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82
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
Economic forecasting
, 2007
"... Forecasts guide decisions in all areas of economics and finance and their value can only be understood in relation to, and in the context of, such decisions. We discuss the central role of the loss function in helping determine the forecaster’s objectives. Decision theory provides a framework for bo ..."
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Cited by 65 (3 self)
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Forecasts guide decisions in all areas of economics and finance and their value can only be understood in relation to, and in the context of, such decisions. We discuss the central role of the loss function in helping determine the forecaster’s objectives. Decision theory provides a framework for both the construction and evaluation of forecasts. This framework allows an understanding of the challenges that arise from the explosion in the sheer volume of predictor variables under consideration and the forecaster’s ability to entertain an endless array of forecasting models and timevarying specifications, none of which may coincide with the ‘true’ model. We show this along with reviewing methods for comparing the forecasting performance of pairs of models or evaluating the ability of the best of many models to beat a benchmark specification.
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.
Forecasting economic time series using targeted predictors
 Journal of Econometrics
, 2008
"... This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be nonlinear. Second, the factors used in the forecasting equation are estimated in a way t ..."
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Cited by 58 (1 self)
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This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be nonlinear. Second, the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series. This is accomplished by applying the method of principal components to ‘targeted predictors ’ selected using hard and soft thresholding rules. Our three main findings can be summarized as follows. First, we find improvements at all forecast horizons over the current diffusion index forecasts by estimating the factors using fewer but informative predictors. Allowing for nonlinearity often leads to additional gains. Second, forecasting the volatile one month ahead inflation warrants a high degree of targeting to screen out the noisy predictors. A handful of variables, notably relating to housing starts and interest rates, are found to have systematic predictive power for inflation at all horizons. Third, the targeted predictors selected by both soft and hard thresholding changes with the forecast horizon and the sample period. Holding the set of predictors fixed as is the current practice of factor forecasting is unnecessarily restrictive.
Estimating the intertemporal riskreturn tradeoff using the implied cost of capital
, 2006
"... We reexamine the timeseries relation between the conditional mean and variance of stock market returns. To proxy for the conditional mean return, we use the implied cost of capital, computed using analyst forecasts. The usefulness of this proxy is shown in simulations. In empirical analysis, we con ..."
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Cited by 57 (3 self)
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We reexamine the timeseries relation between the conditional mean and variance of stock market returns. To proxy for the conditional mean return, we use the implied cost of capital, computed using analyst forecasts. The usefulness of this proxy is shown in simulations. In empirical analysis, we construct the time series of the implied cost of capital for the G7 countries. We find strong support for a positive intertemporal meanvariance relation at both the country level and the world market level. Some of our evidence is consistent with international integration of the G7 financial markets.
Transition Modelling and Econometric Convergence Tests
, 2006
"... A new panel data model is proposed to represent the behavior of economies in transition allowing for a wide range of possible time paths and individual heterogeneity. The model has both common and individual specific components and is formulated as a nonlinear time varying factor model. When applied ..."
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Cited by 34 (5 self)
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A new panel data model is proposed to represent the behavior of economies in transition allowing for a wide range of possible time paths and individual heterogeneity. The model has both common and individual specific components and is formulated as a nonlinear time varying factor model. When applied to a micro panel, the decomposition provides flexibility in idiosyncratic behavior over time and across section, while retaining some commonality across the panel by means of an unknown common growth component. This commonality means that when the heterogeneous time varying idiosyncratic components converge over time to a constant, a form of panel convergence holds, analogous to the concept of conditional sigma convergence. The paper provides a framework of asymptotic representations for the factor components which enables the development of econometric procedures of estimation and testing. In particular, a simple regression based convergence test is developed, whose asymptotic properties are analyzed under both null and local alternatives, and a new method of clustering panels into club convergence groups is constructed. These econometric methods are applied to analyze convergence in cost of living indices among 19 US. metropolitan cities.
2006) “Instrumental Variable Estimation in a Data Rich Environment”, mimeo
"... We consider estimation of parameters in a regression model in which the endogenous regressors are just a few of the many other endogenous variables driven by a small number of unobservable exogenous common shocks. We show the method of principal components can be used to estimate factors that can be ..."
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Cited by 29 (6 self)
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We consider estimation of parameters in a regression model in which the endogenous regressors are just a few of the many other endogenous variables driven by a small number of unobservable exogenous common shocks. We show the method of principal components can be used to estimate factors that can be used as instrumental variables. These are not only valid instruments, they are more efficient than the observed variables in our framework. Consistency and asymptotic normality of the single equation factor instrumental variable estimator (FIV) is established. We also show that consistent estimates can be obtained from large panel data regressions by constructing valid instruments from the endogenous regressors that are themselves invalid instrument in a conventional sense. To reduce the bias that might arise from using too many instruments, we use boosting to select out the most relevant ones. Boosting necessitates a stopping rule. We derive the condition on the stopping parameter that arises from boosting estimated factors instead of observed variables.
Choice of Sample Split in OutofSample Forecast Evaluation
, 2011
"... Outofsample tests of forecast performance depend on how a given data set is split into estimation and evaluation periods, yet no guidance exists on how to choose the split point. Empirical forecast evaluation results can therefore be di ¢ cult to interpret, particularly when several values of the ..."
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Cited by 22 (2 self)
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Outofsample tests of forecast performance depend on how a given data set is split into estimation and evaluation periods, yet no guidance exists on how to choose the split point. Empirical forecast evaluation results can therefore be di ¢ cult to interpret, particularly when several values of the split point might have been considered. While the probability of spurious rejections is highest when a short outofsample period is used, conversely the power of outofsample forecast evaluation tests is strongest when the sample split occurs early in the sample. We show that very large size distortions can occur, more than tripling the rejection rates of conventional tests of predictive accuracy, when the sample split is viewed as a choice variable, rather than being …xed ex ante. To deal with this issue, we propose a test statistic that is robust to the e¤ect of mining over the start of the outofsample period. Empirical applications to predictability of stock returns and in‡ation demonstrate that outofsample forecast evaluation results can critically depend on how the sample split is determined. Keywords: Outofsample forecast evaluation; data mining; recursive estimation; predictability of stock returns; in‡ation forecasting. JEL Classi…cation: C12, C53, G17. 1 1
Should macroeconomic forecasters use daily financial data and how?
, 2009
"... Hundreds of daily financial series contain information about the economy. Can we use all this information for improving and/or updating macroeconomic forecasts? We introduce easy to implement regressionbased methods for predicting inflation and real activity that rely on MIDAS regressions either us ..."
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Cited by 21 (0 self)
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Hundreds of daily financial series contain information about the economy. Can we use all this information for improving and/or updating macroeconomic forecasts? We introduce easy to implement regressionbased methods for predicting inflation and real activity that rely on MIDAS regressions either using a combinations of MIDAS regressions involving daily series or using a small set of financial daily factors. Both have the important features that: (1) they allow us to clearly show the incremental value of daily financial series in terms of forecasting, (2) they provide a succinct summary of huge amounts of daily financial data, (3) they allow for realtime updates of forecasting or so called nowcasting. ∗The second author benefited from funding by the Federal Reserve Bank of New York through the
Productionbased measures of risk for asset pricing
 Journal of Monetary Economics
, 2010
"... A stochastic discount factor for asset returns is recovered from equilibrium marginal rates of transformation of output across states of nature, inferred from the producers’ first order conditions. The marginal rate of transformation implies a novel macrofactor asset pricing model that does a reason ..."
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Cited by 20 (4 self)
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A stochastic discount factor for asset returns is recovered from equilibrium marginal rates of transformation of output across states of nature, inferred from the producers’ first order conditions. The marginal rate of transformation implies a novel macrofactor asset pricing model that does a reasonable job explaining the cross section of stock returns with plausible parameter values. Using a flexible representation of the firms ’ production technology, the producers ’ ability to transform output across states of nature is estimated to be high, in contrast with what is typically assumed in standard aggregate representations of the firms ’ production technology.