Peter Reinhard Hansen

Realized Variance and Market Microstructure Noise

We study market microstructure noise in high-frequency data and analyze its implications for the realized variance (RV) under a general specification for the noise. We show that kernel-based estimators can unearth important characteristics of market microstructure noise and that a simple kernel-based estimator dominates the RV for the estimation of integrated variance (IV). An empirical analysis of the Dow Jones Industrial Average stocks reveals that market microstructure noise is time-dependent and correlated with increments in the efficient price. This has important implications for volatility estimation based on high-frequency data. Finally, we apply cointegration techniques to decompose transaction prices and bid–ask quotes into an estimate of the efficient price and noise. This framework enables us to study the dynamic effects on transaction prices and quotes caused by changes in the efficient price.

A Test for Superior Predictive Ability

We propose a new test for superior predictive ability. The new test compares favorably to the reality check (RC) for data snooping, because it is more powerful and less sensitive to poor and irrelevant alternatives. The improvements are achieved by two modifications of the RC. We use a studentized test statistic that reduces the influence of erratic forecasts and invoke a sample-dependent null distribution. The advantages of the new test are confirmed by Monte Carlo experiments and an empirical exercise in which we compare a large number of regression-based forecasts of annual U.S. inflation to a simple random-walk forecast. The random-walk forecast is found to be inferior to regression-based forecasts and, interestingly, the best sample performance is achieved by models that have a Phillips curve structure.

A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data

We consider the problem of deriving an empirical measure of daily integrated variance (IV) in the situation where high-frequency price data are unavailable for part of the day. We study three estimators in this context and characterize the assumptions that justify their use. We show that the optimal combination of the realized variance and squared overnight return can be determined, despite the latent nature of IV, and we discuss this result in relation to the problem of combining forecasts. Finally, we apply our theoretical results and construct four years of daily volatility estimates for the 30 stocks of the Dow Jones Industrial Average. Copyright 2005, Oxford University Press.

Structural changes in the cointegrated vector autoregressive model

We generalize the cointegrated vector autoregressive model of Johansen (1988, 1991) to allow for structural breaks. We derive the likelihood ratio test for structural breaks occurring at fixed points in time, and show that it is asymptotically chi-squared. Moreover, we show how inference can be made when the null hypothesis is presence of structural breaks. The estimation technique derived for this purpose can be applied to several other generalizations of the standard model, beyond the structural breaks treated here. For example, the new technique can be applied to estimate models with heteroskedasticity. We apply our generalized model to US term structure data, accounting for structural breaks that coincide with the changes in the Feds policy in September 1979 and October 1982. Contrary to previous findings we cannot reject the long-run implications of the expectations hypothesis.

Choosing the best volatility models: the model confidence set approach

This paper applies the model confidence set (MCS) procedure of Hansen, Lunde and Nason (2003) to a set of volatility models. An MCS is analogous to the confidence interval of a parameter in the sense that it contains the best forecasting model with a certain probability. The key to the MCS is that it acknowledges the limitations of the information in the data. The empirical exercise is based on 55 volatility models and the MCS includes about a third of these when evaluated by mean square error, whereas the MCS contains only a VGARCH model when mean absolute deviation criterion is used. We conduct a simulation study which shows that the MCS captures the superior models across a range of significance levels. When we benchmark the MCS relative to a Bonferroni bound, the latter delivers inferior performance.

Subsampling Realised Kernels

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.

Moving Average-Based Estimators of Integrated Variance

We examine moving average (MA) filters for estimating the integrated variance (IV) of a financial asset price in a framework where high-frequency price data are contaminated with market microstructure noise. We show that the sum of squared MA residuals must be scaled to enable a suitable estimator of IV. The scaled estimator is shown to be consistent, first-order efficient, and asymptotically Gaussian distributed about the integrated variance under restrictive assumptions. Under more plausible assumptions, such as time-varying volatility, the MA model is misspecified. This motivates an extensive simulation study of the merits of the MA-based estimator under misspecification. Specifically, we consider nonconstant volatility combined with rounding errors and various forms of dependence between the noise and efficient returns. We benchmark the scaled MA-based estimator to subsample and realized kernel estimators and find that the MA-based estimator performs well despite the misspecification.

Soccer Improves Fitness and Attenuates Cardiovascular Risk Factors in Hypertensive Men

INTRODUCTION The present study investigated the fitness and health effects of medium-term soccer training for untrained hypertensive middle-age men. METHODS Thirty-three untrained males (31-54 yr) with mild-to-moderate hypertension were randomized 2:1 to a soccer training group (STG, two 1-h sessions per week, n = 22, 68% on medication) and a doctor advice group receiving traditional physician-guided recommendations on cardiovascular risk factor modification (DAG, n = 11, 73% on medication). Two-way repeated-measures ANOVA time-group statistics was applied. RESULTS During soccer training, average HR was 155 ± 9 bpm or 85% ± 7% HRmax. In STG, systolic and diastolic blood pressures decreased (P < 0.01) over 6 months from 151 ± 10 to 139 ± 10 mm Hg and from 92 ± 7 to 84 ± 6 mm Hg, respectively, with smaller (P < 0.05) decreases in DAG (from 153 ± 8 to 145 ± 8 mm Hg and from 96 ± 6 to 93 ± 6 mm Hg, respectively). In STG, V˙O2max increased (P < 0.01) from 32.6 ± 4.9 to 35.4 ± 6.6 mL·min-1·kg-1 and relative V˙O2 during cycling at 100 W was lowered (P < 0.05) from 55% ± 7% to 50% ± 8% V˙O2max over 6 months, with no changes in DAG. In STG, resting HR was lowered by 8 ± 11 bpm (P < 0.05), and the augmentation index (a measure of arterial stiffness) was lowered (P < 0.05) by 7.3 ± 14.0 over 6 months, with no change in DAG. CONCLUSIONS Six months of soccer training improved aerobic fitness, reduced blood pressure, and resulted in an array of other favorable effects on cardiovascular risk profile for untrained middle-age hypertensive men. Soccer training, therefore, may be a better nonpharmacological treatment for hypertensive men than traditional physician-guided advice.

Testing the Significance of Calendar Effects

This paper studies tests of calendar effects in equity returns. It is necessary to control for all possible calendar effects to avoid spurious results. The authors contribute to the calendar effects literature and its significance with a test for calendar-specific anomalies that conditions on the nuisance of possible calendar effects. Thus, their approach to test for calendar effects produces robust data-mining results. Unfortunately, attempts to control for a large number of possible calendar effects have the downside of diminishing the power of the test, making it more difficult to detect actual anomalies. The authors show that our test achieves good power properties because it exploits the correlation structure of (excess) returns specific to the calendar effect being studied. We implement the test with bootstrap methods and apply it to stock indices from Denmark, France, Germany, Hong Kong, Italy, Japan, Norway, Sweden, the United Kingdom, and the United States. Bootstrap p-values reveal that calendar effects are significant for returns in most of these equity markets, but end-of-the-year effects are predominant. It also appears that, beginning in the late 1980s, calendar effects have diminished except in small-cap stock indices.

An Unbiased Measure of Realized Variance

The realized variance (RV) is known to be biased because intraday returns are contaminated with market microstructure noise, in particular if intraday returns are sampled at high frequencies. In this paper, we characterize the bias under a general specification for the market microstructure noise, where the noise may be autocorrelated and need not be independent of the latent price process. Within this framework, we propose a simple Newey-West type correction of the RV that yields an unbiased measure of volatility, and we characterize the optimal unbiased RV in terms of the mean squared error criterion. Our empirical analysis of the 30 stocks of the Dow Jones Industrial Average index shows the necessity of our general assumptions about the noise process. Further, the empirical results show that the modified RV is unbiased even if intraday returns are sampled every second.