Search

Short memory models contaminated by level shifts have similar long-memory features as fractionally integrated processes. This makes it hard to verify whether the true data generating process is a pure fractionally integrated process when employing standard estimation methods based on the autocorrelation function or the periodogram. In this paper, we propose a robust testing procedure, based on an encompassing parametric specification that allows us to disentangle the level shifts from the fractionally integrated component. The estimation is carried out on the basis of a state-space methodology and it leads to a robust estimate of the fractional integration parameter also in presence of level shifts. Once the memory parameter is correctly estimated, we use the KPSS test for presence of level shift. The Monte Carlo simulations show how this approach produces unbiased estimates of the memory parameter when shifts in the mean, or other slowly varying trends, are present in the data. Therefore, this subsequent robust version of the KPSS test for the presence of level shifts has proper size and by far the highest power compared to other existing tests. Finally, we illustrate the usefulness of the proposed approach on financial data, such as daily bipower variation and turnover.

The persistent nature of equity volatility is investigated by means of a multi-factor stochastic volatility model with time varying parameters. The parameters are estimated by means of a sequential matching procedure which adopts as auxiliary model a time-varying generalization of the HAR model for the realized volatility series. It emerges that during the recent financial crisis the relative weight of the daily component dominates over the monthly term. The estimates of the two factor stochastic volatility model suggest that the change in the dynamic structure of the realized volatility during the financial crisis is due to the increase in the volatility of the persistent volatility term. A set of Monte Carlo simulations highlights th correctness of the methodology adopted to extract the variability in the parameters.

During the last decades a wide literature has focused on the relationship volume-volatility on financial markets. This paper investigates the temporal dynamics of volatility and volumes, supposing, as in Bollerslev and Jubinsky (1999), that the link has to be found in their long-run dependencies, that are supposed to be driven by the same informative process. We analyze the volume-volatility relationship using IBM stocks data. In particular, we rely on the realized volatility based on five minutes stock prices. Tail dependence analysis is carried out with two alternative estimators of the continuous part of the volatility process. The analysis shows that log-realized volatility and log-volumes are characterized by upper and lower tail dependence, where the positive tail dependence is mainly due to the jump component. We also investigate the possibility that volumes and volatility are driven by a common fractionally integrated stochastic trend, i.e. they have the same degree of long memory and are fractionally cointegrated as the Mixture Distribution Hypotesis prescribes. Moreover, we estimate a bivariate ARFIMA specification that explicitly considers the long run relationship between the two series and the tail dependence in the shocks, by parameterizing the joint density by means of different copula functions. The evidence from the model estimates, the simulation results and the forecasts comparison with HAR model highlight the ability of the bivariate ARFIMA with copula density specification to account for the common long memory pattern and tail dependence.