How useful are historical data for forecasting the long-run equity return distribution?

We provide an approach to forecasting the long-run (unconditional) distribution of equity returns making optimal use of historical data in the presence of structural breaks. Our focus is on learning about breaks in real time and assessing their impact on out-of-sample density forecasts. Forecasts use a probability-weighted average of submodels, each of which is estimated over a different history of data. The paper illustrates the importance of uncertainty about structural breaks and the value of modeling higher-order moments of excess returns when forecasting the return distribution and its moments. The shape of the long-run distribution and the dynamics of the higher-order moments are quite different from those generated by forecasts which cannot capture structural breaks. The empirical results strongly reject ignoring structural change in favor of our forecasts which weight historical data to accommodate uncertainty about structural breaks. We also strongly reject the common practice of using a fixed-length moving window. These differences in long-run forecasts have implications for many financial decisions, particularly for risk management and long-run investment decisions.density forecasts, structural change, model risk, parameter uncertainty, Bayesian learning, market returns

Nonlinear Features of Realized FX Volatility

This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to measure ex post latent volatility imply that standard time series models of the conditional variance become variants of an ARMAX model. We explore nonlinear departures from these linear specifications using a doubly stochastic process under duration-dependent mixing. This process can capture large abrupt changes in the level of volatility, time varying persistence, and time-varying variance of volatility. The results have implications for forecast precision, hedging, and pricing of derivatives. Dans cet article, nous étudions les caractéristiques nonlinéaires de la dynamique de la volatilité des taux de change à l'aide d'estimations de la volatilité quotidienne basées sur la somme du carré des rendements intraquotidiens. Les erreurs de mesure commises en utilisant la volatilité réalisée pour mesurer la volatilité latente ex post font en sorte que les modèles standards de séries chronologiques de la variance conditionnelle deviennent des variantes d'un modèle ARMAX. Nous explorons des alternatives nonlinéaires à ces spécifications linéaires en utilisant un processus doublement stochastique, avec mixage dépendant de la durée. Ce processus peut capter des changements importants et abrupts dans le niveau de la volatilité, de même qu'une persistence et une variance de la volatilité variant dans le temps. Nos résultats influent sur la précision des prévisions, la couverture et l'évaluation des produits dérivés.High-frequency data, realized volatility, semi-Marko, Données à haute fréquence, volatilité réalisée, demi-Markov

How useful are historical data for forecasting the long-run equity return distribution?

We provide an approach to forecasting the long-run (unconditional) distribution of equity returns making optimal use of historical data in the presence of structural breaks. Our focus is on learning about breaks in real time and assessing their impact on out-of-sample density forecasts. Forecasts use a probability-weighted average of submodels, each of which is estimated over a different historyof data. The paper illustrates the importance of uncertainty about structural breaks and the value of modeling higher-order moments of excess returns when forecasting the return distribution and its moments. The shape of the long-run distribution and the dynamics of the higher-order moments are quite different from those generated by forecasts which cannot capture structural breaks. The empirical results strongly reject ignoring structural change in favor of our forecasts which weight historical data to accommodate uncertainty about structural breaks. We also strongly reject the common practice of using a fixed-length moving window. These differences in long-run forecasts have implications for many financial decisions, particularly for risk management and long-run investment decisions.density forecasts, structural change, model risk, parameter uncertainty, Bayesian learning, market returns

Do High-Frequency Measures of Volatility Improve Forecasts of Return Distributions?

Many finance questions require the predictive distribution of returns. We propose a bivariate model of returns and realized volatility (RV), and explore which features of that time-series model contribute to superior density forecasts over horizons of 1 to 60 days out of sample. This term structure of density forecasts is used to investigate the importance of: the intraday information embodied in the daily RV estimates; the functional form for log(RV ) dynamics; the timing of information availability; and the assumed distributions of both return and log(RV) innovations. We find that a joint model of returns and volatility that features two components for log(RV) provides a good fit to S&P 500 and IBM data, and is a significant improvement over an EGARCH model estimated from daily returnsRealized Volatility, multiperiod out-of-sample prediction, term structure of density forecasts, Stochastic Volatility

News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns

This paper models different components of the return distribution which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. This mixture captures occasional large changes in price, due to the impact of news innovations such as earnings surprises, as well as smoother changes in prices which can result from liquidity trading or strategic trading as information disseminates. Unlike typical SV-jump models, previous realizations of both jump and normal innovations can feedback asymmetrically into expected volatility. This is a new source of asymmetry (in addition to good versus bad news) that improves forecasts of volatility particularly after large moves such as the '87 crash. A heterogeneous Poisson process governs the likelihood of jumps and is summarized by a time varying conditional intensity parameter. The model is applied to returns from individual companies and three indices. We provide empirical evidence of the impact and feedback effects of jump versus normal return innovations, contemporaneous and lagged leverage effects, the time-series dynamics of jump clustering, and the importance of modeling the dynamics of jumps around high volatility episodes. Cet article modélise les différentes composantes de la distribution des rendements qui sont supposés être régis par un processus latent de nouvelles. La variance conditionnelle des rendements est une combinaison de sauts et de composantes qui varient continûment. Ce mélange permet de capter les grands changements occasionnels de prix qui sont dus à l'impact des nouvelles, telles que des surprises dans les revenus d'une compagnie, aussi bien que des changements plus lisses des prix qui peuvent résulter de transactions de liquidité ou de transactions stratégiques au fur et à mesure que l'information est disséminée. À la différence des modèles classique de sauts SV, les réalisations précédentes des sauts et des innovations normales peuvent intervenir asymétriquement dans la volatilité espérée. Il s'agit d'une nouvelle source d'asymétrie qui améliore les prévisions de volatilité, en particulier après de grands mouvements tels que le crash de 87. Un processus de Poisson hétérogène régit la probabilité des sauts et est représenté par un paramètre d'intensité conditionnelle qui varie dans le temps. Le modèle est appliqué aux rendements de différentes compagnies et à trois indices. Nous montrons ainsi empiriquement l'impact et les effets de rétroaction des sauts par rapport aux innovations normales, les effets de leviers simultanés et décalés, la dynamique de série temporelle du groupement des sauts, et l'importance de modéliser la dynamique des sauts dans les périodes de volatilité élevée.volatility components, news impacts, conditional jump intensity, jump size, leverage effects, filter, composantes de volatilité, impact des nouvelles, intensité conditionnelle des sauts, taille des sauts, effets de levier, filtre

Do high-frequency measures of volatility improve forecasts of return distributions?

Many finance questions require a full characterization of the distribution of returns. We propose a bivariate model of returns and realized volatility (RV), and explore which features of that time-series model contribute to superior density forecasts over horizons of 1 to 60 days out of sample. This term structure of density forecasts is used to investigate the importance of: the intraday information embodied in the daily RV estimates; the functional form for log(RV) dynamics; the timing of information availability; and the assumed distributions of both return and log(RV) innovations. We find that a joint model of returns and volatility that features two components for log(RV) provides a good fit to S&P 500 and IBM data, and is a significant improvement over an EGARCH model estimated from daily returns.RV, multiperiod, out-of-sample, term structure of density forecasts, observable SV

Extracting bull and bear markets from stock returns

Traditional methods used to partition the market index into bull and bear regimes often sort returns ex post based on a deterministic rule. We model the entire return distribution; two states govern the bull regime and two govern the bear regime, allowing for rich and heterogeneous intra-regime dynamics. Our model can capture bear market rallies and bull market corrections. A Bayesian estimation approach accounts for parameter and regime uncertainty and provides probability statements regarding future regimes and returns. Applied to 123 years of data our model provides superior identification of trends in stock prices.Markov switching, bear market rallies, bull market corrections, Gibbs sampling

Testing the Unbiasedness Hypothesis in the Forward Foreign Exchange Market: A Specification Analysis

This paper evaluates two popular regression methods of testing the unbiasedness hypothesis in the forward foreign exchange market. For the 30-day Canada/United States forward foreign exchange market, the evidence overwhelmingly indicates that it is inappropriate to treat the structure of the systematic and stochastic components of the test relations as constant over time. Hence, conclusions inferred from parameter significance testing based upon full-sample estimation can be very misleading. Accordingly, we argue for a specification analysis of the test relations, and more explicit modelling of market fundamentals.The financial support of the Social Sciences and Humanities Research Council of Canada and the Advisory Research Committee of Queen's University is acknowledged

Sources of Employment Growth by Occupation and Industry in Canada

Dans cet article, nous utilisons des données canadiennes des modèles d'intrants et d'extrants et des recensements de 1961, 1971 et 1981 afin d'identifier les causes des changements dans l'emploi durant chaque décennie. Neuf causes de changement sont retenues. L'objectif de cet article est de déterminer les causes les plus importantes de la croissance de l'emploi agrégé de même que les facteurs expliquant la croissance plus rapide de l'emploi durant les années 1970. De plus, les déterminants des déplacements de l'emploi entre les secteurs de même que des changements dans la composition de la main-d’œuvre sont identifiés. Une attention particulière est prêtée à l'importance des changements dans l'économie de l'information.L'emploi agrégé du secteur privé a crû de 35,3 % durant les années 1970 alors que dans les années 1960, la croissance ne fut que de 24,4 %. Le taux de croissance supérieur des années 1970, qui survint malgré un déclin de celui de la demande finale, fut accompagné d'un déclin du taux de croissance de la productivité du travail. Le déclin du taux de croissance de la demande finale dans cette décennie était dû à un ralentissement de celui des exportations.Les différences sectorielles du taux de croissance de l'emploi durant les années 1960 peuvent être expliquées par des taux de croissance dans la productivité du travail différents entre les secteurs alors que durant les années 1970, celles-ci furent plutôt attribuables à des variations sectorielles du taux de croissance de la demande finale, et en particulier de la consommation. Durant ces deux décennies, ces déterminants des différences sectorielles ont généré une croissance supérieure dans le secteur des services.Par rapport à l'emploi total, la proportion des emplois reliés au domaine de l'information a crû plus rapidement durant les années 1960 que durant les années 1970. La croissance de cette proportion est due en grande partie aux changements dans la composition de la main-d’œuvre. Il y a cependant d'autres explications de ce déplacement vers des emplois reliés au domaine de l'information. Parmi celles-ci, citons les taux de croissance sectoriels de l'emploi différents dus à des différences dans le taux de changement des heures travaillées, de la productivité du travail, de la demande finale et de la matrice d'intrants-extrants.This paper uses Canadian input-output and census data from 1961, 1971 and 1981 to decompose employment changes during each decade into nine sources. The goals are to identify: the main sources of growth in aggregate employment; factors which facilitated the more rapid rate of growth of employment in the 1970s; and some reasons for intersectoral shifts of employment and changes in the occupational composition of employment. We pay particular attention to the changing importance ofthe 'information economy '