Financial Time Series Models Research Articles

Analysis of electricity prices for Central American countries using dynamic conditional score models

In this paper, we compare the performance of dynamic conditional score (DCS) and standard financial time-series models for Central American energy prices. We extend the Student’s t and the exponential generalised beta distribution of the second kind stochastic location and stochastic seasonal DCS models. We consider the generalised t distribution as an alternative for the error term and also consider dynamic specifications of volatility. We use a unique dataset of spot electricity prices for El Salvador, Guatemala and Panama. We consider two data windows for each country, which are defined with respect to the liberalisation and development process of the energy market in Central America. We study the identification of a wide range of DCS specifications, likelihood-based model performance, time-series components of energy prices, maximum likelihood parameter estimates, the discounting property of conditional score, and out-of-sample forecast performance. Our main results are the following. (i) We determine the most robust models of energy prices, with respect to parameter identification, from a wide range of DCS specifications. (ii) For most of the cases, the in-sample statistical performance of DCS is superior to that of the standard model. (iii) For El Salvador and Panama, the standard model provides better point forecasts than DCS, and for Guatemala the point forecast precision of standard and DCS models does not differ significantly. (iv) For El Salvador, the standard model provides better density forecasts than DCS, and for Guatemala and Panama, the density forecast precision of standard and DCS models does not differ significantly.

Recent Developments in Copula Models

Copula models have become very popular and well studied among the scientific community.[...]

Measuring the correlation complexity between return series by multiscale complex analysis on Potts dynamics

Financial market is a complex evolving dynamic system with high volatilities and noises, and the modeling and the analyzing of financial time series are regarded as the rather challenging tasks in financial research. In this work, by applying the Potts dynamic system, a random financial time series model is developed in an attempt to uncover the empirical laws in finance, where the particles in the Potts model are introduced to imitate the attitudes of market traders. Through the computer simulation on the selected data, we present the numerical research in conjunction with statistical analysis and nonlinear analysis to investigate the volatilities of financial time series. The fluctuation behavior of logarithmic returns of the proposed model is investigated by MCID, q-MCID and EMD-MCID analyses. Furthermore, in order to obtain a robust conclusion, the complex dynamic behaviors of return time series of the model are investigated by using multiaspect chaos-exploring methods, phase space reconstruction, correlation dimension analysis, largest Lyapunov exponent, density of Kolmogorov–Sinai entropy and Kolmogorov–Sinai entropy universality. The corresponding daily return behaviors of SSE, SZSE, S&P500, IXIC, FTSE, Nikkei and AEX are considered for comparison.

Regularised gradient boosting for financial time-series modelling

Gradient Boosting (GB) learns an additive expansion of simple basis-models. This is accomplished by iteratively fitting an elementary model to the negative gradient of a loss function with respect to the expansion’s values at each training data-point evaluated at each iteration. For the case of squared-error loss function, the negative gradient takes the form of an ordinary residual for a given training data-point. Studies have demonstrated that running GB for hundreds of iterations can lead to overfitting, while a number of authors showed that by adding noise to the training data, generalisation is impaired even with relatively few basis-models. Regularisation is realised through the shrinkage of every newly-added basis-model to the expansion. This paper demonstrates that GB with shrinkage-based regularisation is still prone to overfitting in noisy datasets. We use a transformation based on a sigmoidal function for reducing the influence of extreme values in the residuals of a GB iteration without removing them from the training set. This extension is built on top of shrinkage-based regularisation. Simulations using synthetic, noisy data show that the proposed method slows-down overfitting and reduces the generalisation error of regularised GB. The proposed method is then applied to the inherently noisy domain of financial time-series modelling. Results suggest that for the majority of datasets the method generalises better when compared against standard regularised GB, as well as against a range of other time-series modelling methods.

Long Memory Models for Financial Time Series of Counts and Evidence of Systematic Market Participant Trading Behaviour Patterns in Futures on US Treasuries

This paper propose to incorporate the family of Gegenbauer Autoregressive Moving Average (GARMA) models and a special sub family called the Autoregressive Fractionally Integrated Moving Average (ARFIMA) models into the mean functions of count distributions, including Poisson, Negative Binomial (NB), Generalized Poisson (GP) and Double Poisson (DP). These distributions display equi-, over- and under-dispersion features and the additional long memory structure enhances modelling flexibility. Furthermore, we define the error terms of the GARMA family under two different approaches, the parameter-driven and observation-driven approaches. To estimate these models, we adopt a Bayesian approach implemented using R package Rstan. Then Deviance Information Criterion is evaluated to select some best-fitting models to undertake forecasting of these different classes of long memory count time series. The models are applied to analyse 136 individual U.S. Commodity Futures Trading Commission (CFTC) time series of counts which are each related to trade volume for futures-only and futures-and-options crossed classified with four fixed income securities provided by the U.S. federal government: Treasury notes (T-notes) at 2, 5 and 10 years and Treasury bonds (T-bonds) at marturities of 20 or 30 year terms. These represent some of the most active futures contracts traded in financial markets. The analysis developed provides the first detailed study of this kind undertaken by market participant type according to the categories of reportables and non-reportables and sub-categories of positions of their trading behaviours categorised by the buy and sell sides of long-call, short-put and spread being the difference between long-call and short-put. Furthermore, we study the disaggregated reportables data according to the CFTC four categories of traders, namely, dealers, asset managers, leveraged funds and other reportables. The studies performed demonstrate particular long-memory structures are consistently observed in these highly liquid and important financial instruments and in particular demonstrate systematic forecastable patterns in trading behaviour and liquidity by market participant type, which is as yet not reported or identified in financial literature. Such findings are then directly used as forecasting tools to study further relationships between price discovery and price volatility dynamics.

Stable Lévy motion with inverse Gaussian subordinator

In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.

Stochastic Volatility Models Based on OU-Gamma Time Change: Theory and Estimation

We consider stochastic volatility models that are defined by an Ornstein–Uhlenbeck (OU)-Gamma time change. These models are most suitable for modeling financial time series and follow the general framework of the popular non-Gaussian OU models of Barndorff-Nielsen and Shephard. One current problem of these otherwise attractive nontrivial models is, in general, the unavailability of a tractable likelihood-based statistical analysis for the returns of financial assets, which requires the ability to sample from a nontrivial joint distribution. We show that an OU process driven by an infinite activity Gamma process, which is an OU-Gamma process, exhibits unique features, which allows one to explicitly describe and exactly sample from relevant joint distributions. This is a consequence of the OU structure and the calculus of Gamma and Dirichlet processes. We develop a particle marginal Metropolis–Hastings algorithm for this type of continuous-time stochastic volatility models and check its performance using simulated data. For illustration we finally fit the model to S&P500 index data.

Complexity and multifractal behaviors of multiscale-continuum percolation financial system for Chinese stock markets

A new financial agent-based time series model is developed and investigated by multiscale-continuum percolation system, which can be viewed as an extended version of continuum percolation system. In this financial model, for different parameters of proportion and density, two Poisson point processes (where the radii of points represent the ability of receiving or transmitting information among investors) are applied to model a random stock price process, in an attempt to investigate the fluctuation dynamics of the financial market. To validate its effectiveness and rationality, we compare the statistical behaviors and the multifractal behaviors of the simulated data derived from the proposed model with those of the real stock markets. Further, the multiscale sample entropy analysis is employed to study the complexity of the returns, and the cross-sample entropy analysis is applied to measure the degree of asynchrony of return autocorrelation time series. The empirical results indicate that the proposed financial model can simulate and reproduce some significant characteristics of the real stock markets to a certain extent.

Measuring Risk with COGARCH(p,q) Models

In this paper we introduce a multivariate Independent Component COGARCH(p,q) model for financial time series. We determine optimal portfolio weights obtained as a solution of different static asset allocation problems. Empirical analysis is conducted on two datasets. The first is composed by 154 European hedge funds tracking the performance of the FTSE100 Index while the second contains the members of FTSE100. The performances of different strategies are investigated from an out-of-sample perspective.

Spillover dynamics for systemic risk measurement using spatial financial time series models

We extend the well-known static spatial Durbin model by introducing a time-varying spatial dependence parameter. The updating steps for this model are functions of past data and have information theoretic optimality properties. The static parameters are conveniently estimated by maximum likelihood. We establish the theoretical properties of the model and show that the maximum likelihood estimators of the static parameters are consistent and asymptotically normal. Using spatial weights based on cross-border lending data and European sovereign CDS spread data over the period 2009–2014, we find evidence of contagion in terms of high, time-varying spatial spillovers in the perceived credit riskiness of European sovereigns during the sovereign debt crisis. We find a particular downturn in spatial dependence in the second half of 2012 after the outright monetary transactions policy measures taken by the European Central Bank. Earlier non-standard monetary operations by the ECB did not induce such changes. The findings are robust to a wide range of alternative model specifications.

Long Memory of Financial Time Series and Hidden Markov Models with Time‐Varying Parameters

Hidden Markov models are often used to model daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time‐varying behavior have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time varying. It is shown that a two‐state Gaussian hidden Markov model with time‐varying parameters is able to reproduce the long memory of squared daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time‐varying behavior of the parameters also leads to improved one‐step density forecasts. Finally, it is shown that the forecasting performance of the estimated models can be further improved using local smoothing to forecast the parameter variations. Copyright © 2016 John Wiley & Sons, Ltd.

Financial time series forecasting using rough sets with time-weighted rule voting

In the paper we investigate experimentally the feasibility of rough sets in building profitable trend prediction models for financial time series. In order to improve the decision process for long time series, a novel time-weighted rule voting method, which accounts for information aging, is proposed. The experiments have been performed using market data of multiple stock market indices. The classification efficiency and financial performance of the proposed rough sets models was verified and compared with that of support vector machines models and reference financial indices. The results showed that the rough sets approach with time weighted rule voting outperforms the classical rough sets and support vector machines decision systems and is profitable as compared to the buy and hold strategy. In addition, with the use of variable precision rough sets, the effectiveness of generated trading signals was further improved.

Gaussian Process Regression Stochastic Volatility Model for Financial Time Series

Traditional economic models have rigid-form transition functions when modeling time-varying volatility of financial time series data and cannot capture other time-varying dynamics in the financial market. In this paper, combining the Gaussian process state-space model framework and the stochastic volatility (SV) model, we introduce a new Gaussian process regression stochastic volatility (GPRSV) model building procedures for financial time series data analysis and time-varying volatility modeling. The GPRSV extends the SV model. The flexible stochastic nature of the Gaussian process state description allows the model to capture more time-varying dynamics of the financial market. We also present the model estimation methods for the GPRSV model. We demonstrate the superior volatility prediction performance of our model with both simulated and empirical financial data.

A stochastic volatility model with flexible extremal dependence structure

Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads to a very strong form of asymptotic independence, that is, the coefficient of tail dependence is equal to $1/2$ for all positive lags. We propose an alternative class of stochastic volatility models with heavy-tailed volatilities and examine their extreme value behavior. In particular, it is shown that, while lagged extreme observations are typically asymptotically independent, their coefficient of tail dependence can take on any value between $1/2$ (corresponding to exact independence) and 1 (related to asymptotic dependence). Hence, this class allows for a much more flexible extremal dependence between consecutive observations than classical SV models and can thus describe the observed clustering of financial returns more realistically. The extremal dependence structure of lagged observations is analyzed in the framework of regular variation on the cone $(0,\infty)^d$. As two auxiliary results which are of interest on their own we derive a new Breiman-type theorem about regular variation on $(0,\infty)^d$ for products of a random matrix and a regularly varying random vector and a statement about the joint extremal behavior of products of i.i.d. regularly varying random variables.

Time-varying copula models for financial time series

AbstractWe perform an analysis of the potential time inhomogeneity in the dependence between multiple financial time series. To this end, we use the framework of copula theory and tackle the question of whether dependencies in such a case can be assumed constant throughout time or rather have to be modeled in a time-inhomogeneous way. We focus on parametric copula models and suitable inference techniques in the context of a special copula-based multivariate time series model. A recent result due to Chanet al.(2009) is used to derive the joint limiting distribution of local maximum-likelihood estimators on overlapping samples. By restricting the overlap to be fixed, we establish the limiting law of the maximum of the estimator series. Based on the limiting distributions, we develop statistical homogeneity tests, and investigate their local power properties. A Monte Carlo simulation study demonstrates that bootstrapped variance estimates are needed in finite samples. Empirical analyses on real-world financial data finally confirm that time-varying parameters are an exception rather than the rule.

Linking market interaction intensity of 3D Ising type financial model with market volatility

Abstract Microscopic interaction models in physics have been used to investigate the complex phenomena of economic systems. The simple interactions involved can lead to complex behaviors and help the understanding of mechanisms in the financial market at a systemic level. This article aims to develop a financial time series model through 3D (three-dimensional) Ising dynamic system which is widely used as an interacting spins model to explain the ferromagnetism in physics. Through Monte Carlo simulations of the financial model and numerical analysis for both the simulation return time series and historical return data of Hushen 300 (HS300) index in Chinese stock market, we show that despite its simplicity, this model displays stylized facts similar to that seen in real financial market. We demonstrate a possible underlying link between volatility fluctuations of real stock market and the change in interaction strengths of market participants in the financial model. In particular, our stochastic interaction strength in our model demonstrates that the real market may be consistently operating near the critical point of the system.

Chaoticity Properties of Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastic Processes

Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations.In this work, we have studied the chaoticity properties of FIGARCH (p,d,q) processes by computing mutual information, correlation dimensions, FNNs (False Nearest Neighbour), the largest Lyapunov exponents (LLE) for both the stochastic difference equation and for the financial time series by applying Wolf’s algorithm, Kant’z algorithm and Jacobian algorithm. Although Wolf’s algorithm produced positive LLE’s, Kantz’s algorithm and Jacobian algorithm which are subsequently developed methods due to insufficiency of Wolf’s algorithm generated negative LLE’s constantly.So, as well as experimenting Wolf’s methods’ inefficiency formerly pointed out by Rosenstein (1993) and later Dechert and Gencay (2000), based on Kantz’s and Jacobian algorithm’s negative LLE outcomes, we concluded that it can be suggested that FIGARCH (p,d,q) is not deterministic chaotic process.

An evolutionary hybrid Fuzzy Computationally Efficient EGARCH model for volatility prediction

Accurate modeling for forecasting of stock market volatility is a widely interesting research area both in academia as well as financial markets. This paper proposes an innovative Fuzzy Computationally Efficient EGARCH model to forecast the volatility of three stock market indexes. The proposed model represents a joint estimation of the membership function parameters of a TSK-type fuzzy inference system along with the leverage effect, asymmetric shock by leverage effect of EGARCH model in forecasting highly nonlinear and complicated financial time series model more accurately. Further unlike the conventional TSK type fuzzy neural network the proposed model uses a functional link neural network (FLANN) in the consequent part of the fuzzy rules to provide an improved mapping. Moreover, a differential evolution (DE) algorithm is suggested to solve the parameters estimation problem of Fuzzy Computationally Efficient EGARCH model. Being a parallel direct search algorithm, DE has the strength of finding global optimal solutions regardless of the initial values of its few control parameters. Furthermore, the DE based algorithm aims to achieve an optimal solution with a rapid convergence rate. The proposed model has been compared with some GARCH family models and hybrid fuzzy systems and GARCH models based on three performance metrics: MSFE, RMSFE, and MAFE. The results indicate that the proposed method offers significant improvements in volatility forecasting performance in comparison with all other specified models.

금융 및 특수시계열 모형의 조망

Contrasted with the standard linear ARMA models, financial time series exhibits non-standard features such as fat-tails, non-normality, volatility clustering and asymmetries which are usually referred to as “stylized facts” in financial time series context (Terasvirta, 2009). We are accordingly led to ad hoc models (apart from ARMA) to accommodate stylized facts (Andersen et al., 2009). The paper aims to give a contemporary overview on financial and special time series models based on the recent literature and on the author’s publications. Various models are illustrated including asymmetric models, integer valued models, multivariate models and high frequency models. Selected statistical issues on the models are discussed, bringing some perspectives to the future works in this area.

Financial Time Series Modelling of Trends and Patterns in the Energy Markets

Precise recognition of a time series path is important to policy makers, statisticians, economists, traders, hedgers and speculators alike. The correct time series path is also a key ingredient in pricing models. This study uses daily futures prices of crude oil and other distillate fuels. This paper considers the statistical properties of energy futures and spot prices and investigates the trends that underlie the price dynamics in order to gain further insights into possible nuances of price discovery and energy market dynamics. The family of ARMA-GARCH models was explored. The trends depict time varying variability and persistence of oil price shocks. The return series conform to a constant mean model with GARCH variance.