure models where the forecastability of bond returns and bond yields is completely summarized by the crosssection of yields or forward rates. An important implication of these findings is that the cyclical behavior of estimated risk premia in both returns and longterm yields depends importantly on whether the information in macroeconomic factors is included in forecasts of excess bond returns. Without the macro factors, risk premia appear virtually acyclical, whereas with the estimated factors risk premia have a marked countercyclical component, consistent with theories that imply investors must be compensated for risks associated with macroeconomic activity. ( JEL E0, E4, G10, G12) 1.
Bayesian Multivariate Time Series Methods for Empirical Macroeconomics
, 2009
"... Macroeconomic practitioners frequently work with multivariate time series models such as VARs, factor augmented VARs as well as timevarying parameter versions of these models (including variants with multivariate stochastic volatility). These models have a large number of parameters and, thus, over ..."
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Cited by 56 (12 self)
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Macroeconomic practitioners frequently work with multivariate time series models such as VARs, factor augmented VARs as well as timevarying parameter versions of these models (including variants with multivariate stochastic volatility). These models have a large number of parameters and, thus, overparameterization problems may arise. Bayesian methods have become increasingly popular as a way of overcoming these problems. In this monograph, we discuss VARs, factor augmented VARs and timevarying parameter extensions and show how Bayesian inference proceeds. Apart from the simplest of VARs, Bayesian inference requires the use of Markov chain Monte Carlo methods developed for state space models and we describe these algorithms. The focus is on the empirical macroeconomist and we offer advice on how to use these models and methods in practice and include empirical illustrations. A website provides Matlab code for carrying out Bayesian inference in these models.
Likelihoodbased analysis for dynamic factor models
, 2008
"... We present new results for the likelihoodbased analysis of the dynamic factor model that possibly includes intercepts and explanatory variables. The latent factors are modeled by stochastic processes. The idiosyncratic disturbances are specified as autoregressive processes with mutually correlated ..."
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Cited by 38 (7 self)
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We present new results for the likelihoodbased analysis of the dynamic factor model that possibly includes intercepts and explanatory variables. The latent factors are modeled by stochastic processes. The idiosyncratic disturbances are specified as autoregressive processes with mutually correlated innovations. The new results lead to computationally efficient procedures for the estimation of the factors and parameter estimation by (quasi)maximum likelihood. An illustration is provided for the analysis of a large panel of macroeconomic time series
Time Series Modelling with Semiparametric Factor Dynamics
, 2008
"... Highdimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the lowdimensional time series analysis. Such highdimensional problems occur frequently in many different fi ..."
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Cited by 28 (6 self)
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Highdimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the lowdimensional time series analysis. Such highdimensional problems occur frequently in many different fields of science. In this paper we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modelling approach poses an important question: Is it justified, from inferential point of view, to base statistical inference on the estimated times series factors? We show that the difference of the inference based on the estimated time series and ‘true ’ unobserved time series is asymptotically negligible. Our results justify fitting vector autoregressive processes to the estimated factors, which allows one to study the dynamics of the whole highdimensional system with a lowdimensional representation. We illustrate the theory with a simulation study. Also, we apply the method to a study of the dynamic behavior of implied volatilities and to the analysis of functional magnetic resonance imaging (fMRI) data.
Comparing forecast accuracy: a Monte Carlo Investigation
, 2008
"... The properties of several tests of equal Mean Square Prediction Error (MSPE) and tests of Forecast Encompassing (FE) are evaluated, using simulation methods, in the context of dynamic regressions. For nested models, larger differences in the behavior of the tests occur when the number of outofsamp ..."
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Cited by 23 (0 self)
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The properties of several tests of equal Mean Square Prediction Error (MSPE) and tests of Forecast Encompassing (FE) are evaluated, using simulation methods, in the context of dynamic regressions. For nested models, larger differences in the behavior of the tests occur when the number of outofsample observations is relatively small compared to the size of the estimation sample. In this case the standard tests of equal MSPE and of FE retain good size properties but they pay a big price in terms of power; overall the FE test ENCF of Clark and McCracken (2001), despite being slightly ovesized, is clearly the most powerful. For longer spans of the prediction sample, the power advantage of ENCF tends to become smaller, and thus a standard FE test, based on Gaussian critical values, may become relatively more attractive. The ranking among the tests does not change significantly for multistep ahead predictions, as well as for cases where the estimated models are partly misspecified. A similar simulation setup is used to analyze the case of nonnested models. Again, we find that FE tests have a significantly better performance with respect to tests of equal MSPE, for discriminating between correct and misspecified models. An empirical example with models of prediction of euroarea and US inflation is provided.
A new panel data treatment for heterogeneity in time trends. Econometric Theory 28
, 2012
"... Abstract Our paper introduces a new estimation method for arbitrary temporal heterogeneity in panel data models. The paper provides a semiparametric method for estimating general patterns of crosssectional specific time trends. The methods proposed in the paper are related to principal component a ..."
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Cited by 15 (2 self)
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Abstract Our paper introduces a new estimation method for arbitrary temporal heterogeneity in panel data models. The paper provides a semiparametric method for estimating general patterns of crosssectional specific time trends. The methods proposed in the paper are related to principal component analysis and estimate the timevarying trend effects using a small number of common functions calculated from the data. An important application for the new estimator is in the estimation of timevarying technical efficiency considered in the stochastic frontier literature. Finite sample performance of the estimators is examined via Monte Carlo simulations. We apply our methods to the analysis of productivity trends in the U.S. banking industry. * Earlier versions of this paper under the title "On Estimating the Mixed Effects Model" were presented at North
Assessing the transmission of monetary policy shocks using dynamic factor models.” Working Papers 0914
, 2009
"... This paper extends the current literature which questions the stability of the monetary transmission mechanism, by using a Dynamic Factor Model with timevarying parameters, which allows fast and efficient inference based on hundreds of explanatory variables. Different specifications are compared whe ..."
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Cited by 11 (6 self)
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This paper extends the current literature which questions the stability of the monetary transmission mechanism, by using a Dynamic Factor Model with timevarying parameters, which allows fast and efficient inference based on hundreds of explanatory variables. Different specifications are compared where the factor loadings, VAR coefficients and error covariances may change gradually in every period or be subject to small breaks. The model is applied to 157 postWorld War II U.S. quarterly macroeconomic variables. The most notable changes were in the responses of real activity measures, prices and monetary aggregates, while other key indicators of the economy remained relatively unaffected.