Comparison of the finite mixture of ARMA-GARCH,back propagation neural networks and support-vector machines in forecasting financial returns

The use of GARCH type models and computational-intelligence-based techniques for forecasting financial time series has been proved extremely successful in recent times. In this article, we apply the finite mixture of ARMA-GARCH model instead of AR or ARMA models to compare with the standard BP and SVM in forecasting financial time series (daily stock market index returns and exchange rate returns). We do not apply the pure GARCH model as the finite mixture of the ARMA-GARCH model outperforms the pure GARCH model. These models are evaluated on five performance metrics or criteria. Our experiment shows that the SVM model outperforms both the finite mixture of ARMA-GARCH and BP models in deviation performance criteria. In direction performance criteria, the finite mixture of ARMA-GARCH model performs better. The memory property of these forecasting techniques is also examined using the behavior of forecasted values vis-à-vis the original values. Only the SVM model shows long memory property in forecasting financial returns.     

Data cloning estimation of GARCH and COGARCH models

GARCH models include most of the stylized facts of financial time series and they have been largely used to analyse discrete financial time series. In the last years, continuous-time models based on discrete GARCH models have been also proposed to deal with non-equally spaced observations, as COGARCH model based on Lévy processes. In this paper, we propose to use the data cloning methodology in order to obtain estimators of GARCH and COGARCH model parameters. Data cloning methodology uses a Bayesian approach to obtain approximate maximum likelihood estimators avoiding numerically maximization of the pseudo-likelihood function. After a simulation study for both GARCH and COGARCH models using data cloning, we apply this technique to model the behaviour of some NASDAQ time series.     

Estimation and prediction of time-varying GARCH models through a state-space representation: a computational approach

We propose a state-space approach for GARCH models with time-varying parameters able to deal with non-stationarity that is usually observed in a wide variety of time series. The parameters of the non-stationary model are allowed to vary smoothly over time through non-negative deterministic functions. We implement the estimation of the time-varying parameters in the time domain through Kalman filter recursive equations, finding a state-space representation of a class of time-varying GARCH models. We provide prediction intervals for time-varying GARCH models and, additionally, we propose a simple methodology for handling missing values. Finally, the proposed methodology is applied to the Chilean Stock Market (IPSA) and to the American Standard&Poor's 500 index (S&P500).     

基于GARCH族模型的中国旅游酒店板块指数收益率波动分析

运用GARCH族模型分析旅游酒店板块指数日收益率的波动特征,研究表明：旅游酒店板块收益率是一个平稳过程,其波动具有“聚集”现象和“非对称效应”。GARCH（2,1）模型比GARCH（1,1）模型更好地消除了收益率序列的异方差性;TARCH（2,1）模型的拟合效果最好;GARCH—M模型和非对称的CARCH（1,1）模型都不适用于描述收益率的波动特征。     

A General Multivariate Threshold GARCH Model With Dynamic Conditional Correlations

We introduce a new multivariate GARCH model with multivariate thresholds in conditional correlations and develop a two-step estimation procedure that is feasible in large dimensional applications. Optimal threshold functions are estimated endogenously from the data and the model conditional covariance matrix is ensured to be positive definite. We study the empirical performance of our model in two applications using U.S. stock and bond market data. In both applications our model has, in terms of statistical and economic significance, higher forecasting power than several other multivariate GARCH models for conditional correlations.     

Testing for Equal Predictability of Stationary ARMA Processes

In this work we use a measure of predictability of a time series following a stationary ARMA process to develop a test of equal predictability of two or more time series. The test is derived by a set of propositions which links the structure of the AR and MA coefficients to the predictability measure. A particular case of this general approach is constituted by time series having a Wold decomposition with weights having the same sign; in this framework the equal predictability is equivalent to parallelism among ARMA models and the null hypothesis of equal predictability is simply a set of linear restrictions. The ARMA representation of the GARCH models presents non-negative weights, so that this test can be extended to verify the equal predictability of squared time series following GARCH structures.     

Assessing the bias of maximum likelihood estimates of contaminated garch models

It is well known that Gaussian maximum likelihood estimates of time series models are not robust. In this paper we prove this is also the case for the Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. By expressing the Gaussian maximum likelihood estimates as Ψ estimates and by assuming the existence of a contaminated process, we prove they possess zero breakdown point and unbounded influence curves. By simulating GARCH processes under several proportions of contaminations we assess how much biased the maximum likelihood estimates may become and compare these results to a robust alternative. The t-student maximum likelihood estimates of GARCH models are also considered.     

Detecting level shifts in ARMA-GARCH (1,1) Models

The purpose of this article is to present a new method to detect level shifts in the context of conditional heteroscedastic models. First, we define precisely what type of outlier we are referring to, a concept that has been scarcely touched in the field of GARCH (1,1) models, and then we go on to present our methodology based on the nature of the Lagrange multiplier tests. The validity and efficiency of the proposed procedure are demonstrated through different simulation experiments. To conclude, we present a practical application of the method to the time series of returns of US short-term interest rates.     

ASSESSING AND TESTING FOR THRESHOLD NONLINEARITY IN STOCK RETURNS

This paper proposes a test for threshold nonlinearity in a time series with generalized autore‐gressive conditional heteroscedasticity (GARCH) volatility dynamics. This test is used to examine whether financial returns on market indices exhibit asymmetric mean and volatility around a threshold value, using a double‐threshold GARCH model. The test adopts the reversible‐jump Markov chain Monte Carlo idea of Green, proposed in 1995, to calculate the posterior probabilities for a conventional GARCH model and a double‐threshold GARCH model. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity with asymmetric behaviour of the mean and volatility. Simulation experiments demonstrate that the test works very well in distinguishing between the conventional GARCH and the double‐threshold GARCH models. In an application to eight international financial market indices, including the G‐7 countries, clear evidence supporting the hypothesis of threshold nonlinearity is discovered, simultaneously indicating an uneven mean‐reverting pattern and volatility asymmetry around a threshold return value.     

On change point test for ARMA–GARCH models: Bootstrap approach

The problem of testing for a parameter change has been a core issue in time series analysis. It is well known that the estimates-based CUSUM test often suffers from severe size distortions in general GARCH type models. The residual-based CUSUM test has been used as an alternative, which, however, has a defect not to detect the ARMA parameter changes in ARMA–GARCH models. As a remedy, one can employ the score vector-based CUSUM test in ARMA–GARCH models as in Oh and Lee (0000). However, it shows some size distortions for relatively small samples. Hence, we consider the bootstrap counterpart for obtaining a more stable test. Focus is made on the verification of the weak consistency of the proposed test. An empirical study is illustrated for its evaluation.     

A tobit model with garch errors

In the context of time series regression, we extend the standard Tobit model to allow for the possibility of conditional heteroskedastic error processes of the GARCH type. We discuss the likelihood function of the Tobit model in the presence of conditionally heteroskedastic errors. Expressing the exact likelihood function turns out to be infeasible, and we propose an approximation by treating the model as being conditionally Gaussian. The performance of the estimator is investigated by means of Monte Carlo simulations. We find that, when the error terms follow a GARCH process, the proposed estimator considerably outperforms the standard Tobit quasi maximum likelihood estimator. The efficiency loss due to the approximation of the likelihood is finally evaluated.     

On double hysteretic heteroskedastic model

ABSTRACT

This paper proposes a hysteretic autoregressive model with GARCH specification and a skew Student's t-error distribution for financial time series. With an integrated hysteresis zone, this model allows both the conditional mean and conditional volatility switching in a regime to be delayed when the hysteresis variable lies in a hysteresis zone. We perform Bayesian estimation via an adaptive Markov Chain Monte Carlo sampling scheme. The proposed Bayesian method allows simultaneous inferences for all unknown parameters, including threshold values and a delay parameter. To implement model selection, we propose a numerical approximation of the marginal likelihoods to posterior odds. The proposed methodology is illustrated using simulation studies and two major Asia stock basis series. We conduct a model comparison for variant hysteresis and threshold GARCH models based on the posterior odds ratios, finding strong evidence of the hysteretic effect and some asymmetric heavy-tailness. Versus multi-regime threshold GARCH models, this new collection of models is more suitable to describe real data sets. Finally, we employ Bayesian forecasting methods in a Value-at-Risk study of the return series.     

Surveillance of the covariance matrix of multivariate nonlinear time series

In this paper, sequential procedures for the surveillance of the covariance matrices of multivariate nonlinear time series are introduced. Two different types of control charts are proposed. The first type is based on the exponential smoothing of each component of a local measure for the covariances. The control statistic is equal to the Mahalanobis distance of this quantity with its in-control mean. In our second approach, the Mahalanobis distance is first determined and after that it is exponentially smoothed. We discuss three examples of local measures.

Several properties of the proposed schemes are discussed assuming the target process to be generated by a multivariate GARCH(1, 1) model. The generalization to the family of spherical distributions allows the modelling of frequently observed fat tails in financial data. Some results of an extensive Monte Carlo simulation study are provided in order to judge the performance of the presented control schemes. As a performance measure we use the average run length. An empirical example illustrates the importance of the fast detection of the changes in the covariance structure of the returns of financial assets.     

An alternative method for forecasting price volatility by combining models

In this article, we study the volatility in the monthly price series of edible oils in domestic and international markets using the two popular family of nonlinear time-series models, viz, Generalized autoregressive conditional heteroscedastic (GARCH) models and Stochastic volatility (SV) models. To improve the forecasts of the volatility process, we also propose a new method of combining the volatility of these two competing models using the powerful technique of Kalman filter. The individual models as well as the combined models are assessed on their ability to predict the correct directional change (CDC) in future values as well as other goodness-of-fit statistics. Further, forecasting performance are also evaluated by computing various measures to validate the proposed methodology.     

Parameter changes in GARCH model

A new method for detecting the parameter changes in generalized autoregressive heteroskedasticity GARCH (1,1) model is proposed. In the proposed method, time series observations are divided into several segments and a GARCH (1,1) model is fitted to each segment. The goodness-of-fit of the global model composed of these local GARCH (1,1) models is evaluated using the corresponding information criterion (IC). The division that minimizes IC defines the best model. Furthermore, since the simultaneous estimation of all possible models requires huge computational time, a new time-saving algorithm is proposed. Simulation results and empirical results both indicate that the proposed method is useful in analysing financial data.     

A Class of Markov Chain Models for Average Run Length Computations for Autocorrelated Processes

The average run length (ARL) of conventional control charts is typically computed assuming temporal independence. However, this assumption is frequently violated in practical applications. Alternative ARL computations have often been conducted via time consuming and yet not necessarily very accurate simulations. In this article, we develop a class of Markov chain models for evaluating the run length performance of traditional control charts for autocorrelated processes. We show extensions from the univariate AR(1) model to the general multivariate VARMA(p, q) time series. The results of the proposed method are highly comparable to those of simulations and with significantly less computational overhead.     

Semiparametric Time Series Models with Log‐concave Innovations: Maximum Likelihood Estimation and its Consistency

We study semiparametric time series models with innovations following a log‐concave distribution. We propose a general maximum likelihood framework that allows us to estimate simultaneously the parameters of the model and the density of the innovations. This framework can be easily adapted to many well‐known models, including autoregressive moving average (ARMA), generalized autoregressive conditionally heteroscedastic (GARCH), and ARMA‐GARCH models. Furthermore, we show that the estimator under our new framework is consistent in both ARMA and ARMA‐GARCH settings. We demonstrate its finite sample performance via a thorough simulation study and apply it to model the daily log‐return of the FTSE 100 index.     

Inference for the Hyperparameters of Structural Models Under Classical and Bayesian Perspectives: A Comparison Study

Structural models—or dynamic linear models as they are known in the Bayesian literature—have been widely used to model and predict time series using a decomposition in non observable components. Due to the direct interpretation of the parameters, structural models are a powerful and simple methodology to analyze time series in several areas, such as economy, climatology, environmental sciences, among others. The parameters of such models can be estimated either using maximum likelihood or Bayesian procedures, generally implemented using conjugate priors, and there are plenty of works in the literature employing both methods. But are there situations where one of these approaches should be preferred? In this work, instead of conjugate priors for the hyperparameters, the Jeffreys prior is used in the Bayesian approach, along with the uniform prior, and the results are compared to the maximum likelihood method, in an extensive Monte Carlo study. Interval estimation is also evaluated and, to this purpose, bootstrap confidence intervals are introduced in the context of structural models and their performance is compared to the asymptotic and credibility intervals. A real time series of a Brazilian electric company is used as illustration.     

Stepwise local influence in generalized autoregressive conditional heteroskedasticity models

Detection of outliers or influential observations is an important work in statistical modeling, especially for the correlated time series data. In this paper we propose a new procedure to detect patch of influential observations in the generalized autoregressive conditional heteroskedasticity (GARCH) model. Firstly we compare the performance of innovative perturbation scheme, additive perturbation scheme and data perturbation scheme in local influence analysis. We find that the innovative perturbation scheme give better result than other two schemes although this perturbation scheme may suffer from masking effects. Then we use the stepwise local influence method under innovative perturbation scheme to detect patch of influential observations and uncover the masking effects. The simulated studies show that the new technique can successfully detect a patch of influential observations or outliers under innovative perturbation scheme. The analysis based on simulation studies and two real data sets show that the stepwise local influence method under innovative perturbation scheme is efficient for detecting multiple influential observations and dealing with masking effects in the GARCH model.     

BL-GARCH models and asymmetries in volatility

In this paper the class of Bilinear GARCH (BL-GARCH) models is proposed. BL-GARCH models allow to capture asymmetries in the conditional variance of financial and economic time series by means of interactions between past shocks and volatilities. The availability of likelihood based inference is an attractive feature of BL-GARCH models. Under the assumption of conditional normality, the log-likelihood function can be maximized by means of an EM type algorithm. The main reason for using the EM algorithm is that it allows to obtain parameter estimates which naturally guarantee the positive definiteness of the conditional variance with no need for additional parameter constraints. We also derive a robust LM test statistic which can be used for model identification. Finally, the effectiveness of BL-GARCH models in capturing asymmetric volatility patterns in financial time series is assessed by means of an application to a time series of daily returns on the NASDAQ Composite stock market index.