Andrew Patton's research page

 

Research keywords: econometrics, financial economics, forecasting, copulas, time series, dependence, volatility, hedge funds.

 

BibTeX list of these papers (text file)

Working Papers

 

Asymptotic Inference about Predictive Accuracy using High Frequency Data, with Jia Li, working paper, September 2013. news
Paper (PDF), Abstract (HTML), Supplemental Appendix (PDF)

 

The Impact of Hedge Funds on Asset Markets, with Mathias Kruttli and Tarun Ramadorai, working paper, June 2013. news
Paper (PDF), Abstract (HTML), Web Appendix (PDF)

 

Dynamic Copula Models and High Frequency Data, with Irving De Lira Salvatierra, working paper, June 2013. news
Paper (PDF), Abstract (HTML), Web Appendix (PDF)

 

Daily House Price Indexes: Construction, Modeling, and Longer-Run Predictions, with Tim Bollerslev and Wenjing Wang, working paper, June 2013. Revised January 2014. news
Paper (PDF), Abstract (HTML) , Web Appendix (PDF)

 

Time-Varying Systemic Risk: Evidence from a Dynamic Copula Model of CDS Spreads, with Dong Hwan Oh, working paper, May 2013.
Paper (PDF), Abstract (HTML), Web Appendix (PDF)

 

Does Anything Beat 5-Minute RV?  A Comparison of Realized Measures Across Multiple Asset Classes, with Lily Liu and Kevin Sheppard, December 2012.
Paper (PDF), Abstract (HTML), Slides Oct12 (PDF)

 

Modelling Dependence in High Dimensions with Factor Copulas, with Dong Hwan Oh, working paper, May 2011. Revised December 2012.
Paper (PDF), Abstract (HTML), Web Appendix (PDF), Slides Sep12 (PDF)

 

Good Volatility, Bad Volatility: Signed Jumps and the Persistence of Volatility , with Kevin Sheppard, working paper, February 2011. Revised November 2013.
Paper (PDF), Abstract (HTML) , Web Appendix (PDF)

 

 

Publications in academic journals

 

Copulas in Econometrics, with Yanqin Fan, October 2013. Forthcoming in the Annual Review of Economics.
Paper (PDF), Abstract (HTML)

 

Change You Can Believe In? Hedge Fund Data Revisions, with Tarun Ramadorai and Michael Streatfield, revised March 2013. Forthcoming in the Journal of Finance.
Paper (PDF), Abstract (HTML), Slides Mar12 (PDF), Web Appendix (PDF)

-- This paper was reviewed in The Telegraph (Nov 2011), BBC News (June 2012), The Economist (April 2013).

              -- Previously circulated as "The Reliability of Voluntary Disclosures: Evidence from Hedge Funds"

 

Simulated Method of Moments Estimation for Copula-Based Multivariate Models, with Dong Hwan Oh, 2013, Journal of the American Statistical Association, 108(502), 689-700.
Paper (PDF), Abstract (HTML), Supplemental Appendix (PDF)

 

On the High Frequency Dynamics of Hedge Fund Risk Exposures, with Tarun Ramadorai, 2013, Journal of Finance, 68(2), 597-635.
Paper (PDF), Abstract (HTML), Slides Jun11 (PDF), Web Appendix (PDF)

 

-- An earlier version of this paper was circulated as On the High Frequency Dynamics of Hedge Fund Risk Exposures, April 2010.

 

Does Beta Move with News? Firm-Specific Information Flows and Learning about Profitability, with Michela Verardo, 2012, Review of Financial Studies, 25(9), 2789-2839.
Paper (PDF), Abstract (HTML), Slides Sep09 (PDF)

 

-- An early version of this paper was circulated as Financial Markets Group Discussion Paper 630, London School of Economics.

 

A Review of Copula Models for Economic Time Series, 2012, Journal of Multivariate Analysis, 110, 4-18.
Paper (PDF), Abstract (HTML)

 

-- A longer and more detailed version of this review is my 2012 Handbook of Economic Forecasting chapter.

 

Forecast Rationality Tests Based on Multi-Horizon Bounds, with Allan Timmermann, 2012, Journal of Business and Economic Statistics, 30(1), 1-17.
Paper (PDF), Abstract (HTML), Slides Nov10 (PDF)

 

-- This paper was the JBES Invited Address at the 2011 ASSA meetings.

-- The discussions (Croushore, Lahiri, Rossi, Hoogerheide-Ravazzolo-van Dijk, West) and rejoinder are available here.

 

Data-Based Ranking of Realised Volatility Estimators, 2011,  Journal of Econometrics, 161(2), 284-303.
Paper (PDF), Abstract (HTML), Slides May08 (PDF)

 

Predictability of Output Growth and Inflation: A Multi-Horizon Survey Approach, with Allan Timmermann, 2011, Journal of Business and Economic Statistics, 29(3), 397-410.
Paper (PDF), Abstract (HTML), Slides Nov07 (PDF)

 

-- Some of the results in the above paper (and the JME paper below) were previously presented in “Learning in Real Time: Theory and Empirical Evidence from the Term Structure of Survey Forecasts”, Centre for Economic Policy Research Discussion Paper DP6526. An early version of that paper was circulated as "How Quickly is Macroeconomic Uncertainty Resolved? Theory and Evidence from the Term Structure of Forecast Errors".

 

Volatility Forecast Comparison using Imperfect Volatility Proxies, 2011, Journal of Econometrics, 160(1), 246-256.
Paper (PDF), Abstract (HTML), Slides July06 (PDF), Code (MATLAB)


-- 
Longer working paper version: “Volatility Forecast Comparison using Imperfect Volatility Proxies, April 2006, Quantitative Finance Research Centre, University of Technology Sydney, Research Paper 175. 

Why do Forecasters Disagree? Lessons from the Term Structure of Cross-Sectional Dispersion, with Allan Timmermann, 2010, Journal of Monetary Economics, 57(7), 803-820.
Paper (PDF), Abstract (HTML), Slides Nov07 (PDF)

 

Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM and Portfolios Sorts, with Allan Timmermann, 2010. Journal of Financial Economics, 98(3), 605-625.         
Paper (PDF), Abstract (HTML), Slides Jun09 (PDF), Code (MATLAB)


-- An earlier version of this paper was circulated as Portfolio Sorts and Tests of Cross-Sectional Patterns in Expected Returns, February 2008.

Optimal Combinations of Realised Volatility Estimators, with Kevin Sheppard , 2009, International Journal of Forecasting, 25(2), 218-238.
Paper (PDF), Abstract (HTML), Slides Mar09 (PDF)

                                                                                                                                                                                     

Are "Market Neutral" Hedge Funds Really Market Neutral?, 2009, Review of Financial Studies, 22(7), 2495-2530.
Paper (PDF), Abstract (HTML), Slides June05 (PDF)

-- This paper was reviewed in the Financial Times: 27 May 2005 (PDF), 9 May 2005 (PDF), 30 April 2004 (PDF) 
-- This paper was awarded the Inquire UK best paper award, 2004.

 

Testing Forecast Optimality under Unknown Loss, with Allan Timmermann, 2007, Journal of the American Statistical Association, 102(480), 1172-1184.
Paper (PDF), Abstract (HTML), Slides May06 (PDF)

 

Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity, with Allan Timmermann, 2007, Journal of Econometrics, 140(2), 884-918.
Paper (PDF), Abstract (HTML), Slides July03 (PDF)

 

Modelling Asymmetric Exchange Rate Dependence, 2006, International Economic Review, 47(2), 527-556. 
Paper (PDF), Abstract (HTML), Slides June01 (PDF), Code (MATLAB)

-- This paper was previously circulated as “Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula”, University of California, San Diego, Discussion Paper 01-09.
-- The Joe-Clayton and symmetrised Joe-Clayton copula density functions can be found here (PDF). Matlab functions for these can be found here.

 

Common Factors in Conditional Distributions for Bivariate Time Series, with Clive W. J. Granger and Timo Teräsvirta, 2006, Journal of Econometrics, 132(1), 43-57.
Paper (PDF), Abstract (HTML), Code (MATLAB)

Estimation of Multivariate Models for Time Series of Possibly Different Lengths, 2006, Journal of Applied Econometrics, 21(2), 147-173.
Paper (PDF), Abstract (HTML), Slides Nov01 (PDF), Code (MATLAB)

-- This paper was previously circulated as: “Estimation of Copula Models for Time Series of Possibly Different Lengths”, University of California, San Diego, Discussion Paper 01-17.
-- The full set of results for simulations in this paper are available here.

 

On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation, 2004, Journal of Financial Econometrics, 2(1), 130-168.
Paper (PDF), Abstract (HTML), Slides Oct02 (PDF), Code (MATLAB)

-- This paper received the Journal of Financial Econometrics' Engle prize
-- This paper was reviewed in the Financial Times: June 2003 (PDF) 
-- Two corrections of typos in Appendix B can be found here (PDF).
-- The Joe-Clayton and symmetrised Joe-Clayton copula density functions can be found here (PDF). Matlab functions for these can be found here (ZIP).

 

Impacts of Trades in an Error-Correction Model of Quote Prices, with Robert F. Engle, 2004, Journal of Financial Markets, 7(1), 1-25.
Paper (PDF), Abstract (HTML)

 

What Good is a Volatility Model?, with Robert F. Engle, 2001, Quantitative Finance, 1(2), 237-245.
Paper (PDF), Abstract (HTML)

-- The data used in this paper (ASCII).
-- This paper was re-printed in:
Forecasting Volatility in the Financial Markets, Third Edition, 2007, J. Knight and S. Satchell (eds), Butterworth-Heinemann.
-- And also in: Beyond Equilibrium and Efficiency
, 2007, J.D. Farmer and J. Geanakoplos (eds), Oxford University Press.

 

Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary System, with Colm Kearney, 2000, The Financial Review, 35(1), 25-46.
Abstract (HTML).

 

 

Other publications

 

Copula Methods for Forecasting Multivariate Time Series, May 2012, in G. Elliott and A. Timmermann  (eds.) Handbook of Economic Forecasting, Volume 2, Springer Verlag, forthcoming.
Paper (PDF), Abstract (HTML), Code (MATLAB).

 

Generalized Forecast Errors, A Change of Measure, and Forecast Optimality Conditions, with Allan Timmermann, 2010, in Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle, edited by T. Bollerslev, J.R. Russell and M.W. Watson, Oxford University Press.
Paper (PDF), Abstract (HTML)

-- This paper, along with my Journal of Econometrics and JASA papers with Allan Timmermann, nests our earlier working paper: “Properties of Optimal Forecasts, August 2003, Centre for Economic Policy Research Discussion Paper DP4037.

 

Correction to “Automatic Block-Length Selection for the Dependent Bootstrap”, with Dimitris N. Politis and Halbert White, 2009, Econometric Reviews, 28(4), 372-375.
Paper (PDF), Code (MATLAB), Original paper by Politis and White, 2004, Econometric Reviews, (PDF)

Copula-Based Models for Financial Time Series, 2009, in T.G. Andersen, R.A. Davis, J.-P. Kreiss and T. Mikosch  (eds.) Handbook of Financial Time Series, Springer Verlag.
Paper (PDF), Abstract (HTML), Code (MATLAB)

 

Evaluating Volatility and Correlation Forecasts, with Kevin Sheppard, 2009, in T.G. Andersen, R.A. Davis, J.-P. Kreiss and T. Mikosch  (eds.) Handbook of Financial Time Series, Springer Verlag.
Paper (PDF), Abstract (HTML)

 

Non-Linearities and Stress Testing, with Mathias Drehmann and Steffen Sorensen, March 2006, forthcoming in the Proceedings of the Fourth Joint Central Bank Research Conference on Risk Measurement and Systemic Risk.
Paper (PDF), Abstract (HTML)

 

Book review: "Copula Methods in Finance", by U. Cherubini, E. Luciano and W. Vecchiato, 2004, John Wiley & Sons. In RISK, June 2005, 18(6).
Paper (PDF)

 

Applications of Copula Theory in Financial Econometrics, June 2002.
Ph.D. dissertation
Department of Economics,
University of California, San Diego.
Abstract (HTML).

 

 

Computer code

 

Matlab code for some of the computations in the above papers can be found here.

 

Upcoming seminars/conferences

 

Econometric Society North American winter meetings, Philadelphia (3-5 January 2014)

University College London, Department of Economics (4 March 2014)

University of Cambridge, Faculty of Economics (5-7 March 2014)

University of Maryland, Smith School of Business (28 March 2014)

Napa Conference on Financial Markets Research (5 April 2014)

Q Group Spring conference, Charleston (6-9 April 2014)

Global ARC conference, London (19-21 May 2014)

Joint Statistical Meetings, Boston (2-7 August, 2014)

 

 


 

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Abstracts


Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the European Monetary System
(co-authored with Colm Kearney)

Abstract
We construct a series of 3-, 4- and 5-variable multivariate GARCH models of exchange rate volatility transmission across some of the important European Monetary System currencies, including the French franc, the German mark, the Italian lira, the British pound and the European Currency Unit. The models are estimated without imposing the common restriction of constant correlation on both daily and weekly data from April 1979 to March 1997. Our results indicate the importance of checking for specification robustness in multi- variate GARCH modeling; we find that increased temporal aggregation reduces observed volatility transmission, and that the mark plays a dominant position in terms of volatility transmission.

Keywords: volatility, GARCH, exchange rates, time-varying correlation.
J.E.L. Codes: C32, F31, G15.

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Impacts of Trades in an Error-Correction Model of Quote Prices
(co-authored with Rob Engle)

Abstract
In this paper we analyze and interpret the quote price dynamics of 100 NYSE stocks with varying average trade frequencies. We specify an error-correction model for the log-difference of the bid and the ask price, with the spread acting as the error-correction term, and include as regressors the character- istics of the trades occurring between quote observations, if any. We find that short duration and medium to large volume trades have the largest impacts on quote prices for one hundred stocks, and that buyer-initiated trades primarily move the ask price while seller-initiated trades primarily move the bid price. Trades have a greater impact on quotes in both the short and the long run for the infrequently traded stocks than for the more actively traded stocks. Finally, we find strong evidence that the spread is mean-reverting.

Keywords: market microstructure, error correction, vector autoregression, price dynamics.
J.E.L. Codes: C32, G0, G1.

__________________________________________

What Good Is A Volatility Model?
(co-authored with Rob Engle)

Abstract
A volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications. In this paper we outline some stylised facts about volatility that should be incorporated in a model; pronounced persistence and mean-reversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre- determined variables influencing volatility. We use data on the Dow Jones Industrial index to illustrate these stylised facts, and the ability of GARCH- type models to capture these features. We conclude with some challenges for future research in this area.

Keywords: volatility modeling, ARCH, GARCH, volatility forecasting.
J.E.L. Codes: C22.

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Modelling Asymmetric Exchange Rate Dependence 
previously circulated as: Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula

Abstract
We test for asymmetry in a model of the dependence between the Deutsche mark and the Yen, in the sense that a different degree of correlation is exhibited during joint appreciations against the U.S. dollar versus during joint depreciations. Such a dependence structure is not consistent with the commonly employed normal or Student's t distribution assumptions. We verify that the theory of copulas may be extended to conditional distributions, and employ it to construct flexible models of the conditional dependence structure of these exchange rates. We find evidence that the mark-dollar and Yen-dollar exchange rates are more correlated when they are depreciating against the dollar than when they are appreciating. We also find strong evidence of a structural break in conditional density of these exchange rates upon the introduction of the euro.

Keywords: exchange rates, density forecasting, copulas, multivariate GARCH, asymmetry.
J.E.L. Codes: C32, C51, C52, F31.

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Estimation of Multivariate Models for Time Series of Possibly Different Lengths

Abstract
We consider the problem of estimating parametric multivariate density models when unequal amounts of data are available on each variable. We focus in particular on the case that the unknown parameter vector may be partitioned into elements relating only to a marginal distribution and elements relating to the copula. In such a case we propose using a multi-stage maximum likelihood estimator (MSMLE) based on all available data rather than the usual one-stage maximum likelihood estimator (1SMLE) based only on the overlapping data. We provide conditions under which the MSMLE is not less asymptotically efficient than the 1SMLE, and we examine the small sample efficiency of the estimators via simulations. The analysis in this paper is motivated by a model of the joint distribution of daily Japanese yen - U.S. dollar and euro - U.S. dollar exchange rates. We find significant evidence of time variation in the conditional copula of these exchange rates, and evidence of greater dependence during extreme events than under the normal distribution.

Keywords: copulas, maximum likelihood, two-stage estimation, exchange rates, missing data.
J.E.L. Codes: C13, C32, C51, F31.

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On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation

Abstract
Recent studies in the empirical finance literature have reported evidence of two types of asymmetries in the joint distribution of stock returns. The first is skewness in the distribution of individual stock returns. The second is an asymmetry in the dependence between stocks: stock returns appear to be more highly correlated during market downturns than during market upturns. In this paper we examine the economic and statistical significance of these asymmetries for asset allocation decisions in an out-of-sample setting. We consider the problem of a CRRA investor allocating wealth between the risk-free asset, a small-cap and a large-cap portfolio. We use models that can capture time-varying moments up to the fourth order, and we use copula theory to construct models of the time-varying dependence structure that allow for different dependence during bear markets than bull markets. The importance of these two asymmetries for asset allocation is assessed by comparing the performance of a portfolio based on a normal distribution model with a portfolio based on a more flexible distribution model. For investors with no short sales constraints we find that knowledge of higher moments and asymmetric dependence leads to gains that are economically significant, and statistically significant in some cases. For short sales constrained investors the gains are limited.

Keywords: stock returns, forecasting, density forecasting, normality, asymmetry, copulas.
J.E.L. Codes: G11, C32, C51.

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Applications of Copula Theory in Financial Econometrics
Ph.D. dissertation, Department of Economics, University of California, San Diego.

Abstract
The work presented in this dissertation was motivated by the widely accepted observation that many economic variables are non-normally distributed. They exhibit fat-tails, skewness, and recent work suggests that some also exhibit 'asymmetric dependence', where some pairs of variables are more highly correlated during negative movements than positive movements.

This observation raises two important problems: the construction of alternative, more palatable, density specifications, and the description and analysis of dependence between these variables in a more general manner than linear correlation, as when the joint distribution of the variables of interest is non-elliptical the correlation coefficient is no longer sufficient to describe the dependence structure.

The four chapters of this dissertation investigate applications of copula theory to address these problems. The theory of copulas allows us to consider the dependence between two random variables in a general way, and to construct flexible parametric multivariate distributions.

Chapter One, titled Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula, extends the existing theory of copulas to allow for conditioning variables, and shows how to construct and evaluate flexible parametric multivariate distributions using copula theory through an application to a model of the joint distribution of the Deutsche mark - U.S. dollar and Japanese yen - U.S. dollar exchange rates.

Chapter Two, titled Estimation of Copula Models for Time Series of Possibly Different Lengths, looks at the multi-stage maximum likelihood estimation of parametric multivariate time series models constructed using copula theory, allowing for the possibility that we have more data available on one variable than another.

Chapter Three, titled Skewness, Asymmetric Dependence, and Portfolios, provides a link between two findings in the empirical finance literature: those of skewness in individual asset returns and asymmetric dependence between asset returns. I show that the presence of asymmetric dependence between two assets can lead to skewed portfolios even if the individual assets themselves are not skewed.

Chapter Four, titled On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation, investigates the importance of skewness and asymmetric dependence for asset allocation in an out-of-sample study. The goal of this chapter was to determine for a particular pair of assets whether flexible density models lead to better portfolio decisions than a multivariate normal distribution model. I find significant improvements, both economically and statistically.

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Common Factors in Conditional Distributions for Bivariate Time Series
(co-authored with Clive Granger and Timo Teräsvirta)

Abstract
A definition for a common factor for bivariate time series is suggested by considering the decomposition of the conditional density into the product of the marginals and the copula, with the conditioning variable being a common factor if it does not directly enter the copula. We show the links between this definition and the idea of a common factor as a dominant feature in standard linear representations. An application using a business cycle indicator as the common factor in the relationship between U.S. income and consumption found that both series held the factor in their marginals but not in the copula.

Keywords: common factors, copulas, business cycles.
J.E.L. Codes: C32, C53.

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Properties of Optimal Forecasts
(co-authored with Allan Timmermann)

Abstract
Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results we show in this paper that all the standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. Our theoretical results suggest that many of the conclusions in the empirical literature concerning suboptimality of forecasts could be premature. We extend the properties that an optimal forecast should have to a more general setting than previously considered in the literature. We also present new results on forecast error properties that may be tested when the forecaster's loss function is unknown but restrictions can be imposed on the data generating process, and introduce a change of measure, following which the optimum forecast errors for general loss functions have the same properties as optimum errors under MSE loss.

Keywords: forecast evaluation, loss function, rationality, efficient markets.
J.E.L. Codes: C53, C22, C52.

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Are "Market Neutral" Hedge Funds Really Market Neutral?

Abstract
Using a variety of different definitions of "neutrality", this paper presents significant evidence against the neutrality to market risk of hedge funds in a range of style categories, including the "market neutral" category. I suggest that the completeness of the neutrality of a fund to market risks can be considered by generalizing standard definitions of "market neutrality", and propose five different neutrality concepts: "Mean neutrality" nests the standard correlation-based definition of neutrality, "variance neutrality" and "tail neutrality" relate to the neutrality of the risk of the hedge fund to market risks, and "complete neutrality" corresponds to independence of the fund to market risks. I suggest statistical tests for each neutrality concept, and apply the tests to a combined database of monthly returns on 1,423 hedge funds from five fund style categories. For the so-called "market neutral" style, I find that around one-quarter of funds exhibit some significant exposure to market risk; this proportion is statistically significantly different from zero, but less than the proportion of significant exposures for other hedge fund styles.


Keywords: diversification, alternative investments, correlation, portfolio decisions.
J.E.L. Codes: G23, G11.

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Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity
(co-authored with Allan Timmermann)

Abstract
Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. We establish instead that a suitable transformation of the forecast error - known as the generalized forecast error - possesses an equivalent set of properties. The paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts.


Keywords: loss function, nonlinear data generating process, rationality, market efficiency, prediction.
J.E.L. Codes: C53, C22, C52.

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Testing Forecast Optimality under Unknown Loss
(co-authored with Allan Timmermann)

Abstract
Empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function. This paper establishes new testable properties that hold when the forecaster's loss function is unknown but testable restrictions can be imposed on the data generating process, trading off conditions on the data generating process against conditions on the loss function. We propose flexible estimation of the forecaster's loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable. We apply our results to the problem of evaluating the Federal Reserve's forecasts of output growth. Forecast optimality is rejected if the Fed's loss only depends on the forecast error. However, the empirical findings are consistent with forecast optimality provided that over-predictions of output growth are costlier to the Fed than under-predictions, particularly during periods of low economic growth.

Keywords: Federal Reserve, output growth, forecast evaluation, loss function, forecast efficiency.
J.E.L. Codes: C53, C22, C52

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Non-Linearities and Stress Testing
(co-authored with Mathias Drehmann and Steffen Sorensen)

Abstract
We explore the impact of possible non-linearities on aggregate credit risk in a vector autoregression framework. By using aggregate data on corporate credit in the UK we investigate the non-linear transmission of macroeconomic shocks to aggregate corporate default probability. We show two important results: firstly, we find that non-linearities matter for the level and shape of impulse response functions of credit risk following small as well as large shocks to systematic risk factors. Secondly, we show that ignoring estimation uncertainty in stress tests can lead to a substantial underestimation of credit risk, particularly in extreme conditions.

Keywords: credit risk, impulse response functions, stress testing, nonlinear time series, VAR models
J.E.L. Codes: G33, C32.

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Volatility Forecast Comparison using Imperfect Volatility Proxies

Abstract
The use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We derive necessary and sufficient conditions on functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some useful special cases of this class of "robust" loss functions. We motivate the theory with analytical results on the distortions caused by some widely-used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.

Keywords: forecast evaluation, forecast comparison, loss functions, realised variance, range.
J.E.L. Codes: C53, C52, C22.

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Corporate Defaults and Macroeconomic Shocks: Non-linearities and Uncertainty
(co-authored with Mathias Drehmann and Steffen Sorensen)

Abstract
We propose a framework to explore the impact of non-linearities in the transmission of macroeconomic shocks to corporate credit risk. A number of models used in the literature assume a linear relation between credit risk and the macroeconomic shocks. Using a rich database containing more than 30,000 public and private firms in the U.K., we present strong evidence against such an assumption. We present four main results: First, the impacts of macroeconomic shocks on credit risk are economically and statistically significantly non-linear. Second, the impact of a shock depends significantly on the starting level of macroeconomic variables at the time of the shock. Third, macroeconomic shocks have a different impact on credit risk in different corporate sectors. Finally, we show that ignoring uncertainty in estimates of credit risk can lead to a substantial underestimation of risk, especially during adverse macroeconomic conditions.

Keywords: credit risk, impulse response functions, nonlinear time series, VAR models.
J.E.L. Codes: G33, C32.

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Time-Varying Liquidity in Hedge Fund Returns
(co-authored with Sheng Li)

Abstract
The liquidity of hedge funds' investments is of great interest both to hedge fund investors and to market regulators. We propose a method for determining the factors that affect the (unobservable) liquidity of hedge fund investments. Our method exploits the link between illiquidity and serial correlation in hedge fund returns established by Getmansky, Lo and Makarov (2004), and does not require information on the actual positions taken by the hedge fund, nor even the `style' of the hedge fund; we use only the returns reported by the hedge fund and other easily observed information.
Using a panel of monthly returns on over 600 individual hedge funds, we find significant evidence of time variation in the degree of liquidity of hedge fund investments. Broadly stated, hedge funds in equity-based styles, such as equity market neutral and equity hedge or non-hedge, exhibit decreases in liquidity when stock market returns are low and bond market returns are high. In contrast, hedge funds in fixed income styles, such as convertible arbitrage or fixed income, exhibit lower liquidity when equity market volatility is high, and when the fund experiences in-flows or out-flows of funds.

Keywords: liquidity, serial correlation, return smoothing, hedge funds
J.E.L. Codes: G23, G11, C22.

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Copula-Based Models for Financial Time Series

Abstract
The number of papers on copula theory in finance and economics has grown enormously in recent years. One of the most influential of the 'early' papers on copulas in finance is that of Embrechts, McNeil and Straumann (2002). Since then, scores of papers have been written, exploring the uses of copulas in finance, macroeconomics, microeconomics, as well as developing the estimation and evaluation theory required for these applications. Nelsen (2006) and Joe (1997) provide detailed introductions to copulas and their statistical and mathematical foundations, while Cherubini, et al. (2004) focus primarily on applications of copulas in mathematical finance and derivatives pricing. In this survey I focus on financial time series applications of copulas.

Keywords: multivariate models, dependence, rank correlation, conditional copulas.
J.E.L. Codes: C32, C22, C13.

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Evaluating Volatility Forecasts
(co-authored with Kevin Sheppard)

Abstract
This chapter considers the problem of evaluation and comparison of univariate and multivariate volatility forecasts, with explicit attention paid to the fact that in such applications the object of interest is unobservable, even ex post. Thus the evaluation and comparison of volatility forecasts must rely on direct or indirect methods of overcoming this difficulty. Direct methods use a "volatility proxy", i.e. some observable variable that is related to the latent variable of interest. Indirect methods of overcoming the latent nature of the variable of interest include comparing forecasts via mean-variance portfolio decisions or comparisons based on portfolio "tracking error". The main results of this chapter can be summarised as follows. Firstly, we suggest a minor modification of the widely-used Mincer-Zarnowitz regression for testing volatility forecast optimality which exploits the additional structure that holds under the null hypothesis. This "MZ-GLS" test has good size and much better finite sample power than other MZ tests. Secondly, we find that the use of loss functions that are "non-robust", in the sense of Patton (2006) can yield perverse rankings of forecasts, even when accurate volatility proxies are employed. Finally, consistent with the large and growing literature on realised volatility, our simulations clearly demonstrated the value of higher-precision volatility proxies, such as realised variance Andersen, et al. (2003) or daily high-low range. Even simple estimators based on 30-minute returns provide large gains in power and improvements in finite-sample size.

Keywords: variance, covariance, realized volatility, volatility proxies, Mincer-Zarnowitz.
J.E.L. Codes: C53, C12, C22.

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Predictability of Output Growth and Inflation: A Multi-Horizon Survey Approach
(co-authored with Allan Timmermann)

Abstract
We develop an unobserved components approach to study surveys of forecasts containing multiple forecast horizons. Under the assumption that forecasters optimally update their beliefs about past, current and future state variables as new information arrives, we use our model to extract information on the degree of predictability of the state variable and the importance of measurement errors on that variable. Empirical estimates of the model are obtained using survey forecasts of annual GDP growth and inflation in the US with forecast horizons ranging from 1 to 24 months, and the model is found to closely match the joint realization of forecast errors at different horizons. Our empirical results confirm several findings in the existing literature that were obtained using very different data sets: professional forecasters face severe measurement error problems for GDP growth in real time, while this is not an problem for inflation; inflation exhibits greater persistence, and thus is predictable at longer horizons, than GDP growth; the persistent component of both of these variables is well-approximated by a low-order autoregressive specification.

Keywords: Fixed-event forecasts, multiple forecast horizons, Kalman filtering, survey data.

J.E.L. Codes:  E37, C53, C32.

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Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM and Portfolios Sorts

 (co-authored with Allan Timmermann)

Abstract
Many theories in finance imply monotonic patterns in expected returns and other financial variables: The liquidity preference hypothesis predicts higher expected returns for bonds with longer times to maturity; the CAPM implies higher expected returns for stocks with higher betas; and standard asset pricing models imply that the pricing kernel is declining in market returns. The full set of implications of monotonicity is generally not exploited in empirical work, however. This paper proposes new and simple ways to test for monotonicity in financial variables and compares the proposed tests with extant alternatives such as t-tests, Bonferroni bounds and multivariate inequality tests through empirical applications and simulations.


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Generalized Forecast Errors, A Change of Measure, and Forecast Optimality Conditions
(co-authored with Allan Timmermann)

Abstract
This paper establishes properties of optimal forecasts under general loss functions, extending existing results obtained under specific functional forms and data generating processes. We propose a new method that changes the probability measure under which the well-known properties of optimal forecasts under mean squared error loss can be recovered. We illustrate the proposed methods through an empirical application to U.S. inflation forecasting.

Keywords: forecast evaluation, loss function, rationality tests.
J.E.L. Codes: C53, C22, C52.


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Data-Based Ranking of Realised Volatility Estimators

Abstract
This paper presents new methods for formally comparing the accuracy of estimators of the quadratic variation of a price process. I provide conditions under which the relative average accuracy of competing estimators can be consistently estimated (as T-> +inf) from available data, and show that existing tests from the forecast evaluation literature may be adapted to the problem of ranking these estimators. The proposed methods eliminate the need for specific assumptions about the properties of the microstructure noise, and the need to estimate quantities such as integrated quarticity or the noise variance, and facilitate comparisons of estimators that would be difficult using methods from the extant literature, such as those based on different sampling schemes (calendar-time vs. tick-time). In an application to high frequency IBM stock price data between 1996 and 2007, I find that tick-time sampling is generally preferable to calendar-time sampling, and that the optimal sampling frequency is between 15 seconds and 5 minutes, when using standard realised variance.

Keywords: realised variance, volatility forecasting, forecast comparison.
J.E.L. Codes: C52, C22, C53.

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Why do Forecasters Disagree? Lessons from the Term Structure of Cross-Sectional Dispersion
(co-authored with Allan Timmermann)


Abstract
Using data on cross-sectional dispersion in forecasters' long- and short-run predictions of macroeconomic variables, we identify key sources of disagreement. Dispersion among forecasters is highest at long horizons where private information is of limited value and lower at short forecast horizons. Moreover, differences in views persist through time. Such differences in opinion cannot be explained by differences in information sets; our results indicate they stem from heterogeneity in priors or models. We also find evidence that differences in opinion move countercyclically, with heterogeneity being strongest during recessions where forecasters appear to place greater weight on their prior beliefs.


Keywords: fixed-event forecasts, Kalman filtering, optimal updating, dispersion in beliefs.

J.E.L. Codes: E37, C53, C32.

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Optimal Combinations of Realised Volatility Estimators
(co-authored with
Kevin Sheppard)


Abstract
Recent advances in financial econometrics have led to the development of new estimators of asset price variability using frequently-sampled price data, known as "realised volatility estimators" or simply "realised measures". These estimators rely on a variety of different assumptions and take many different functional forms. Motivated by the empirical success of combination forecasts, this paper presents a novel approach for combining individual realised measures to form new estimators of price variability. In an application to high frequency IBM price data over the period 1996-2008, we consider 32 different realised measures from 8 distinct classes of estimators. We find that a simple equally-weighted average of these estimators cannot generally be out-performed, in terms of accuracy, by any individual estimator. Moreover, we find that none of the individual estimators encompasses the information in all other estimators, providing further support for the use of combination realised measures.


Keywords: realised variance, volatility forecasting, forecast comparison, forecast combination.

J.E.L. Codes: C52, C22, C53.

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Does Beta Move with News? Firm-Specific Information Flows and Learning about Profitability
(co-authored with Michela Verardo)


Abstract

We investigate whether the betas of individual stocks vary with the release of firm-specific news. Using daily firm-level betas estimated from intra-day prices for all constituents of the S&P 500 index, we find that the betas of individual stocks increase by an economically and statistically significant amount on days of quarterly earnings announcements, and revert to their average levels two to five days later. The increase in betas is greater for announcements with larger positive or negative earnings surprises, with greater analyst forecast dispersion, and occurring earlier in the earnings season. Furthermore, the increase in betas is greater for stocks with higher turnover and analyst coverage and for stocks whose fundamentals are more connected with market-wide fundamentals. These findings are consistent with a framework of information spillovers in which investors learn about the profitability of a given firm by using information on other firms.


Keywords: Realized covariance, realized volatility, earnings announcements, high-frequency data.

J.E.L. Codes: G14, G12, C32.

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On the Dynamics of Hedge Fund Risk Exposures
(co-authored with Tarun Ramadorai)


Abstract

We propose a new method to capture changes in hedge funds' exposures to risk factors, exploiting information from relatively high frequency conditioning variables. In a large sample of funds, we find substantial evidence that hedge fund risk exposures vary significantly across and within months, and that capturing within-month variation is more important for hedge funds than mutual funds. We consider different within-month functional forms, and uncover patterns such as day-of-the-month variation in risk exposures. We also find that changes in portfolio allocations, rather than changes in the risk exposures of the underlying assets, are the main drivers of hedge funds' risk exposure variation.


Keywords: beta, time-varying risk, performance evaluation, window-dressing, hedge funds, mutual funds

J.E.L. Codes: G23, G11, C22
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Forecast Rationality Tests Based on Multi-Horizon Bounds
(co-authored with Allan Timmermann)

Abstract

Forecast rationality under squared error loss implies various bounds on second moments of the data across forecast horizons. For example, the mean squared forecast error should be increasing in the horizon, and the mean squared forecast should be decreasing in the horizon. We propose rationality tests based on these restrictions, including new ones that can be conducted without data on the target variable, and implement them via tests of inequality constraints in a regression framework. A new optimal revision test based on a regression of the target variable on the long-horizon forecast and the sequence of interim forecast revisions is also proposed. The size and power of the new tests are compared with those of extant tests through Monte Carlo simulations. An empirical application to the Federal Reserve's Greenbook forecasts is presented.

    

Keywords: Forecast optimality, real-time data, survey forecasts, forecast horizon

JEL Codes: C53, C22, C52.

 

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Good Volatility, Bad Volatility: Signed Jumps and the Persistence of Volatility
(co-authored with Kevin Sheppard)

Abstract

Using recently proposed estimators of the variation of positive and negative returns (“realized semivariances”), and high frequency data for the S&P 500 index and 105 individual stocks, this paper sheds new light on the predictability of equity price volatility. We show that future volatility is much more strongly related to the volatility of past negative returns than to that of positive returns, and this effect is stronger than that implied by standard asymmetric GARCH models. We also find that the impact of a jump on future volatility critically depends on the sign of the jump, with negative (positive) jumps in prices leading to significantly higher (lower) future volatility. A simple model exploiting these findings leads to significantly better out-of-sample forecast performance, across forecast horizons ranging from 1 day to 3 months.

 

Keywords: Realized variance, semivariance, volatility forecasting, jumps, leverage effect

J.E.L. Codes: C58, C22, C53

 

 

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Modelling Dependence in High Dimensions with Factor Copulas

(co-authored with Dong Hwan Oh)

Abstract

This paper presents new models for the dependence structure, or copula, of economic variables based on a factor structure. The proposed models are particularly attractive for high dimensional applications, involving fifty or more variables. This class of models generally lacks a closed-form density, but analytical results for the implied tail dependence can be obtained using extreme value theory, and estimation via a simulation-based method using rank statistics is simple and fast. We study the finite-sample properties of the estimation method for applications involving up to 100 variables, and apply the model to daily returns on all 100 constituents of the S&P 100 index. We find significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms. We also show that the proposed factor copula model provides superior estimates of some measures of systemic risk.

 

Keywords: Correlation, dependence, copulas, tail risk.

JEL Codes: C32, C51, C53.

 

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Change You Can Believe In? Hedge Fund Data Revisions

(co-authored with Tarun Ramadorai and Michael Streatfield)

Abstract

 

We analyze the reliability of voluntary disclosures of financial information, focusing on widely-employed publicly available hedge fund databases. Tracking changes to statements of historical performance recorded at different points in time between 2007 and 2011, we find that historical returns are routinely revised. These revisions are not merely random or corrections of earlier mistakes; they are partly forecastable by fund characteristics. Moreover, funds that revise their performance histories significantly and predictably underperform those that have never revised, suggesting that unreliable disclosures constitute a valuable source of information for current and potential investors. These results speak to current debates about mandatory disclosures by financial institutions to market regulators.

 

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Simulated Method of Moments Estimation for Copula-Based Multivariate Models

(co-authored with Dong Hwan Oh)

Abstract

This paper considers the estimation of the parameters of a copula via a simulated method of moments type approach. This approach is attractive when the likelihood of the copula model is not known in closed form, or when the researcher has a set of dependence measures or other functionals of the copula that are of particular interest. The proposed approach naturally also nests method of moments and generalized method of moments estimators. Drawing on results for simulation based estimation and on recent work in empirical copula process theory, we show the consistency and asymptotic normality of the proposed estimator, and obtain a simple test of over-identifying restrictions as a goodness-of-fit test. The results apply to both iid and time series data. We analyze the finite-sample behavior of these estimators in an extensive simulation study. We apply the model to a group of seven financial stock returns and find evidence of statistically significant tail dependence, and mild evidence that the dependence between these assets is stronger in crashes than booms.

 


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A Review of Copula Models for Economic Time Series


Abstract

This survey reviews the large and growing literature on copula-based models for economic and financial time series. Copula-based multivariate models allow the researcher to specify the models for the marginal distributions separately from the dependence structure that links these distributions to form a joint distribution. This allows for a much greater degree of flexibility in specifying and estimating the model, freeing the researcher from considering only existing multivariate distributions. The author surveys estimation and inference methods and goodness-of-fit tests for such models, as well as empirical applications of these copulas for economic and financial time series.


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Copula Methods for Forecasting Multivariate Time Series


Abstract

Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing the researcher to specify the models for the marginal distributions separately from the dependence structure (copula) that links them to form a joint distribution. In addition to flexibility, this often also facilitates estimation of the model in stages, reducing the computational burden. This chapter reviews the growing literature on copula-based models for economic and financial time series data, and discusses in detail methods for estimation, inference, goodness-of-fit testing, and model selection that are useful when working with these models. A representative data set of two daily equity index returns is used to illustrate all of the main results.


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Does Anything Beat 5-Minute RV?  A Comparison of Realized Measures Across Multiple Asset Classes

(co-authored with Lily Liu and Kevin Sheppard)


Abstract

We study the accuracy of a wide variety of estimators of asset price variation constructed from high-frequency data (so-called "realized measures"), and compare them with a simple "realized variance" (RV) estimator. In total, we consider over 350 different estimators, applied to 11 years of data on 31 different financial assets spanning five asset classes, including equities, equity indices, exchange rates and interest rates. We apply data-based ranking methods to the realized measures and to forecasts based on these measures, for forecast horizons ranging from 1 to 50 trading days. When 5-minute RV is taken as the benchmark realized measure, we find little evidence that it is outperformed by any of the other measures. When using inference methods that do not require specifying a benchmark, we find some evidence that more sophisticated realized measures significantly outperform 5-minute RV. In forecasting applications, we find that a 5-minute "truncated" RV outperforms most other realized measures. Overall, we conclude that it is difficult to significantly beat 5-minute RV.


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Time-Varying Systemic Risk: Evidence from a Dynamic Copula Model of CDS Spreads

(co-authored with Dong Hwan Oh)

Abstract

This paper proposes a new class of copula-based dynamic models for high dimension conditional distributions, facilitating the estimation of a wide variety of measures of systemic risk. Our proposed models draw on successful ideas from the literature on modeling high dimension covariance matrices and on recent work on models for general time-varying distributions. Our use of copula-based models enable the estimation of the joint model in stages, greatly reducing the computational burden. We use the proposed new models to study a collection of daily credit default swap (CDS) spreads on 100 U.S. firms over the period 2006 to 2012. We find that while the probability of distress for individual firms has greatly reduced since the financial crisis of 2008-09, the joint probability of distress (a measure of systemic risk) is substantially higher now than in the pre-crisis period.


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Daily House Price Indexes: Construction, Modeling, and Longer-Run Predictions

(co-authored with Tim Bollerslev and Wenjing Wang)

Abstract

We construct daily house price indexes for ten major U.S. metropolitan areas. Our calculations are based on a comprehensive database of several million residential property transactions and a standard repeat-sales method that closely mimics the procedure used in the construction of the popular monthly Case-Shiller house price indexes. Our new daily house price indexes exhibit similar characteristics to other daily asset prices, with mild autocorrelation and strong conditional heteroskedasticity, which are well described by a relatively simple multivariate GARCH type model. The sample and model-implied correlations across house price index returns are low at the daily frequency, but rise monotonically with the return horizon, and are all commensurate with existing empirical evidence for the existing monthly and quarterly house price series. A simple model of daily house price index returns produces forecasts of monthly house price changes that are superior to various alternative forecast procedures based on lower frequency data, underscoring the informational advantages of our new more finely sampled daily price series.


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Dynamic Copula Models and High Frequency Data

(co-authored with Irving De Lira Salvatierra)

Abstract

This paper proposes a new class of dynamic copula models for daily asset returns that exploits information from high frequency (intra-daily) data. We augment the generalized autoregressive score (GAS) model of Creal, et al. (2012) with high frequency measures such as realized correlation to obtain a "GRAS" model. We find that the inclusion of realized measures significantly improves the in-sample fit of dynamic copula models across a range of U.S. equity returns. Moreover, we find that out-of-sample density forecasts from our GRAS models are superior to those from simpler models. Finally, we consider a simple portfolio choice problem to illustrate the economic gains from exploiting high frequency data for modeling dynamic dependence.


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The Impact of Hedge Funds on Asset Markets

(co-authored with Mathias Kruttli and Tarun Ramadorai)

Abstract

While there has been enormous interest in hedge funds from academics, prospective and current investors, and policymakers, rigorous empirical evidence of their impact on asset markets has been difficult to find. We construct a simple measure of the aggregate illiquidity of hedge fund portfolios, and show that it has strong in- and out-of-sample forecasting power for 72 portfolios of international equities, corporate bonds, and currencies over the 1994 to 2011 period. The forecasting ability of hedge fund illiquidity for asset returns is in most cases greater than, and provides independent information relative to, well-known predictive variables for each of these asset classes. We construct a simple equilibrium model to rationalize our findings, and empirically verify auxiliary predictions of the model.


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Asymptotic Inference about Predictive Accuracy using High Frequency Data

(co-authored with Jia Li)

Abstract

This paper provides a general framework that enables many existing inference methods for predictive accuracy to be used in applications that involve forecasts of latent target variables. Such applications include the forecasting of volatility, correlation, beta, quadratic variation, jump variation, and other functionals of an underlying continuous-time process. We provide primitive conditions under which a "negligibility" result holds, and thus the asymptotic size of standard predictive accuracy tests, implemented using a high-frequency proxy for the latent variable, is controlled. An extensive simulation study verifies that the asymptotic results apply in a range of empirically relevant applications, and an empirical application to correlation forecasting is presented.

 


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Copulas in Economics

(co-authored with Yanqin Fan)

Abstract

Copulas are functions that describe the dependence between two or more random variables. This article provides a brief review of copula theory and two areas of economics in which copulas have played important roles: multivariate modeling and partial identification of parameters that depend on the joint distribution of two random variables with fixed or known marginal distributions. We focus on bivariate copulas, but provide references on recent advances in constructing higher dimensional copulas.

 

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Contact Information

 

Andrew Patton

Department of Economics

Duke University

213 Social Sciences Building, Box 90097

Durham  NC  27708-0097

USA

 

and

Oxford-Man Institute of Quantitative Finance

University of Oxford

 

Email:  andrew.patton@duke.edu
Phone:  +1 919 660 1849
Fax:      +1 919 684 8974
Web:
http://econ.duke.edu/~ap172
__________________________________________


Last updated: July 2013.



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