High Frequency Time Scales Research Articles

Quasi-likelihood analysis for Student-Lévy regression

We consider the quasi-likelihood analysis for a linear regression model driven by a Student-t Lévy process with constant scale and arbitrary degrees of freedom. The model is observed at high frequency over an extending period, under which we can quantify how the sampling frequency affects estimation accuracy. In that setting, joint estimation of trend, scale, and degrees of freedom is a non-trivial problem. The bottleneck is that the Student-t distribution is not closed under convolution, making it difficult to estimate all the parameters fully based on the high-frequency time scale. To efficiently deal with the intricate nature from both theoretical and computational points of view, we propose a two-step quasi-likelihood analysis: first, we make use of the Cauchy quasi-likelihood for estimating the regression-coefficient vector and the scale parameter; then, we construct the sequence of the unit-period cumulative residuals to estimate the remaining degrees of freedom. In particular, using full data in the first step causes a problem stemming from the small-time Cauchy approximation, showing the need for data thinning.

The Epps effect under alternative sampling schemes

Time and the choice of measurement time scales is fundamental to how we choose to represent information and data in finance. This choice implies both the units and the aggregation scales for the resulting statistical measurables used to describe a financial system. It also defines how we measure the relationship between different traded instruments. As we move from high-frequency time scales, when individual trade and quote events occur, to the mesoscales when correlations emerge in ways that can conform to various latent models; it remains unclear what choice of time and sampling rates are appropriate to faithfully capture system dynamics and asset correlations for decision making. The Epps effect is the key phenomenology that couples the emergence of correlations to the choice of sampling time scales. Here we consider and compare the Epps effect under different sampling schemes in order to contrast three choices of time: calendar time, volume time and trade time. Using a toy model based on a Hawkes process, we are able to achieve simulation results that conform well with empirical dynamics. Concretely, we find that the Epps effect is present under all three definitions of time and that correlations emerge faster under trade time compared to calendar time, whereas correlations emerge linearly under volume time.

Roles of TAO/TRITON and Argo in tropical Pacific observing system: An OSSE study for multiple time scale variability

AbstractIn this study, a series of ocean observing system simulation experiments (OSSEs) are conducted in support of the tropical Pacific observing system (TPOS) 2020 Project (TPOS 2020) which was established in 2014, with aims to develop a more sustainable and resilient observing system for the tropical Pacific. The experiments are based on an ocean data assimilation system that is under development at the Joint Center for Satellite Data Assimilation (JCSDA) and the Environmental Modeling Center (EMC)/National Centers for Environmental Prediction (NCEP). The atmospheric forcing and synthetic ocean observations are generated from a nature run, which is based on a modified CFSv2 with a vertical ocean resolution of 1-meter near the ocean surface. To explore the efficacy of TAO/TRITON and Argo observations in TPOS, synthetic ocean temperature and salinity observations were constructed by sampling the nature run following their present distributions. Our experiments include a free run with no “observations” assimilated, and assimilation runs with the TAO/TRITON and Argo synthetic observations assimilated separately or jointly. These experiments were analyzed by comparing their long-term mean states and variabilities at different time scales [i.e., low-frequency (>90 days), intraseasonal (20~90 days), and high-frequency (<20 days)]. It was found that (1) both TAO/TRITON and especially Argo effectively improve the estimation of mean states and low-frequency variations; (2) on the intraseasonal time scale, Argo has more significant improvements than TAO/TRITON (except for regions close to TAO/TRITON sites); (3) on the high-frequency time scale, both TAO/TRITON and Argo have evident deficits (although for TAO/TRITON, limited improvements were present close to TAO/TRITON sites).

The Volume-Price Relationship at the High-Frequency Scale: Evidence From DCC-GARCH

This article investigates the time-varying high-frequency price-volume relationship from two perspectives. At the high-frequency time scale, we show that the time varying conditional correlation between price and volume changes exhibits distinct excitational spike regimes that provide a rich set of patterns unexplored before. Impulse response analysis based on a high-frequency Vector-autoregressive specification show that volume has greater impact on price than vice versa. Our results therefore suggests that volume can be seen as a proxy for information flows. Due to market micro-structure contamination, we show that smoothing and pre-averaging is necessary to uncover the high-frequency relationship between price and volume.

Identifying and characterising large ramps in power output of offshore wind farms

Recently there has been a significant change in the distribution of wind farms in Great Britain with the construction of clusters of large offshore wind farms. These clusters can produce large ramping events (i.e. changes in power output) on temporal scales which are critical for managing the power system (30 minute, 60 minute and 4 hours). This study analyses generation data from the Thames Estuary cluster in conjunction with meteorological observations to determine the magnitude and frequency of ramping events and the meteorological mechanism. Over a 4 hour time window, the extreme ramping events of the Thames Estuary cluster were caused by the passage of a cyclone and associated weather fronts. On shorter time scales, the largest ramping events over 30 minute and 60 minute time windows are not associated with the passage of fronts. They are caused by three main meteorological mechanisms; (1) very high wind speeds associated with a cyclone causing turbine cut-out (2) gusts associated with thunderstorms and (3) organised band of convection following a front. Despite clustering offshore capacity, the addition of offshore wind farms has increased the mean separation between capacity and therefore reduced the variability in nationally aggregated generation on high frequency time scales.

Linear models for the impact of order flow on prices. I. History dependent impact models

Market impact is a key concept in the study of financial markets and several models have been proposed in the literature so far. The propagator model posits that the price at high frequency time scales is a linear combination of the signs of the past executed market orders, weighted by a so-called propagator function. This model needs to be extended since prices are a priori influenced not only by the past order flow, but also by the past realization of returns themselves. In this paper, we propose a two-event framework, where price-changing and non price-changing events are considered separately. We show that two-event propagator models provide a remarkable improvement of the description of the market impact, especially for large tick stocks, where the events of price changes are very rare and very informative. Specifically the extended approach captures the excess anti-correlation between past returns and subsequent order flow which is missing in one-event models.

Continuous-Time Random Walk with multi-step memory: an application to market dynamics

An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism.

Extreme-volatility dynamics in crude oil markets

Based on concepts and methods from statistical physics, we investigate extreme-volatility dynamics in the crude oil markets, using the high-frequency data from 2006 to 2010 and the daily data from 1986 to 2016. The dynamic relaxation of extreme volatilities is described by a power law, whose exponents usually depend on the magnitude of extreme volatilities. In particular, the relaxation before and after extreme volatilities is time-reversal symmetric at the high-frequency time scale, but time-reversal asymmetric at the daily time scale. This time-reversal asymmetry is mainly induced by exogenous events. However, the dynamic relaxation after exogenous events exhibits the same characteristics as that after endogenous events. An interacting herding model both with and without exogenous driving forces could qualitatively describe the extreme-volatility dynamics.

The Trading Profits of High Frequency Traders

We examine the profitability of a specific class of intermediaries, high frequency traders (HFTs). Using transaction level data with user identifications, we find that high frequency trading (HFT) is highly profitable: 31 HFTs earn over $33 million in trading profits in one E-mini S&P 500 futures contract during one month. The profits of HFTs are mainly derived from fundamental (institutional) and small (retail) traders, but not from non-HFT market makers. While HFTs bear some risk, they generate an unusually high average Sharpe ratio of 10.2. These results provide insight in to the efficiency of markets at high-frequency time scales and raise the question of why we don’t see more competition among HFTs.

Backward jump continuous-time random walk: An application to market trading

The backward jump modification of the continuous-time random walk model or the version of the model driven by the negative feedback was herein derived for spatiotemporal continuum in the context of a share price evolution on a stock exchange. In the frame of the model, we described stochastic evolution of a typical share price on a stock exchange with a moderate liquidity within a high-frequency time scale. The model was validated by satisfactory agreement of the theoretical velocity autocorrelation function with its empirical counterpart obtained for the continuous quotation. This agreement is mainly a result of a sharp backward correlation found and considered in this article. This correlation is a reminiscence of such a bid-ask bounce phenomenon where backward price jump has the same or almost the same length as preceding jump. We suggested that this correlation dominated the dynamics of the stock market with moderate liquidity. Although assumptions of the model were inspired by the market high-frequency empirical data, its potential applications extend beyond the financial market, for instance, to the field covered by the Le Chatelier-Braun principle of contrariness.

High-Frequency Variability in Hurricane Power Dissipation and Its Relationship to Global Temperature

The power dissipation of Atlantic tropical cyclones has risen dramatically during the last decades and the increase is correlated with an increase in the underlying sea surface temperature (SST) at low (decadal) frequencies. Because of the large positive correlation between global mean surface air temperature (GT) and Atlantic SST it has been speculated that increases in the power dissipation might, in part, be related to human activity. Here we investigate the question of the relationship between GT and hurricane power dissipation directly using statistical analysis and show that after removing the effect of SST, the correlation between GT and hurricane power dissipation is negative. This suggests that the positive influence of global temperature on Atlantic hurricanes appears to be limited to an indirect connection with tropical Atlantic SST. We also show that the relationship between hurricane power dissipation and Atlantic SST is significant at the high-frequency time scales. El Niño–Southern Oscillation (ENSO) plays an important role in statistically explaining the variations in hurricane power at these higher frequencies.

Variability of surface heat flux over the Indian Ocean

The variability of surface heat flux over the Indian Ocean is investigated using in situ observational data. First, the Indian Ocean is divided into eight regions and the power spectra of surface heat fluxes are calculated for each region. Consequently it is shown that the surface heat flux over the Indian Ocean has three characteristic timescales: (1) the high frequency timescale (periods shorter than 20 months), (2) the middle frequency timescale (periods between 20 and 60 months), and (3) the low frequency timescale (periods longer than 60 months). Seasonal variation is dominant for the high frequency timescale, with shortwave radiation and the latent heat flux being the principal components of the variability at this timescale. Furthermore, the seasonal variation can be divided into three patterns depending on the region. The variation of shortwave radiation and the latent heat flux are also dominant in the middle‐frequency timescale. In some regions, heat flux variation for this timescale appears to be associated with El Niño. For the low‐frequency timescale, the latent heat flux is dominant. It should be noted that the heat flux from the ocean to the atmosphere has clearly increased since the late 1970s as a result of increases in wind speeds and the specific humidity difference.

Sahel droughts and Enso dynamics

Correlations between summer Sahel rainfall and Southern Oscillation Index has increased during the last thirty years. At high frequency time scale (periods lower than 8 years), an intertropical Atlantic zonal divergent circulation anomaly is forced by the difference of sea surface temperature (SST) anomalies between the eastern equatorial parts of Pacific and Atlantic. This zonal connection worked well during most of the El Nino/Southern Oscillation (ENSO) events occurring after 1970; positive/negative SST anomalies in the eastern Pacific/Atlantic led to rainfall deficits over the whole West Africa. At low frequency time scale (periods greater than 8 years), positive SST anomalies in the Indian ocean and in equatorial Pacific existing after 1970 have been associated with decreasing rainfall intensity over West Africa through another zonal divergent circulation. These different time scales remote SST forcings are combined to provide a global zonal divergent circulation anomaly pattern which could explain the strong association between Sahel drought and ENSO dynamics after 1970.