Dynamic Conditional Score Models Research Articles

Score-driven exponential random graphs: A new class of time-varying parameter models for temporal networks.

Motivated by the increasing abundance of data describing real-world networks that exhibit dynamical features, we propose an extension of the exponential random graph models (ERGMs) that accommodates the time variation of its parameters. Inspired by the fast-growing literature on dynamic conditional score models, each parameter evolves according to an updating rule driven by the score of the ERGM distribution. We demonstrate the flexibility of score-driven ERGMs (SD-ERGMs) as data-generating processes and filters and show the advantages of the dynamic version over the static one. We discuss two applications to temporal networks from financial and political systems. First, we consider the prediction of future links in the Italian interbank credit network. Second, we show that the SD-ERGM allows discriminating between static or time-varying parameters when used to model the U.S. Congress co-voting network dynamics.

An autocorrelation incremental fuzzy clustering framework based on dynamic conditional scoring model

This paper focuses on the real-time dynamic clustering analysis of power load data based on the dynamic conditional score (DCS) model, and an autocorrelation increment fuzzy C-means clustering algorithm based on the DCS model is proposed. (1) The paper addresses the problem that current power load clustering methods, when performing time series data mining, tend to focus on capturing the mean structure while ignoring the variance characteristics of the data, making it difficult to effectively capture the structural information of time series data. The DCS model is used as the statistical model basis for clustering analysis, and the time series is clustered based on the estimated conditional moment characteristics of the model, dynamically capturing data features such as the mean, variance, and sequence correlation of time series data, effectively improving the clustering performance. (2) This paper also addresses the issue that current power load clustering methods tend to focus on static datasets of user power loads and cannot effectively handle the data stream clustering problem with time series characteristics in practical applications. The DCS model parameter dataset and the autocorrelation increment fuzzy clustering algorithm are used to conduct a dynamic data flow analysis of user electricity behaviour evolution and pattern continuous updating research for power loads. The clustering results are dynamically updated based on the user's power load data stream using the proposed algorithm, achieving research on a universal clustering model and secure and efficient algorithms in a big data environment. (3) The paper verifies the clustering performance of the proposed method using power load time series data provided by a Chinese power supply company as a case dataset. The clustering evaluation index shows that the proposed algorithm has high clustering accuracy and good clustering performance. Additionally, different power supply recommendations are proposed for different customer electricity types in the obtained clustering results to provide more personalized power services.

Dynamic conditional score model-based weighted incremental fuzzy clustering of consumer power load data

This study proposes a weighted incremental fuzzy C-mean power load clustering algorithm based on the dynamic conditional score model to solve the problems that the predominant power load data mining method only captures the mean characteristics of time series and ignores the heteroscedasticity and sequence correlations. Consequently, this method has unsatisfactory time series clustering and low clustering accuracy. A dynamic conditional score model is constructed to analyze and extract statistical characteristic parameters of a time series to calculate the autocorrelation value of the parameter series. A weighted fuzzy C-mean clustering analysis is performed, and the obtained data weight information is used as input for incremental clustering to improve the clustering accuracy. The DCS model parameter dataset and data weight information are combined, and the clustering analysis of the consumer power load data stream is performed. The power load time series of different companies is given, and the clustering validity indices are defined for the performance analysis to verify the proposed clustering algorithm. The experimental results show that the proposed algorithm achieves satisfactory clustering and improves the performance.

A method for predicting VaR by aggregating generalized distributions driven by the dynamic conditional score

Constructing a more effective value at risk (VaR) prediction model has long been a goal in financial risk management. In this paper, we propose a novel parametric approach and provide a standard paradigm to demonstrate the modeling. We establish a dynamic conditional score (DCS) model based on high-frequency data and a generalized distribution (GD), namely, the GD-DCS model, to improve the forecasts of daily VaR. The model assumes that intraday returns at different moments are independent of each other and obey the same kind of GD, whose dynamic parameters are driven by DCS. By predicting the motion law of the time-varying parameters, the conditional distribution of intraday returns is determined; then, the bootstrap method is used to simulate daily returns. An empirical analysis using data from the Chinese stock market shows that Weibull-Pareto -DCS model incorporating high-frequency data is superior to traditional benchmark models, such as RGARCH, in the prediction of VaR at high risk levels, which proves that this approach contributes to the improvement of risk measurement tools.

Weighted score-driven fuzzy clustering of time series with a financial application

Time series data are commonly clustered based on their distributional characteristics. The moments play a central role among such characteristics because of their relevant informative content. This paper aims to develop a novel approach that faces still open issues in moment-based clustering. First of all, we deal with a very general framework of time-varying moments rather than static quantities. Second, we include in the clustering model high-order moments. Third, we avoid implicit equal weighting of the considered moments by developing a clustering procedure that objectively computes the optimal weight for each moment. As a result, following a fuzzy approach, two weighted clustering models based on both unconditional and conditional moments are proposed. Since the Dynamic Conditional Score model is used to estimate both conditional and unconditional moments, the resulting framework is called weighted score-driven clustering. We apply the proposed method to financial time series as an empirical experiment.

A dynamic conditional score model for the log correlation matrix

This paper proposes a new model for the dynamics of correlation matrices, where the dynamics are driven by the likelihood score with respect to the matrix logarithm of the correlation matrix. In analogy to the exponential GARCH model for volatility, this transformation ensures that the correlation matrices remain positive definite, even in high dimensions. For the conditional distribution of returns, we assume a student-t copula to explain the dependence structure and univariate student-t for the marginals with potentially different degrees of freedom. The separation into volatility and correlation parts allows for a two-step estimation, which facilitates estimation in high dimensions. We derive estimation theory for one-step and two-step estimation. In an application to a set of six asset indices including financial and alternative assets we show that the model performs well in terms of diagnostics, specification tests, and out-of-sample forecasting.

Dynamic conditional eigenvalue GARCH

In this paper we introduce a multivariate generalized autoregressive conditional heteroskedastic (GARCH) class of models with time-varying conditional eigenvalues. The dynamics of the eigenvalues is derived for the cases with underlying Gaussian and Student’s t-distributed innovations based on the general theory of dynamic conditional score models by Creal, Koopman and Lucas (2013) and Harvey (2013). The resulting time-varying eigenvalue GARCH models – labeled ‘λ-GARCH’ models – differ for the two cases of innovations, similar to, and generalizing, univariate linear Gaussian GARCH and Student’s t-based Beta-t-GARCH models. Asymptotic theory is provided for the Gaussian-based quasi-maximum likelihood estimator (QMLE). In addition, and in order to test for the number of (linear combinations of) the time-varying eigenvalues, we consider testing and inference under the hypothesis of reduced rank of the GARCH loading matrices. The conditional Gaussian and Student’s t distributed λ-GARCH models are applied to US return data, and it is found that the eigenvalue structure for the sample considered indeed satisfies the hypothesis of reduced rank. Specifically, it is possible to disentangle time-varying linear combinations of the eigenvalues, or factors, from time-invariant factors which drive the dynamics of the conditional covariance.

Robustness of score-driven location and scale models to extreme observations: An application to the Chinese stock market

Recently, the use of dynamic conditional score (DCS) time series models are suggested in the body of literature on time series econometrics. DCS models are robust to extreme observations because those observations are discounted by the score function that updates each dynamic equation. Examples of the DCS models are the quasi-autoregressive (QAR) model and the Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model, which measure the dynamics of location and scale, respectively, of the dependent variable. Both QAR and Beta-t-EGARCH discount extreme observations according to a smooth form of trimming. Classical dynamic location and scale models (for example, the AR and the GARCH models) are sensitive to extreme observations. Thus, the AR and the GARCH modelsmay provide imprecise estimates of location and scale dynamics. In the application presented in this paper, we use data from the Shanghai Stock Exchange A-Share Index and the Shenzhen Stock Exchange A-Share Index for the period of 5th January 1998 to 29th December 2017. For the corresponding stock index return time series, a relatively high number of extreme values are observed during the sample period. We find that the statistical performance of QAR plus Beta-t-EGARCH is superior to that of AR plus t-GARCH, due to the robustness of QAR plus Beta-t-EGARCH to extreme unexpected returns.

Modelling stock returns volatility with dynamic conditional score models and random shifts

I propose and study a dynamic conditional score model with random shifts, the RS-Beta-t-EGARCH model, for modelling volatility in financial markets. The addition of random shifts can explain the high volatility persistence typically estimated for these financial series. This setting constitutes an alternative approach to long memory models; moreover, the new model identifies volatility clusters. I apply the model to stock returns in South American emerging markets. The estimates for the random shifts fit the main regime disturbance events in the period of study. Monte Carlo simulations show that the new model replicates the time and spectral domain properties of the original series. Finally, out-sample forecast evidence favors the new specification.

Robustness of score-driven location and scale models to extreme observations: An application to the Chinese stock market

Recently, the use of dynamic conditional score (DCS) time series models are suggested in the body of literature on time series econometrics. DCS models are robust to extreme observations because those observations are discounted by the score function that updates each dynamic equation. Examples of the DCS models are the quasi-autoregressive (QAR) model and the Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model, which measure the dynamics of location and scale, respectively, of the dependent variable. Both QAR and Beta-t-EGARCH discount extreme observations according to a smooth form of trimming. Classical dynamic location and scale models (for example, the AR and the GARCH models) are sensitive to extreme observations. Thus, the AR and the GARCH modelsmay provide imprecise estimates of location and scale dynamics. In the application presented in this paper, we use data from the Shanghai Stock Exchange A-Share Index and the Shenzhen Stock Exchange A-Share Index for the period of 5th January 1998 to 29th December 2017. For the corresponding stock index return time series, a relatively high number of extreme values are observed during the sample period. We find that the statistical performance of QAR plus Beta-t-EGARCH is superior to that of AR plus t-GARCH, due to the robustness of QAR plus Beta-t-EGARCH to extreme unexpected returns.

A value‐at‐risk computation based on heavy‐tailed distribution for dynamic conditional score models

AbstractThe purpose of this study is to evaluate the estimating ability of GAS models in the computation of the value‐at‐risk by applying the extreme‐value theory. Our approach is the limiting result of an infinity shift of location. In this work, we use the generalized pareto distribution since it plays a central role in modelling heavy tail phenomena in many applications. A simulation study is performed to assess the estimated value‐at‐risk. Moreover, we examine the performance of the proposed method with daily returns of three stock market indices. The results prove that the presented approach gives good predictions for all indices.

A coupled component DCS-EGARCH model for intraday and overnight volatility

We propose a semi-parametric coupled component exponential GARCH model for intraday and overnight returns that allows the two series to have different dynamical properties. We adopt a dynamic conditional score model with t-distributed innovations that captures the very heavy tails of overnight returns. We propose a several-step estimation procedure that captures the nonparametric slowly moving components by kernel estimation and the dynamic parameters by maximum likelihood. We establish the consistency, asymptotic normality, and semiparametric efficiency of our semiparametric estimation procedures. We extend the modelling to the multivariate case where we allow time varying correlation between stocks. We apply our model to the study of Dow Jones industrial average component stocks and CRSP size-based portfolios over the period 1993–2017. We show that the ratio of overnight to intraday volatility has actually increased in importance for Dow Jones stocks during the last two decades. This ratio has also increased for large stocks in the CRSP database, but decreased for small stocks in CRSP.

Dynamic conditional score models: a review of their applications

ABSTRACTIn this paper, applications of dynamic conditional score (DCS) models are reviewed and those models are discussed in relation to classical time series models from the literature. DCS models are robust to outliers, which improves their statistical performance compared to classical models. Three applications are presented in order to compare the statistical performances of DCS and classical models in three very different contexts: (i) The QAR (quasi-autoregressive) plus Beta-t-EGARCH (exponential autoregressive conditional heteroscedasticity) model is presented, which is a score-driven expected return plus volatility model. This model is used for daily returns on the DAX (Deutscher Aktienindex) equity index for the period of January 1988 to December 2017. (ii) The score-driven local level and seasonality plus Beta-t-EGARCH model is presented, which is used for daily AFN/USD (Afghan Afghani/United States Dollar) currency exchange rates for the period of March 2007 to July 2017. (iii) The Seasonal-t-QVAR (quasi-vector autoregressive) model is presented, which is a score-driven multivariate dynamic model of location. For this model, monthly US inflation rate and US unemployment rate are used for the period of January 1948 to December 2017. For all applications, the statistical performance of each DCS model is superior to that of a corresponding classical alternative.

Score-driven models of stochastic seasonality in location and scale: an application case study of the Indian rupee to USD exchange rate

ABSTRACTWe estimate the stochastic seasonality of the Indian rupee (INR) to United States dollar (USD) exchange rate by using new dynamic conditional score (DCS) specifications. We use the DCS-Skew-Gen- (DCS-skewed generalized t distribution) and DCS-NIG (DCS-normal-inverse Gaussian distribution) models, which are alternatives to the DCS- (DCS-Student’s -distribution) and DCS-EGB2 (DCS-exponential generalized beta distribution of the second kind) models from the literature. DCS models are robust to outliers, and such models effectively disentangle the local level, seasonality and irregular components. For the latter, we apply DCS-EGARCH (DCS-exponential generalized autoregressive conditional heteroscedasticity) scale dynamics, and we use new DCS models with seasonal volatility. We use INR/USD data for the period of 1 January 1982 to 7 July 2017. We find that the DCS-Skew-Gen- and DCS-NIG models are superior to the DCS- and DCS-EGB2 models, respectively. The amplitude of the INR/USD seasonality is relatively high during the last decade of the sample. We explain this by using the currency movements that are related to increased seasonal exports and imports of India. We show the robustness of our results for different exchange rate regimes: (i) pegged exchange rate regime period (until February 1993); (ii) liberalized exchange rate management system period (since March 1993).

Dynamic Conditional Eigenvalue GARCH

In this paper we consider a multivariate generalized autoregressive conditional heteroskedastic (GARCH) class of models where the eigenvalues of the conditional covariance matrix are time-varying. The proposed dynamics of the eigenvalues is based on applying the general theory of dynamic conditional score models as proposed by Creal, Koopman and Lucas (2013) and Harvey (2013). We denote the obtained GARCH model with dynamic conditional eigenvalues (and constant conditional eigenvectors) as the λ-GARCH model. We provide new results on asymptotic theory for the Gaussian QMLE, and for testing of reduced rank of the (G)ARCH loading matrices of the time-varying eigenvalues. The theory is applied to US data, where we find that the eigenvalue structure can be reduced similar to testing for the number in factors in volatility models.

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.

Robustness of score-driven location and scale models to extreme observations: An application to the Chinese stock market

Recently, the use of dynamic conditional score (DCS) time series models are suggested in the body of literature on time series econometrics. DCS models are robust to extreme observations because those observations are discounted by the score function that updates each dynamic equation. Examples of the DCS models are the quasi-autoregressive (QAR) model and the Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model, which measure the dynamics of location and scale, respectively, of the dependent variable. Both QAR and Beta-t-EGARCH discount extreme observations according to a smooth form of trimming. Classical dynamic location and scale models (for example, the AR and the GARCH models) are sensitive to extreme observations. Thus, the AR and the GARCH modelsmay provide imprecise estimates of location and scale dynamics. In the application presented in this paper, we use data from the Shanghai Stock Exchange A-Share Index and the Shenzhen Stock Exchange A-Share Index for the period of 5th January 1998 to 29th December 2017. For the corresponding stock index return time series, a relatively high number of extreme values are observed during the sample period. We find that the statistical performance of QAR plus Beta-t-EGARCH is superior to that of AR plus t-GARCH, due to the robustness of QAR plus Beta-t-EGARCH to extreme unexpected returns.

Score-driven copula models for portfolios of two risky assets

ABSTRACTThe precise measurement of the association between asset returns is important for financial investors and risk managers. In this paper, we focus on a recent class of association models: Dynamic Conditional Score (DCS) copula models. Our contributions are the following: (i) We compare the statistical performance of several DCS copulas for several portfolios. We study the Clayton, rotated Clayton, Frank, Gaussian, Gumbel, rotated Gumbel, Plackett and Student's t copulas. We find that the DCS model with the Student's t copula is the most parsimonious model. (ii) We demonstrate that the copula score function discounts extreme observations. (iii) We jointly estimate the marginal distributions and the copula, by using the Maximum Likelihood method. We use DCS models for mean, volatility and association of asset returns. (iv) We estimate robust DCS copula models, for which the probability of a zero return observation is not necessarily zero. (v) We compare different patterns of association in different regions of the distribution for different DCS copulas, by using density contour plots and Monte Carlo (MC) experiments. (vi) We undertake a portfolio performance study with the estimation and backtesting of MC Value-at-Risk for the DCS model with the Student's t copula.

Equity market neutral hedge funds and the stock market: an application of score-driven copula models

ABSTRACTIn this article, we study the time-varying market neutrality of equity market neutral hedge funds. We use data from the Hedge Fund Research™ Equity Market Neutral Index (HFRX EH), which represents the performance of a portfolio of individual equity market neutral hedge funds. For each day, we measure different levels of association of the Standard and Poor’s 500 (S&P 500) index and the HFRX EH. We use non-linear dynamic conditional score models of location, scale and copula that, to the best of our knowledge, have not yet been applied in the body of literature on hedge funds. We study whether the neutrality of the HFRX EH that is evidenced in the body of literature for the period of April 1993–April 2003 also holds for the following decade, for the period of May 2003–December 2016. We estimate different average levels of association for the pre-, during- and post-periods of the US financial crisis of 2008. We find that the association of the S&P 500 and the HFRX EH, on average, is significantly positive for the pre- and post-periods of the financial crisis, and it is significantly negative for the period during the financial crisis.

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.