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Register a new userLong-term Memory and Volatility Clustering in Daily and High-frequency Price Changes
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We study the long-term memory in diverse stock market indices and foreign exchange rates using the Detrended Fluctuation Analysis(DFA). For all daily and high-frequency market data studied, no significant long-term memory property is detected in the return series, while a strong long-term memory property is found in the volatility time series. The possible causes of the long-term memory property are investigated using the return data filtered by the AR(1) model, reflecting the short-term memory property, and the GARCH(1,1) model, reflecting the volatility clustering property, respectively. Notably, we found that the memory effect in the AR(1) filtered return and volatility time series remains unchanged, while the long-term memory property either disappeared or diminished significantly in the volatility series of the GARCH(1,1) filtered data. We also found that in the high-frequency data the long-term memory property may be generated by the volatility clustering as well as higher autocorrelation. Our results imply that the long-term memory property of the volatility time series can be attributed to the volatility clustering observed in the financial time series.
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We study the return interval $tau$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poors 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold $q$, the probability density function $P_q(tau)$ scales with the mean interval $bar{tau}$ as $P_q(tau)={bar{tau}}^{-1}f(tau/bar{tau})$, similar to that found in daily volatilities. Since the intraday records have significantly more data points compared to the daily records, we could probe for much higher thresholds $q$ and still obtain good statistics. We find that the scaling function $f(x)$ is consistent for all 31 intraday datasets in various time resolutions, and the function is well approximated by the stretched exponential, $f(x)sim e^{-a x^gamma}$, with $gamma=0.38pm 0.05$ and $a=3.9pm 0.5$, which indicates the existence of correlations. We analyze the conditional probability distribution $P_q(tau|tau_0)$ for $tau$ following a certain interval $tau_0$, and find $P_q(tau|tau_0)$ depends on $tau_0$, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval $<tau|tau_0>$ increases with $tau_0$, consistent with the memory found for $P_q(tau|tau_0)$. Moreover, we find that return interval records have long term correlations with correlation exponents similar to that of volatility records.
The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic. To this end we consider the volatility at both short (a few days) and long (a few months)time scales as a Markovian process and estimate for it the coefficients of the Kramers-Moyal expansion using the data for Dow-Jones Index. It has been found that the empirical data allow to take only the first two coefficients of expansion to be non zero that define form of the volatility stochastic differential equation of Ito. It proved to be that for the long time scale the empirical data support the ExpOU model. At the short time scale the empirical model coincides with ExpOU model for the small volatility quantities only.
Financial trading is at the forefront of time-series analysis, and has grown hand-in-hand with it. The advent of electronic trading has allowed complex machine learning solutions to enter the field of financial trading. Financial markets have both long term and short term signals and thus a good predictive model in financial trading should be able to incorporate them together. One of the most sought after forms of electronic trading is high-frequency trading (HFT), typically known for microsecond sensitive changes, which results in a tremendous amount of data. LSTMs are one of the most capable variants of the RNN family that can handle long-term dependencies, but even they are not equipped to handle such long sequences of the order of thousands of data points like in HFT. We propose very-long short term memory networks, or VLSTMs, to deal with such extreme length sequences. We explore the importance of VLSTMs in the context of HFT. We compare our model on publicly available dataset and got a 3.14% increase in F1-score over the existing state-of-the-art time-series forecasting models. We also show that our model has great parallelization potential, which is essential for practical purposes when trading on such markets.
Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the S&P 500, FTSE100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TARCH and EGARCH. We also test for asymmetry after controlling for the effect of macroeconomic factors on stock market returns using TAR and M-TAR specifications within a VAR framework. Our results show that the conditional variance is an asymmetric function of past innovations raising proportionately more during market declines, a phenomenon known as the leverage effect. However, when we control for the effect of changes in macroeconomic variables, we find no significant evidence of asymmetric behaviour of the stock market returns. There are some signs that the Portuguese Stock Market tends to show somewhat less market efficiency than other markets since the effect of the shocks appear to take a longer time to dissipate.
We investigate the statistical properties of the EBS order book for the EUR/USD and USD/JPY currency pairs and the impact of a ten-fold tick size reduction on its dynamics. A large fraction of limit orders are still placed right at or halfway between the old allowed prices. This generates price barriers where the best quotes lie for much of the time, which causes the emergence of distinct peaks in the average shape of the book at round distances. Furthermore, we argue that this clustering is mainly due to manual traders who remained set to the old price resolution. Automatic traders easily take price priority by submitting limit orders one tick ahead of clusters, as shown by the prominence of buy (sell) limit orders posted with rightmost digit one (nine).
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