Essays on financial time series with a focus on high-frequency data

Abstract

This thesis contains six essays on financial time series. Special attention is paid to the opportunities that high-frequency data offers for modeling and forecasting the return and the risk, measured by the volatility or beta, of an asset.

After an introduction in the first chapter, Chapter 2 shows that, using a variety of high-frequency based explanatory variables, the sign of daily stock returns is predictable in an out-of-sample environment. This predictability is of a magnitude that is statistically significant and consistent over time. Even after accounting for transaction costs, a simple trading strategy based on directional forecasts yields a Sharpe ratio that is nearly double that of the market and an annualized alpha of more than eight percent in a multi-factor model. Consequently, standard risk based models are not able to explain the returns generated by this strategy.

Chapter 3 provides a simple approach to estimate the volatility of economy wide risk factors such as size or value. Models based on these factors are ubiquitous in asset pricing. Therefore, portfolio allocation and risk management require estimates of the volatility of these factors. While realized measures based on high-frequency observations, such as realized variance, have become the standard tools for the estimation of the volatility of liquid individual assets, these measures are difficult to obtain for economy wide risk factors that include smaller illiquid stocks that are not traded at a high frequency. The approach suggested in Chapter 3 improves on this issue as it yields an estimate that is close in precision to realized variance. The efficacy of this approach is demonstrated using Monte Carlo simulations and forecasts of the variance of the market factor.

Chapter 4 shows that realized variance underestimates the variance of daily stock index returns by an average of 14 percent. This is documented for a wide range of international stock indices, using the fact that the average of realized variance and that of squared returns should be the same over longer time horizons. It is shown that the magnitude of this bias cannot be explained by market microstructure noise. Instead, it can be attributed to correlation between the continuous components of intra-day returns.

Chapter 5 reveals that beta series show consistent long-memory properties. This result is based on the analysis of the realized beta series of over 800 stocks. Researchers and practitioners employ a variety of time-series processes to forecast beta series, using either short-memory models or implicitly imposing infinite memory. The results in Chapter 5 suggest that both approaches are inadequate. A pure long-memory model reliably provides superior beta forecasts compared to all alternatives.

Building on the result that beta series can be best described by long-memory processes, Chapter 6 suggests a new multivariate approach to estimate the long-memory parameter robust to low-frequency contaminations. This estimator requires a priori knowledge of the cointegration rank. Since low-frequency contaminations bias inference on the cointegration rank, a robust estimator of the cointegration rank is also provided. An extensive Monte Carlo exercise shows the applicability of the estimators in finite samples. Furthermore, the procedures are applied to the realized beta series of two American energy companies discovering that the series are fractionally cointegrated. As the series exhibit low-frequency contaminations, standard procedures are unable to detect this relation.

Finally, Chapter 7 presents the R package \emph{memochange}. The package includes several change-in-mean tests that are applicable under long memory as standard change-in-mean tests are invalid in this case. Moreover, the package contains various tests for a break in persistence. These can be used to detect a change in the memory parameter.