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on Econometric Time Series |
| By: | Fulvio Corsi; Davide Pirino; Roberto Reno |
| Abstract: | This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is correctly separated into its continuous and discontinuous component. To this purpose, we introduce the concept of threshold multipower variation (TMPV), which is based on the joint use of bipower variation and threshold estimation. With respect to alternative methods, our TMPV estimator provides less biased and robust estimates of the continuous quadratic variation and jumps. This technique also provides a new test for jump detection which has substantially more power than traditional tests. We use this separation to forecast volatility by employing an heterogeneous autoregressive (HAR) model which is suitable to parsimoniously model long memory in realized volatility time series. Empirical analysis shows that the proposed techniques improve significantly the accuracy of volatility forecasts for the S&P500 index, single stocks and US bond yields, especially in periods following the occurrence of a jump. |
| Keywords: | volatility forecasting, jumps, bipower variation, threshold estimation, stock, bond |
| JEL: | G1 C1 C22 C53 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd08-036&r=ets |
| By: | Isao Ishida; Toshiaki Watanabe |
| Abstract: | In this paper, we apply the ARFIMA-GARCH model to the realized volatility and the continuous sample path variations constructed from high-frequency Nikkei 225 data. While the homoskedastic ARFIMA model performs excellently in predicting the Nikkei 225 realized volatility time series and their square-root and log transformations, the residuals of the model suggest presence of strong conditional heteroskedasticity similar to the finding of Corsi et al. (2007) for the realized S&P 500 futures volatility. An ARFIMA model augmented by a GARCH(1,1) specification for the error term largely captures this and substantially improves the fit to the data. In a multi-day forecasting setting, we also find some evidence of predictable time variation in the volatility of the Nikkei 225 volatility captured by the ARFIMA-GARCH model. |
| Keywords: | ARFIMA-GARCH, Volatility of realized volatility, Realized bipower variation, Jump detection, BDS test, Hong-Li test, High-frequency Nikkei 225 data |
| JEL: | C22 C53 G15 |
| Date: | 2009–02 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd08-032&r=ets |
| By: | Federico M. Bandi; Roberto Reno |
| Abstract: | Using recent advances in the nonparametric estimation of continuous-time processes under mild statistical assumptions as well as recent developments on nonparametric volatility estimation by virtue of market microstructure noise-contaminated high-frequency asset price data, we provide (i) a theory of spot variance estimation and (ii) functional methods for stochastic volatility modelling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, jumps in returns and volatility with possibly state-dependent jump intensities, as well as nonlinear risk-return trade-offs. Our identification approach and asymptotic results apply under weak recurrence assumptions and, hence, accommodate the persistence properties of variance in finite samples. Functional estimation of a generalized (i.e., nonlinear) version of the square-root stochastic variance model with jumps in both volatility and returns for the S&P500 index suggests the need for richer variance dynamics than in existing work. We find a linear specification for the variance's diffusive variance to be misspecified (and inferior to a more flexible CEV specification) even when allowing for jumps in the variance dynamics. |
| Keywords: | Spot variance, stochastic volatility, jumps in returns, jumps in volatility, leverage effects, risk-return trade-offs, kernel methods, recurrence, market microstructure noise. |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd08-035&r=ets |
| By: | Hiroki Masuda; Takayuki Morimoto |
| Abstract: | In Japanese stock markets, there are two kinds of breaks, i.e., nighttime and lunch break, where we have no trading, entailing inevitable increase of variance in estimating daily volatility via naive realized variance (RV). In order to perform a much more stabilized estimation, we are concerned here with a modification of the weighting technique of Hansen and Lunde (2005). As an empirical study, we estimate optimal weights in a certain sense for Japanese stock data listed on the Tokyo Stock Exchange. We found that, in most stocks appropriate use of the optimally weighted RV can lead to remarkably smaller estimation variance compared with naive RV, hence substantially to more accurate forecasting of daily volatility. |
| Keywords: | high-frequency data, market microstructure noise, realized volatility, Japanese stock markets, variance of realized variance |
| JEL: | C19 C22 C51 |
| Date: | 2009–02 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd08-033&r=ets |
| By: | Torben G. Andersen; Dobrislav Dobrev; Ernst Schaumburg |
| Abstract: | We develop a novel approach to estimating the integrated variance of a general jump-diffusion with stochastic volatility. Our approach exploits the relationship between the speed (distance traveled per fixed time unit) and passage time (time taken to travel a fixed distance) of the Brownian motion. The new class of duration-based IV estimators derived in this paper is shown to be robust to both jumps and market microstructure noise. Moreover, their asymptotic and finite sample properties compare favorably to those of commonly used robust IV estimators. |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd08-034&r=ets |
| By: | Li, Yushu (Centre for Labour Market Policy Research (CAFO)); Shukur, Ghazi (Centre for Labour Market Policy Research (CAFO)) |
| Abstract: | In this paper, we use the wavelet technique to improve the over-rejection problem of the traditional Dickey-Fuller test for unit root when the data suffers from GARCH (1,1) effect. The logic is based on that the wavelet spectrum decomposition can separate out information of different frequencies in the data series. We prove that the asymptotic distribution of our test is similar to the traditional Dickey-Fuller(1979 and 1981) type of tests. The small sample distribution of the new test is assessed by means of Monte Carlo simulation. An empirical example with data on immigration to Sweden during the period 1950 to 2000 is used to illustrate the test. The results reveal that using the traditional Dickey-Fuller type of test, the unit root is rejected while our wavelet improved test shows the opposite result. |
| Keywords: | Dickey-Fuller test; GARCH (1:1); Wavelet spectrum decomposition; MODWT |
| JEL: | C15 C52 |
| Date: | 2009–02–26 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:vxcafo:2009_007&r=ets |
| By: | Li, Yushu (Centre for Labour Market Policy Research (CAFO)); Shukur, Ghazi (Centre for Labour Market Policy Research (CAFO)) |
| Abstract: | In this paper, we propose a Nonlinear Dickey-Fuller F test for unit root against first order Logistic Smooth Transition Autoregressive LSTAR (1) model with time as the transition variable. The Nonlinear Dickey-Fuller F test statistic is established under the null hypothesis of random walk without drift and the alternative model is a nonlinear LSTAR (1) model. The asymptotic distribution of the test is analytically derived while the small sample distributions are investigated by Monte Carlo experiment. The size and power properties of the test have been investigated using Monte Carlo experiment. The results have shown that there is a serious size distortion for the Nonlinear Dickey-Fuller F test when GARCH errors appear in the Data Generating Process (DGP), which lead to an over-rejection of the unit root null hypothesis. To solve this problem, we use the Wavelet technique to count off the GARCH distortion and to improve the size property of the test under GARCH error. We also discuss the asymptotic distributions of the test statistics in GARCH and wavelet environments. Finally, an empirical example is used to compare our test with the traditional Dickey-Fuller F test. |
| Keywords: | Unit root Test; Dickey-Fuller F test; STAR model; GARCH (1: 1) Wavelet method; MODWT |
| JEL: | C15 C52 |
| Date: | 2009–02–26 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:vxcafo:2009_006&r=ets |
| By: | Hanck Christoph (METEOR) |
| Abstract: | This paper proposes a new testing approach for panel unit roots that is, unlike previously suggested tests, robust to nonstationarity in the volatility process of the innovations of the time series in the panel. Nonstationarity volatility arises for instance when there are structural breaks in the innovation variances. A prominent example is the reduction in GDP growth variances enjoyed by many industrialized countries, known as the `Great Moderation.'' The panel test is based on Simes'' [Biometrika 1986, "An Improved Bonferroni Procedure for Multiple Tests of Significance''''] classical multiple test, which combines evidence from time series unit root tests of the series in the panel. As time series unit root tests, we employ recently proposed tests of Cavaliere and Taylor [Journal of Time Series Analysis 2008, "Time-Transformed Unit Root Tests for Models with Non-Stationary Volatility'''']. The panel test is robust to general patterns of cross-sectional dependence and yet straightforward to implement, only requiring valid p-values of time series unit root tests, and no resampling. Monte Carlo experiments show that other panel unit root tests suffer from sometimes severe size distortions in the presence of nonstationary volatility, and that this defect can be remedied using the test proposed here. The new test is applied to test for a unit root in an OECD panel of gross domestic products, yielding inference robust to the ''Great Moderation''. We find little evidence of trend stationarity. |
| Keywords: | macroeconomics ; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009009&r=ets |