Returns In Financial Time Series Research Articles

Online Learning with Radial Basis Function Networks

The authors provide multi-horizon forecasts on the returns of financial time series. Their sequentially optimised radial basis function network (RBFNet) outperforms a random-walk baseline and several powerful supervised learners. Their RBFNets naturally measure the similarity between test samples and prototypes that capture the characteristics of the feature space. The authors show that the training set financial time series returns have low similarity with their test set counterparts, highlighting the challenges faced in particular by kernel-based methods that use the training set returns as test-time prototypes; in contrast, their online learning RBFNets have hidden units that retain greater similarity across time.

Financial time series modelling: return on assets

The paper discovers certain aspects of financial time series, in particular, modeling of return on assets. The object of research is a system of indicators for analyzing the returns of financial time series. There is a key feature that distinguishes the analysis of financial time series from the analysis of other time series, as financial theory and its empirical time series contain an element of uncertainty. As a result of this additional uncertainty, statistical theory and its methods and models play an important role in the analysis of financial time series.One of the most problematic places is the use of asset prices and their volatility in the analysis and forecasting of financial time series, which is false because such series contain an element of uncertainty. Therefore, the so-called return on financial assets and instruments should be used in tasks of this type.The paper deals with the types of return on financial assets that can be used in mathematical modeling and forecasting of stock indices. Static methods are used to eliminate the disadvantages of using financial asset prices in the analysis and forecasting of financial time series. The empirical properties of financial time series are examined using the PFTS (First Stock Trading System) and S&P 500 indices.A comprehensive system of indicators of time series analysis of financial assets is obtained. The proposed system involves the use of numerous methods of calculating the profitability (return) of assets in order to determine significant statistical characteristics of the data. Compared to similarly known methods of using prices (rather than profitability) of assets, this provides a key advantage that allows elements of uncertainty in financial and economic data.

Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm

This paper presents a novel four-stage algorithm for the measurement of the rank correlation coefficients between pairwise financial time series. In first stage returns of financial time series are fitted as skewed-t distributions by the generalized autoregressive conditional heteroscedasticity model. In the second stage, the joint probability density function (PDF) of the fitted skewed-t distributions is computed using the symmetrized Joe–Clayton copula. The joint PDF is then utilized as the scoring scheme for pairwise sequence alignment in the third stage. After solving the optimal sequence alignment problem using the dynamic programming method, we obtain the aligned pairs of the series. Finally, we compute the rank correlation coefficients of the aligned pairs in the fourth stage. To the best of our knowledge, the proposed algorithm is the first to use a sequence alignment technique to pair numerical financial time series directly, without initially transforming numerical values into symbols. Using practical financial data, the experiments illustrate the method and demonstrate the advantages of the proposed algorithm.

Microscopic understanding of heavy-tailed return distributions in an agent-based model

The distribution of returns in financial time series exhibits heavy tails. It has been found that gaps between the orders in the order book lead to large price shifts and thereby to these heavy tails. We set up an agent-based model to study this issue and, in particular, how the gaps in the order book emerge. The trading mechanism in our model is based on a double-auction order book. In situations where the order book is densely occupied with limit orders we do not observe fat-tailed distributions. As soon as less liquidity is available, a gap structure forms which leads to return distributions with heavy tails. We show that return distributions with heavy tails are an order-book effect if the available liquidity is constrained. This is largely independent of specific trading strategies.

Long term memory in extreme returns of financial time series

It is well known that while daily price returns of financial markets are uncorrelated, their absolute values (‘volatility’) are long-term correlated. Here we provide evidence that certain subsequences of the returns themselves also exhibit long-term memory. These subsequences consist of maxima (or minima) of returns in consecutive time windows of R days. Our analysis shows that for both stocks and currency exchange rates, long-term correlations are significant for R ≥ 4 . We argue that this long-term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation.

Multivariate distribution of returns in financial time series

Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an approximate scaling and heavy tails of the return distributions, long-ranged volatility-volatility correlations (volatility clustering) and return-volatility correlations (leverage effect). Free parameters of the model are fixed over the long term by fitting 100+ years of daily prices of the Dow Jones 30 Industrial Average. The multivariate probability density functions which we have constructed can be used for pricing derivative securities and risk management.

On the power of generalized extreme value (GEV) and generalized Pareto distribution (GPD) estimators for empirical distributions of stock returns

Using synthetic tests performed on time series with time dependence in the volatility with both Pareto and Stretched-Exponential distributions, it is shown that for samples of moderate sizes the standard generalized extreme value (GEV) estimator is quite inefficient due to the possibly slow convergence toward the asymptotic theoretical distribution and the existence of biases in the presence of dependence between data. Thus, it cannot distinguish reliably between rapidly and regularly varying classes of distributions. The Generalized Pareto distribution (GPD) estimator works better, but still lacks power in the presence of strong dependence. Applied to 100 years of daily returns of the Dow Jones Industrial Average and over one years of five-minutes returns of the Nasdaq Composite index, the GEV and GDP estimators are found insufficient to prove that the distributions of empirical returns of financial time series are regularly varying, because the rapidly varying exponential or stretched exponential distri...

Empirical distributions of stock returns: between the stretched exponential and the power law?

A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. We develop a battery of new non-parametric and parametric tests to characterize the distributions of empirical returns of moderately large financial time series, with application to 100 years of daily returns of the Dow Jones Industrial Average, to 1 year of 5-min returns of the Nasdaq Composite index and to 17 years of 1-min returns of the Standard & Poor's 500. We propose a parametric representation of the tail of the distributions of returns encompassing both a regularly varying distribution in one limit of the parameters and rapidly varying distributions of the class of the stretched-exponential (SE) and the log-Weibull or Stretched Log-Exponential (SLE) distributions in other limits. Using the method of nested hypothesis testing (Wilks‘ theorem), we conclude that both the SE distributions and Pareto distributions provide reliable descriptions of the data but are hardly distinguishable for sufficiently high thresholds. Based on the discovery that the SE distribution tends to the Pareto distribution in a certain limit, we demonstrate that Wilks‘ test of nested hypothesis still works for the non-exactly nested comparison between the SE and Pareto distributions. The SE distribution is found to be significantly better over the whole quantile range but becomes unnecessary beyond the 95% quantiles compared with the Pareto law. Similar conclusions hold for the log-Weibull model with respect to the Pareto distribution, with a noticeable exception concerning the very-high-frequency data. Summing up all the evidence provided by our tests, it seems that the tails ultimately decay slower than any SE but probably faster than power laws with reasonable exponents. Thus, from a practical viewpoint, the log-Weibull model, which provides a smooth interpolation between SE and PD, can be considered as an appropriate approximation of the sample distributions.

Estimating value-at-risk: a point process approach

We consider the modelling of extreme returns in financial time series, and introduce a marked point process model for the exceedances of a high threshold. This model has a self-exciting, Hawkes-process structure in which recent events affect the current intensity of threshold exceedances more than distant ones. Estimates of value-at-risk are derived for real datasets and the success of the estimation method is evaluated in backtests.

Empirical Distributions of Log-Returns: Between the Stretched Exponential and the Power Law?

A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. First, we show by synthetic tests performed on time series with time dependence in the volatility with both Pareto and Stretched-Exponential distributions that for sample of moderate size, the standard generalized extreme value (GEV) estimator is quite inefficient due to the possibly slow convergence toward the asymptotic theoretical distribution and the existence of biases in presence of dependence between data. Thus it cannot distinguish reliably between rapidly and regularly varying classes of distributions. The Generalized Pareto distribution (GPD)estimator works better, but still lacks power in the presence of strong dependence. Then, we use a parametric representation of the tail of the distributions of returns of 100 years of daily return of the Dow Jones Industrial Average and over 1 years of 5-minutes returns of the Nasdaq Composite index, encompassing both a regularly varying distribution in one limit of the parameters and rapidly varying distributions of the class of the Stretched-Exponential (SE) and Log-Weibull distributions in other limits. Using the method of nested hypothesis testing (Wilks' theorem), we conclude that both the SE distributions and Pareto distributions provide reliable descriptions of the data and cannot be distinguished for sufficiently high thresholds. However, the exponent b of the Pareto increases with the quantiles and its growth does not seem exhausted for the highest quantiles of three out of the four tail distributions investigated here. Correlatively, the exponent c of the SE model decreases and seems to tend to zero. Based on the discovery that the SE distribution tends to the Pareto distribution in a certain limit such that the Pareto (or power law) distribution can be approximated with any desired accuracy on an arbitrary interval by a suitable adjustment of the parameters of the SE distribution,we demonstrate that Wilks' test of nested hypothesis still works for the non-exactly nested comparison between the SE and Pareto distributions. The SE distribution is found significantly better over the whole quantile range but becomes unnecessary beyond the 95% quantiles compared with the Pareto law. Similar conclusions hold for the log-Weibull model with respect to the Pareto distribution. Summing up all the evidence provided by our battery of tests, it seems that the tails ultimately decay slower than any SE but probably faster than power laws with reasonable exponents. Thus, from a practical view point, the log-Weibull model, which provides a smooth interpolation between SE and PD, can be considered as an appropriate approximation of the sample distributions. We finally discuss the implications of our results on the moment condition failure and for risk estimation and management.

Heteroscedasticity in non-stationary time series, some Monte Carlo evidence

A frequent question raised by practitioners doing unit root tests is whether these tests are sensitive to the presence of heteroscedasticity. Theoretically this is not the case for a wide range of heteroscedastic models. However, for some limiting cases such as degenerate and integrated heteroscedastic processes it is not obvious whether this will have an effect. In this paper we report a Monte Carlo study analyzing the implications of various types of heteroscedasticity on three types of unit root tests: The usual Dickey-Fuller test, Phillips' (1987) semi-parametric test and finally a Dickey-Fuller type test using White's (1980) heteroscedasticity consistent standard errors. The sorts of heteroscedasticity we examine are the GARCH model of Bollerslev (1986) and the Exponential ARCH model of Nelson (1991). In particular, we call attention to situations where the conditional variances exhibit a high degree of persistence as is frequently observed for returns of financial time series, and the case where, in fact, the variance process for the first class of models becomes degenerate.