117 research outputs found
Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets
This paper investigates the presence of bull and bear market states in stock price dynamics. A new definition of bull and bear market states based on sequences of stopping times tracing local peaks and troughs in stock prices is proposed. Duration dependence in stock prices is investigated through posterior mode estimates of the hazard function in bull and bear markets. We find that the longer a bull market has lasted, the lower is the probability that it will come to a termination. In contrast, the longer a bear market has lasted, the higher is its termination probability. Interest rates are also found to have an important effect on cumulated changes in stock prices: increasing interest rates are associated with an increase in bull market hazard rates and a decrease in bear market hazard rates.
Realized Variance and IID Market Microstructure Noise
We analyze the properties of a bias-corrected realized variance (RV) in the presence of iid market microstructure noise. The bias correction is based on the first-order autocorrelation of intraday returns and we derive the optimal sampling frequency as defined by the mean squared error (MSE) criterion. The bias-corrected RV is benchmarked to the standard measure of RV and an empirical analysis shows that the former can reduce the MSE by 50%-90%. Our empirical analysis also shows that the iid noise assumption does not hold in practice. While this need not affect the RVs that are based on low-frequency intraday returns, it has important implications for those based on high-frequency returnsRealized Variance; High-Frequency Data; Integrated Variance.
Hybrid scheme for Brownian semistationary processes
We introduce a simulation scheme for Brownian semistationary processes, which
is based on discretizing the stochastic integral representation of the process
in the time domain. We assume that the kernel function of the process is
regularly varying at zero. The novel feature of the scheme is to approximate
the kernel function by a power function near zero and by a step function
elsewhere. The resulting approximation of the process is a combination of
Wiener integrals of the power function and a Riemann sum, which is why we call
this method a hybrid scheme. Our main theoretical result describes the
asymptotics of the mean square error of the hybrid scheme and we observe that
the scheme leads to a substantial improvement of accuracy compared to the
ordinary forward Riemann-sum scheme, while having the same computational
complexity. We exemplify the use of the hybrid scheme by two numerical
experiments, where we examine the finite-sample properties of an estimator of
the roughness parameter of a Brownian semistationary process and study Monte
Carlo option pricing in the rough Bergomi model of Bayer et al. [Quant. Finance
16(6), 887-904, 2016], respectively.Comment: 33 pages, 4 figures, v4: minor revision, in particular we have
derived a new expression (3.5), equivalent to the previous one but
numerically more convenient, for the off-diagonal elements of the covariance
matrix Sigm
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.
The Local Fractional Bootstrap
We introduce a bootstrap procedure for high-frequency statistics of Brownian
semistationary processes. More specifically, we focus on a hypothesis test on
the roughness of sample paths of Brownian semistationary processes, which uses
an estimator based on a ratio of realized power variations. Our new resampling
method, the local fractional bootstrap, relies on simulating an auxiliary
fractional Brownian motion that mimics the fine properties of high frequency
differences of the Brownian semistationary process under the null hypothesis.
We prove the first order validity of the bootstrap method and in simulations we
observe that the bootstrap-based hypothesis test provides considerable
finite-sample improvements over an existing test that is based on a central
limit theorem. This is important when studying the roughness properties of time
series data; we illustrate this by applying the bootstrap method to two
empirical data sets: we assess the roughness of a time series of high-frequency
asset prices and we test the validity of Kolmogorov's scaling law in
atmospheric turbulence data
Model confidence sets for forecasting models
The paper introduces the model confidence set (MCS) and applies it to the selection of forecasting models. An MCS is a set of models that is constructed so that it will contain the ābestā forecasting model, given a level of confidence. Thus, an MCS is analogous to a confidence interval for a parameter. The MCS acknowledges the limitations of the data so that uninformative data yield an MCS with many models, whereas informative data yield an MCS with only a few models. We revisit the empirical application in Stock and Watson (1999) and apply the MCS procedure to their set of inflation forecasts. In the first pre-1984 subsample we obtain an MCS that contains only a few models, notably versions of the Solow-Gordon Phillips curve. On the other hand, the second post-1984 subsample contains little information and results in a large MCS. Yet, the random walk forecast is not contained in the MCS for either of the samples. This outcome shows that the random walk forecast is inferior to inflation forecasts based on Phillips curve-like relationships.
Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise
This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice.Bipower variation, Long run variance estimator, Market frictions, Quadratic variation, Realised variance
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