Financial Time Series Models Research Articles

An Introduction to Bootstrap Theory in Time Series Econometrics

This article provides an introduction to methods and challenges underlying application of the bootstrap in econometric modelling of economic and financial time series. Validity, or asymptotic validity, of the bootstrap is discussed as this is a key element in deciding whether the bootstrap is applicable in empirical contexts. That is, as detailed here, bootstrap validity relies on regularity conditions, which need to be verified on a case-by-case basis. To fix ideas, asymptotic validity is discussed in terms of the leading example of bootstrap-based hypothesis testing in the well-known first order auto-regressive model. In particular, bootstrap versions of classic convergence in probability and distribution, and hence of laws of large numbers and central limit theorems, are discussed as crucial ingredients to establish bootstrap validity. Regularity conditions and their implications for possible improvements in terms of (empirical) size and power for bootstrap-based testing, when compared to asymptotic testing, are illustrated by simulations. Following this, an overview of selected recent advances in the application of bootstrap methods in econometrics is also given.

A Data-Driven Market Simulator for Small Data Environments

Neural network based data-driven market simulation unveils a new and flexible way of modelling financial time series without imposing assumptions on the underlying stochastic dynamics. Though in this sense generative market simulation is model-free, the concrete modelling choices are nevertheless decisive for the features of the simulated paths. We give a brief overview of currently used generative modelling approaches and performance evaluation metrics for financial time series, and address some of the challenges to achieve good results in the latter. We also contrast some classical approaches of market simulation with simulation based on generative modelling and highlight some advantages and pitfalls of the new approach. While most generative models tend to rely on large amounts of training data, we present here a generative model that works reliably in environments where the amount of available training data is notoriously small. Furthermore, we show how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series in such environments where available training data is scarce. Finally, we also propose a suitable performance evaluation metric for financial time series and discuss some connections of our Market Generator to deep hedging.

Integral transform methods in goodness-of-fit testing, II: the Wishart distributions

We initiate the study of goodness-of-fit testing for data consisting of positive definite matrices. Motivated by the appearance of positive definite matrices in numerous applications, including factor analysis, diffusion tensor imaging, volatility models for financial time series, wireless communication systems, and polarimetric radar imaging, we apply the method of Hankel transforms of matrix argument to develop goodness-of-fit tests for Wishart distributions with given shape parameter and unknown scale matrix. We obtain the limiting null distribution of the test statistic and a corresponding covariance operator, show that the eigenvalues of the operator satisfy an interlacing property, and apply our test to some financial data. We establish the consistency of the test against a large class of alternative distributions and derive the asymptotic distribution of the test statistic under a sequence of contiguous alternatives. We obtain the Bahadur and Pitman efficiency properties of the test statistic and establish a modified version of Wieand’s condition.

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.

Linnik Lévy process and some extensions

In the literature, the Linnik, Mittag-Leffler, Laplace and asymmetric Laplace distributions are the most known examples of geometric stable distributions. The geometric stable distributions are especially useful in the modeling of leptokurtic data with heavy-tailed behavior. They have found many interesting applications in the modeling of several physical phenomena and financial time-series. In this paper, we define the Linnik Lévy process (LLP) through the subordination of symmetric stable Lévy motion with gamma process. We discuss main properties of LLP like probability density function, Lévy measure and asymptotic forms of marginal densities. We also consider the governing fractional-type Fokker–Planck equation. To show practical applications, we simulate the sample paths of the introduced process. Moreover, we give a step-by-step procedure of the parameters estimation and calibrate the parameters of the LLP with the Arconic Inc equity data taken from Yahoo finance. Further, some extensions of the introduced process are also discussed.

Stochastic Duffing equation in modelling of financial time series

In this study, we aim to introduce a new stochastic modelling and forecasting method for the chaotic noisy Duffing map series and then for the financial time series with similar properties. We examine the fractal properties of the noisy Duffing map by correlation dimension, wavelet analysis and MFDFA analysis. Then, it is shown that the non-linear deterministic multifractal Duffing map with additive white noise process exhibits the telegraph process modulated with the fractional Gaussian noise. The combination of these stochastic processes and the fractional Gaussian noise fit the Duffing map series with white noise which has regime switching and long-range dependent properties and then the real-world financial time series with similar properties. Numerical experiments show that the proposed model generates remarkable forecast result in different horizons when it is compared with the actual outcomes. The results put forward that the chaotic Duffing equation can be a fitting model to certain financial time series or the time series with the same characteristics.

Modeling financial time-series with generative adversarial networks

Financial time-series modeling is a challenging problem as it retains various complex statistical properties and the mechanism behind the process is unrevealed to a large extent. In this paper, a deep neural networks based approach, generative adversarial networks (GANs) for financial time-series modeling is presented. GANs learn the properties of data and generate realistic data in a data-driven manner. The GAN model produces a time-series that recovers the statistical properties of financial time-series such as the linear unpredictability, the heavy-tailed price return distribution, volatility clustering, leverage effects, the coarse-fine volatility correlation, and the gain/loss asymmetry.

Utility of a Shuffled Differential Evolution algorithm in designing of a Pi-Sigma Neural Network based predictor model

Since the last few decades, Artificial Neural Networks have been the center of attraction of a large number of researchers for solving diversified problem domains. Due to its distinguishing features such as generalization ability, robustness and strong ability to tackle nonlinear problems, it appears to be more popular in financial time series modeling and prediction. In this paper, a Pi-Sigma Neural Network is designed for foretelling the future currency exchange rates in different prediction horizon. The unrevealed parameters of the network are interpreted by a hybrid learning algorithm termed as Shuffled Differential Evolution (SDE). The main motivation of this study is to integrate the partitioning and random shuffling scheme of Shuffled Frog Leaping algorithm with evolutionary steps of a Differential Evolution technique to obtain an optimal solution with an accelerated convergence rate. The efficiency of the proposed predictor model is actualized by predicting the exchange rate price of a US dollar against Swiss France (CHF) and Japanese Yen (JPY) accumulated within the same period of time.

Forecasting Realized Correlations: A MIDAS Approach

Mixed data sampling (MIDAS) regression has received much attention in relation to modeling financial time series due to its flexibility. Previous work has mainly focused on forecasting of realized volatilities and has rarely been used to predict realized correlations. This paper considers a MIDAS approach to forecast realized correlation matrices. A MIDAS model is estimated via nonlinear least squares (NLS) using an analytical gradient-based optimization. Based on the model confidence set (MCS) procedure we discover that the introduced approach is superior compared to the established heterogeneous autoregressive (HAR) model in terms of out-of-sample forecasting accuracy. This preeminence is due to the flexible data-driven origin of the MIDAS model. The latter results in higher economic value with regard to portfolio management applications. The improvement is considerable for longer forecasting horizons both in calm times and during the periods of market turbulence.

A semi-parametric method for estimating the beta coefficients of the hidden two-sided asset return jumps

ABSTRACTWe introduce a new methodology for estimating the parameters of a two-sided jump model, which aims at decomposing the daily stock return evolution into (unobservable) positive and negative jumps as well as Brownian noise. The parameters of interest are the jump beta coefficients which measure the influence of the market jumps on the stock returns, and are latent components. For this purpose, at first we use the Variance Gamma (VG) distribution which is frequently used in modeling financial time series and leads to the revelation of the hidden market jumps' distributions. Then, our method is based on the central moments of the stock returns for estimating the parameters of the model. It is proved that the proposed method provides always a solution in terms of the jump beta coefficients. We thus achieve a semi-parametric fit to the empirical data. The methodology itself serves as a criterion to test the fit of any sets of parameters to the empirical returns. The analysis is applied to NASDAQ and Google returns during the 2006–2008 period.

Modeling financial interval time series.

In financial economics, a large number of models are developed based on the daily closing price. When using only the daily closing price to model the time series, we may discard valuable intra-daily information, such as maximum and minimum prices. In this study, we propose an interval time series model, including the daily maximum, minimum, and closing prices, and then apply the proposed model to forecast the entire interval. The likelihood function and the corresponding maximum likelihood estimates (MLEs) are obtained by stochastic differential equation and the Girsanov theorem. To capture the heteroscedasticity of volatility, we consider a stochastic volatility model. The efficiency of the proposed estimators is illustrated by a simulation study. Finally, based on real data for S&P 500 index, the proposed method outperforms several alternatives in terms of the accurate forecast.

Financial interval time series modelling and forecasting using threshold autoregressive models

Financial interval time series (ITS) describe the evolution of the high and low prices of an asset throughout time. Their accurate forecasts play a key role in risk management, derivatives pricing and asset allocation, demanding the development of models able to properly predict these prices. This paper evaluates threshold autoregressive models for financial ITS forecasting as a nonlinear approach for ITS considering as empirical application the main index of the Brazilian stock market, the IBOVESPA. One step ahead interval forecasts are compared against linear and nonlinear time series benchmark methods in terms of traditional accuracy metrics and quality measures designed for ITS. The results indicated the predictability of IBOVESPA ITS and that significant forecast contribution are achieved when nonlinear approaches are considered. Further, nonlinear models do provide higher accuracy when forecasting Brazilian financial ITS.

Financial interval time series modelling and forecasting using threshold autoregressive models

Financial interval time series (ITS) describe the evolution of the high and low prices of an asset throughout time. Their accurate forecasts play a key role in risk management, derivatives pricing and asset allocation, demanding the development of models able to properly predict these prices. This paper evaluates threshold autoregressive models for financial ITS forecasting as a nonlinear approach for ITS considering as empirical application the main index of the Brazilian stock market, the IBOVESPA. One step ahead interval forecasts are compared against linear and nonlinear time series benchmark methods in terms of traditional accuracy metrics and quality measures designed for ITS. The results indicated the predictability of IBOVESPA ITS and that significant forecast contribution are achieved when nonlinear approaches are considered. Further, nonlinear models do provide higher accuracy when forecasting Brazilian financial ITS.

Score-driven currency exchange rate seasonality as applied to the Guatemalan Quetzal/US Dollar

In this paper we introduce new Dynamic Conditional Score (DCS) models for the Skew-Gen-t (Skewed Generalized t) and NIG (Normal-Inverse Gaussian) distributions as alternatives to the recent DCS models for the Student’s-t and EGB2 (Exponential Generalized Beta of the second kind) distributions, respectively. The DCS models we propose include stochastic local level, stochastic seasonality, and irregular components with DCS-EGARCH (Exponential Generalized Autoregressive Conditional Heteroscedasticity) volatility dynamics. DCS models are robust to extreme observations, whereas standard financial time series models are not. We use data from the Guatemalan Quetzal (GTQ) to United States Dollar (USD) exchange rate for the period of 4th January 1994–30th June 2017. This dataset exhibits significant rises and falls in the GTQ/USD that lead to extreme observations, stochastic seasonality with dynamic amplitude, and volatility dynamics. These seasonality dynamics of the GTQ/USD are related to the Guatemalan trade-related currency movements, receipt and payment of foreign loans, and remittance payments of Guatemalans working abroad. We show that the in-sample statistical performance of the DCS-Skew-Gen-t and the DCS-NIG models is superior to that of the DCS-t and the DCS-EGB2 models, respectively. Furthermore, we show that the statistical performance of all DCS models is superior to that of the standard financial time series model.

A Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) for Asset Prices

We propose a new approach for bivariate financial time series modelling which allows for mutual excitation between shocks. Jumps are triggered by changes of regime of a hidden Markov chain whose matrix of transition probabilities is constructed in order to approximate a bivariate Hawkes process. This model, called the Bivariate Mutually-Excited Switching Jump Diffusion (BMESJD) presents several interesting features. Firstly, compared to alternative approaches for modelling the contagion between jumps, the calibration is easier and performed with a modified Hamilton’s filter. Secondly, the BMESJD allows for simultaneous jumps when markets are highly stressed. Thirdly, a family of equivalent probability measures under which the BMESJD dynamics are preserved, is well identified. Finally, the BMESJD is a continuous time process that is well adapted for pricing options with two underlying assets.

Assessing Market Efficiency And Volatility Of Exchange Rates in South Africa and United Kingdom: Analysis Using Hurst Exponent

The possibility of random walk movements in the log-returns of exchange rate series as well as the characterization of returns by periods of tranquility and volatility is of interest in financial time series modelling. These features make the analysis of exchange rates to be important in the design of policy, portfolio and risk management whenever international trade and finance is discussed. This paper investigated the level of exchange rates market efficiency and volatility at three market phases of US Dollar-South African Rands and US Dollars-British Pounds exchange rates for the daily periods from 2 January 1995 to 8 June 2016. This paper applied the modified Hurst exponent' and volatility modelling techniques on the series log-returns, absolute and squared log-returns used as proxies to volatility. The results of the modified Hurst exponent techniques on the log-returns and squared log-returns show that the future path of the exchange rates returns in these markets are not governed by their immediate past in the second and third identified phases. Thus, the two markets have been in the state of weak form of efficiency since 2001 to the current transition, with UK exchange rate market more efficient than South African exchange rate market. Using the efficiency and volatility indices to classify the two exchange rate markets as well as the market phases, we observe similar transition in the level of market efficiency in these markets, this which is as a result of trade partnership between the two countries. In terms of market volatility, we cannot make a clearer judgement between the two economies. This paper has repositioned the stability foreign exchange rates of South Africa, a member of Group of 20 (G20) countries, with that of a member of the G7 countries, that is, the UK. To the government, risk and portfolio managers, the findings emanating from this paper indicated that the South Africa's Rand is also stable like the British Pound, and thus, can be traded on the international currency market without fear of excessive loss/gain.

ModAugNet: A new forecasting framework for stock market index value with an overfitting prevention LSTM module and a prediction LSTM module

Forecasting a financial asset's price is important as one can lower the risk of investment decision- making with accurate forecasts. Recently, the deep neural network is popularly applied in this area of research; however, it is prone to overfitting owing to limited availability of data points for training. We propose a novel data augmentation approach for stock market index forecasting through our ModAugNet framework, which consists of two modules: an overfitting prevention LSTM module and a prediction LSTM module.The performance of the proposed model is evaluated using two different representative stock market data (S&P500 and Korea Composite Stock Price Index 200 (KOSPI200)). The results confirm the excellent forecasting accuracy of the proposed model. ModAugNet-c yields a lower test error than the comparative model (SingleNet) in which an overfitting prevention LSTM module is absent. The test mean squared error (MSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) for S&P500 decreased to 54.1%, 35.5%, and 32.7%, respectively, of the corresponding S&P500 forecasting errors of SingleNet, while the same for KOSPI200 decreased to 48%, 23.9%, and 32.7%, respectively, of the corresponding KOSPI200 forecasting errors of SingleNet. Furthermore, through the analyses of the trained ModAugNet-c, we found that test performance is entirely dependent on the prediction LSTM module.The contribution of this study is its applicability in various instances where it is challenging to artificially augment data, such as medical data analysis and financial time-series modeling.

Inference on the tail process with application to financial time series modeling

To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees et al., (2015) proposed nonparametric estimators of the spectral tail process. The methodology can be extended to the more general setting of a stationary, regularly varying time series. The large-sample distribution of the estimators is derived via empirical process theory for cluster functionals. The finite-sample performance of these estimators is evaluated via Monte Carlo simulations. Moreover, two different bootstrap schemes are employed which yield confidence intervals for the pre-asymptotic spectral tail process: the stationary bootstrap and the multiplier block bootstrap. The estimators are applied to stock price data to study the persistence of positive and negative shocks.

A Bayesian Covariance Graphical and Latent Position Model for Multivariate Financial Time Series

Current understanding holds that financial contagion is driven mainly by system-wide interconnectedness of institutions. A distinction has been made between systematic and idiosyncratic channels of contagion, with shocks transmitted through the latter expected to be substantially more likely to lead to a crisis than through the former. Idiosyncratic connectivity is thought to be driven not simply by obviously shared characteristics among institutions, but more by the latent strategic position of firms in financial markets. We propose a Bayesian hierarchical model for multivariate financial time series that characterizes the interdependence in the idiosyncratic factors of a VAR model via a covariance graphical model whose structure is modeled through a latent position model. We develop an efficient algorithm that samples the network of the idiosyncratic factors and the latent positions underlying the network. We examine the dynamic volatility network and latent positions among 150 publicly listed institutions across the United States and Europe and how they contribute to systemic vulnerabilities and risk transmission.

Multiscale multifractal DCCA and complexity behaviors of return intervals for Potts price model

To investigate the characteristics of extreme events in financial markets and the corresponding return intervals among these events, we use a Potts dynamic system to construct a random financial time series model of the attitudes of market traders. We use multiscale multifractal detrended cross-correlation analysis (MM-DCCA) and Lempel–Ziv complexity (LZC) perform numerical research of the return intervals for two significant China’s stock market indices and for the proposed model. The new MM-DCCA method is based on the Hurst surface and provides more interpretable cross-correlations of the dynamic mechanism between different return interval series. We scale the LZC method with different exponents to illustrate the complexity of return intervals in different scales. Empirical studies indicate that the proposed return intervals from the Potts system and the real stock market indices hold similar statistical properties.