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Correcting the Errors : A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities

Correcting the Errors : A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities

evidence related to the Mincer-Zarnowitz volatility regressions reported in ABDL (2003). 2.3 ABDL (2003) Revisited The forecast comparisons in ABDL (2003) are based on daily realized volatilities constructed from high-frequency half-hourly, or h=1/48, spot exchange rates for the U.S. dollar, the Deutschemark and the Japanese yen spanning twelve-and-a-half years. 7 Separate forecast evaluation regressions are reported for the “in-sample” period comprised of the 2,449 “regular” trading days from December 1, 1986 through December 1, 1996, and the shorter “out-of-sample” forecast period consisting of the 596 days from December 2, 1996 through June 30, 1999. Separate results are also reported for one-day-ahead and ten-days-ahead forecasts. Interestingly, for all series and both sample periods and forecast horizons, a simple AR(5) model estimated directly from the realized volatilities generally performs as well or better than any of the many alternative models considered, including several GARCH type models estimated directly to the high-frequency data (both with and without corrections for the pronounced intradaily seasonal pattern in volatility). The representative R 2 ’s for the DM/$, Yen/$, and Yen/DM forecast regressions for RV t+1 (1/48), RV t+1 (1/48) 1/2 ,
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Efficient estimation using the characteristic function : theory and applications with high frequency data

Efficient estimation using the characteristic function : theory and applications with high frequency data

Mots-Clés: Integrated Volatility, Method of Moment, Microstructure Noise, Realized Kernel, Shrinkage. 1.1 Introduction Since the theoretical works by Jacod (1994), Jacod and Protter (1998) and Barndor¤-Nielsen and Shephard (2002), it is well established that the realized volatility (RV) is a consistent estimator of the integrated volatility (IV) when prices are observed without error (see for example Ait-Sahalia, Mykland and Zhang, 2005). However, it is commonly admitted that recorded stock prices are contaminated with pricing errors known in the literature as the "market microstructure noise" (henceforth "noise"). The causes of this noise are discussed for example in Stoll (1989, 2000) or Hasbrouck (1993,1996). In the words of Hasbrouck (1993), the pricing errors are mainly due to "... discreteness, inventory control, the non-information based component of the bid-ask spread, the transient component of the price response to a block trade, etc.". Its presence in measured prices causes the RV computed with very high frequency data to be a severely biased estimator of the IV.
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Empirical Analysis of Jumps Contribution to Volatility Forecasting Using High Frequency Data

Empirical Analysis of Jumps Contribution to Volatility Forecasting Using High Frequency Data

1 Abstract The aim of this project is to empirically validate, using high frequency data, whether jumps help or not to improve volatility forecasting by comparing the results of two models: the Heterogeneous Autoregressive model of Realized Volatility (HAR-RV), proposed by Corsi F., 2009, and a version of the Heterogeneous Auto-Regressive with Continuous Volatility and Jumps (HAR-CJ) model described in Corsi et al., 2010 1 . Both models assume that log-price follows a jump-diffusion process 2 and consider volatilities realized over different interval horizons in order to capture the heterogeneity of the different participants of the market and the asymmetric propagation of volatility. The difference between them is that the HAR-RV does not split the quadratic variation of the cumulative return process into its continuous and discrete parts, but the HAR-CJ model does. The analysis of the data shows that after a large jump, the daily realized volatility is significantly higher than usual suggesting that jumps may have a positive impact in future volatility. The results we obtain confirm this idea because we demonstrate that the forecasted volatility is improved when the volatility is broken down into continuous variations and jumps. In other words, the volatility forecasting precision of the HAR-CJ model is better than that of the HAR-RV model.
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Bootstrapping high frequency data

Bootstrapping high frequency data

i.i.d. Under these assumptions, the pre-averaged returns are asymptotically independent and play the role of the original returns in the realized volatility estimator when no market microstructure noise exists. Therefore, the proof of the validity of the wild bootstrap in the present context where market microstructure effects exist parallels the proof of the validity of the wild bootstrap in the context of Gonçalves and Meddahi (2009), where the wild bootstrap was proposed for realized volatility under no market microstructure effects. Nevertheless, an important difference between these two applications is the fact that the pre-averaging estimator of integrated volatility entails an analytical bias correction term. As it turns out, this bias correction is only important for the proper centering of the confidence intervals and does not impact the variance of the estimator. As a consequence, we show that no bias correction term is needed in the bootstrap world (because we can always center the bootstrap statistic at its own theoretical mean, without affecting the bootstrap variance). This simplifies the application of the bootstrap in this context and justifies an approach solely based on bootstrapping the pre-averaged returns (as the bias term typically depends on the highest available frequency returns, which we are not resampling in the proposed approach).
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From high frequency data information : four empiricals investigations on risks measurements and asset pricing models

From high frequency data information : four empiricals investigations on risks measurements and asset pricing models

Cette partie est ` a rapprocher des travaux de Gottlieb et Kalay (1985) et de Amilon et Bystr¨ om (2000) qui s’interrogent sur les effets de la pr´ esence de ce type de ph´ enom` ene sur [r]

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Correcting the Errors: A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities

Correcting the Errors: A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities

through any forecast evaluation criterion that simply uses the realized volatility in place of the true (latent) integrated volatility. Although this bias may be large (Andersen and Bollerslev, 1998), it is almost always ignored in empirical applications. This note addresses that issue by developing general model-free adjustment procedures that allow for the calculation of simple unbiased loss functions in realistic forecast situations. Moreover, the adjustments are simple to implement in practice. The derivation exploits the recent asymptotic (for increasing sampling frequency) distributional results in Barndorff- Nielsen and Shephard (2002a). Following Andersen and Bollerslev (1998) and ABDL (2003), we focus our forecast comparisons on the value of the coefficient of multiple correlation, or R 2 , in the Mincer-Zarnowitz style regressions of the ex-post realized volatility on the corresponding model forecasts, 2 but our procedures are general and could be applied in the adjustment of other loss functions used in the evaluation of any arbitrary set of volatility forecasts. On applying the procedures in the context of ABDL (2003), we obtain markedly higher estimates for the true degree of return-volatility predictability, with the adjusted R 2 ’s exceeding their unadjusted counterparts by up to forty-percent.
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Ecological Functioning of the Seine River: From Long-Term Modelling Approaches to High-Frequency Data Analysis

Ecological Functioning of the Seine River: From Long-Term Modelling Approaches to High-Frequency Data Analysis

Josette Garnier, Audrey Marescaux, Sophie Guillon, Lauriane Vilmin, Vincent Rocher, Gilles Billen, Vincent Thieu, Marie Silvestre, Paul Passy, Mélanie. Raimonet, et al[r]

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The Great Synchronisation : tracking the trade collapse with high-frequency data

The Great Synchronisation : tracking the trade collapse with high-frequency data

There are two leading explanations for the remarkable synchronicity. The first con- cerns international supply chains, the second concerns the ultimate cause of the Great Recession. The profound internationalisation of the supply chain that has occurred since the 1980s - specifically, the just-in-time nature of these vertically integrated production networks - served to coordinate, i.e. rapidly transmit, demand shocks. Even a decade ago, a drop in consumer sales in the US or Europe took months to be transmitted back to the factories and even longer to reach the suppliers of those factories. Today, Factory Asia is online. Hesitation by US and European consumers is transmitted almost instantly to the entire supply chain, which reacts almost instantly by produc- ing and buying less; trade drops in synch, both imports and exports. For example, during the 2001 trade collapse, monthly data for 52 nations shows that 39% of the month-nation pairs had negative growth for both imports and exports. In the 2008 crisis the figure is 83%. For details on this point, see Di Giovanni, Julian and Andrei Levchenko (2009), Yi (2009), and the chapters by Rudolfs Bems, Robert Johnson, and Kei-Mu Yi, and by Kiyoyasu Tanaka.
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OPTIMIZATION AND STATISTICAL METHODS FOR HIGH FREQUENCY FINANCE

OPTIMIZATION AND STATISTICAL METHODS FOR HIGH FREQUENCY FINANCE

J n , where P 0 is the opening mid-price, 2δ > 0 is the tick size, N t is the point process associated to the tick times (T n ) n (i.e. the price jump times), and (J n ) n is the marks sequence valued in {+1, −1} indicating whether the price jumped upwards (J n = +1) or downwards (J n = −1) at time T n , called price direction. We use a Markov renewal approach to model the marked point process (T n , J n ). (J n ) is an irreducible Markov chain with symmetric transition matrix of diagonal terms 1+α 2 , and antidiagonal terms 1−α 2 , where α ∈ [−1, 1) represents the correlation between two consecutive price returns. Estimation on real data leads to a negative value of α, meaning that the stock price exhibits a short-term mean-reversion, which is a well-known stylized fact about high-frequency data, also called microstructure noise. Denoting by S n = T n − T n−1 the sequence of inter-arrival times associated to (N t ), we assume that conditionally on the sign J n J n+1 = ±1 of two consecutive price directions, (S n ) n is an independent sequence with distribution: F ± (s) = P[S n+1 ≤ s|J n J n+1 = ±1], and density f ± (s). The distinction between F + and F − models the clustering of trading activity, that is the irregular spacing of tick times according to the mean-reverting or trend period of price jumps. We denote by F = 1+α 2 F + +
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Measuring and Forecasting the Daily Variance Based on High-Frequency Intraday and Electronic Data

Measuring and Forecasting the Daily Variance Based on High-Frequency Intraday and Electronic Data

to our high frequency data. Consequently, by applying this model to different variance measures, we can obtain different series of predicted data that can be used to evaluate the forecasting performance of the variance measures. To forecast one day ahead volatility, we use AR model for each variance estimator separately. Applying AR on optimal estimator of Hansen and Lunde as well as RV_total and comparing the forecasted values show a better forecasting by RV_total.

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On the high frequency limit of the LLL equation

On the high frequency limit of the LLL equation

3.3. Transfer to high frequencies. The interactions between different frequencies, say s and 2s, are always damped by a coefficient 2 1 λs . It suggests that any transfer of energy to high frequencies can only happen at a logarithmic speed - and this should also be the case for the full LLL equation. References

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Design, implementation, and evaluation of high-efficiency high-power radio-frequency inductors

Design, implementation, and evaluation of high-efficiency high-power radio-frequency inductors

solenoid. If these reluctances are equal, they sustain the same MMF drop and hence the same 𝐻 = 𝑑(𝑀 𝑀 𝐹 ) 𝑑𝑙 on both sides of the wire, yielding two layers of conduction. An ANSYS finite element simulation [1] illustrates this effect in Fig. 3-3. Figure 3-3: ANSYS FEA simulation illustrating the current crowding phenomenon. For the conductor on the right, the left hand side of the conductor is adjacent to the barrel of an air-core solenoid, a region with high reluctance and MMF drop com- pared to the outside of the solenoid. This MMF imbalance creates an asymmetry in the current distribution and increases loss. The conductor on the left is a miniatur- ized version of the wire in the proposed inductor and experiences much less current crowding due to the balanced nature of its surrounding magnetic fields. The example simulation runs at 13.56 MHz with an excitation current of 20 𝐴 𝑝𝑘 . The wires are 0.8
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High frequency laser-ultrasonics

High frequency laser-ultrasonics

Boucherville, Québec, J4B 6Y4 ABSTRACT The usual frequency bandwidth of laser-ultrasonics is in most cases of order 1 to 30 MHz. Although this is sufficient for most applications, applications involving attenuation measurements in weakly attenuating materials, or velocity measurement in thin samples or coatings may require a much higher detection bandwidth. By shortening the generation light pulse and improving the interferometer electronics, laser-ultrasonic bandwidths of 500 MHz were achieved. Much higher bandwidths (up to 100 GHz) have been achieved by others using delayed femtosecond laser pulses, but what distinguishes our technique is the capability to acquire a full A-scan with a single generation pulse. The capabilities of high frequency laser-ultrasonics will be illustrated with measurements in aluminum foil and sheet, fused quartz, and galvanized steel.
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A communication analysis of high-frequency ionospheric scattering

A communication analysis of high-frequency ionospheric scattering

Two orthog- onal waveforms are used, and the receiver makes an estimate of the path structure of the channel by crosscorrelating the sum of the two possible signa[r]

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Improved Regional Frequency Analysis of rainfall data

Improved Regional Frequency Analysis of rainfall data

5. Conclusion Our main goal in this work was to show that a simple and fast clustering approach based on an in- terpretable ratio could highlight climatologically coherent regions. One advantage is that this method is fully data driven and avoid the need of finding relevant co-variates. The proposed approach was built on the main RFA idea, i.e. a normalizing factor that can capture well the spatial component in rainfall data. All the inferential part was done by using probability weighted moments, simple quantities to estimate and interpret. We completely bypassed the delicate threshold selection step to define heavy rainfall by fitting the extended Pareto distribution.
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View of High Frequency Oscillation: The End?

View of High Frequency Oscillation: The End?

drome (ARDS). This potentially harmful technique has been enthusiastically promoted by some teams until two high-quality randomized clinical trials on ARDS in adults caused the ruin of this house of cards. Indeed, physiological concepts such as atelectrauma and biotrauma on which HFO was based during ARDS were highly disputable. On the contrary, the concept of volotrauma i.e., end-inspiratory overdistension as the responsible for ventilator-induced lung injury allowed prediction of excess mortality during mecha- nical ventilation of ARDS when inspiratory volumes are too high. This is what happened during a recent study on HFO. This resounding failure of a complex and potentially dange- rous technique must be put in perspective with the dramatic improvement of ARDS prognosis with very simple interven- tions such as tidal volume reduction, early pharmacological paralysis and prone positioning.
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High frequency (>30 MHz) flexible broadband transducers

High frequency (>30 MHz) flexible broadband transducers

The center frequency varied depending on the substrate material as seen in Figs. 2-4 (b). This is probably due to the different resonant conditions determined by the UT configuration with multiple layers, and the acoustic impedance and thickness of each layer. It is noted that a half, a quarter and three quarter wavelength resonant frequencies of the 30-µm thick sol-gel PZT composite film are 37.2 MHz, 18.6 MHz and 55.8 MHz, respectively, assuming that the longitudinal wave velocity of the PZT film is 2230 m/s.

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Frequency approach for detecting nonstationarity in dependent data

Frequency approach for detecting nonstationarity in dependent data

4.2 Empirical size and power evaluation Fundamentally, the statistics Q n,m (s, 1/2) depend on the choice of the bandwidth parameter m and the number of Fourier frequencies s. Our strategy is to calibrate m, s in order to ensure an empirical size that remains smaller than the value α(= 5%) set in advance, in particular when d is very close to 1/2. In doing so, and contrary to the V/S which is known to suffer from high empirical size, we are trying to drastically reduce the likelihood of rejecting the stationarity of processes with strong long memory processes.

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Heating and high frequency nonlinearities in the surface impedance of high Tc superconductors

Heating and high frequency nonlinearities in the surface impedance of high Tc superconductors

experiments at 74 K and 63 K. A very good agreement is observed showing that any observed nonlinearity is the consequence of Joule heating. 4. Concluding remarks The temperature dependence of the resonance frequency is the direct consequence of the increase with temperature of the dielectric constant ǫ(T ) of rutile. Note that this behavior is opposite to the decrease with temperature of the dielectric constant of more commonly used sapphire or MgO resonators. Moreover, the variation with temperature of the MgO resonant frequency is much weaker than that of rutile. By consequence, it is difficult to separate the evolution of the intrinsic change of a MgO or sapphire resonator’s frequency from that caused by the temperature variation of a superposed superconducting film: both weakly decrease as function of temperature. However, the intrinsic evolution of the rutile resonator’s frequency being opposite to that expected from the presence of the superconducting film, the measurement of the rutile’s resonator frequency can unambiguously serve as a local temperature measurement.
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HIGH FREQUENCY GRAVITATIONAL WAVES GENERATION IN LASER PLASMA INTERACTION

HIGH FREQUENCY GRAVITATIONAL WAVES GENERATION IN LASER PLASMA INTERACTION

Another GW source is a thin foil accelerated by a high ablation pressure pro- duced by the laser heating and ablation. 7 In this case, the quadrupolar mass mo- mentum writes: Q zz (t) ' M z 2 , where M is the initial mass foil. We can assume that the mass ablated during the laser interaction is negligible, then the GW emitted power writes: P GW ' GM 2 ( ˙ z ¨ z) 2 /5c 5 and h GW ' GM ˙z 2 /c 4 R. With a high energy

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