Bootstrap prediction intervals for autoregressive conditional duration models

In the recent past, the autoregressive conditional duration (ACD) models have gained popularity in modelling the durations between successive events. The aim of this paper is to propose a simple and distribution free re-sampling procedure for developing the forecast intervals of linear ACD Models. We use the conditional least squares method to estimate the parameters of the ACD Model instead of the conditional Maximum Likelihood Estimation or Quasi-Maximum Likelihood Estimation and show that they are consistent for large samples. The properties of the proposed procedure are illustrated by a simulation study and an application to two real data sets.     

Mixture inverse Gaussian for unobserved heterogeneity in the autoregressive conditional duration model

In this paper, we assume that the duration of a process has two different intrinsic components or phases which are independent. The first is the time it takes for a trade to be initiated in the market (for example, the time during which agents obtain knowledge about the market in which they are operating and accumulate information, which is coherent with Brownian motion) and the second is the subsequent time required for the trade to develop into a complete duration. Of course, if the first time is zero then the trade is initiated immediately and no initial knowledge is required. If we assume a specific compound Bernoulli distribution for the first time and an inverse Gaussian distribution for the second, the resulting convolution model has a mixture of an inverse Gaussian distribution with its reciprocal, which allows us to specify and test the unobserved heterogeneity in the autoregressive conditional duration (ACD) model.

Our proposals make it possible not only to capture various density shapes of the durations but also easily to accommodate the behaviour of the tail of the distribution and the non monotonic hazard function. The proposed model is easy to fit and characterizes the behaviour of the conditional durations reasonably well in terms of statistical criteria based on point and density forecasts.     

Tree-structured generalized autoregressive conditional heteroscedastic models

We propose a new generalized autoregressive conditional heteroscedastic (GARCH) model with tree-structured multiple thresholds for the estimation of volatility in financial time series. The approach relies on the idea of a binary tree where every terminal node parameterizes a (local) GARCH model for a partition cell of the predictor space. The fitting of such trees is constructed within the likelihood framework for non-Gaussian observations: it is very different from the well-known regression tree procedure which is based on residual sums of squares. Our strategy includes the classical GARCH model as a special case and allows us to increase model complexity in a systematic and flexible way. We derive a consistency result and conclude from simulation and real data analysis that the new method has better predictive potential than other approaches.     

Efficient estimation for the conditional autoregressive model

Recently, spatial regression models have been attracting a great deal of attention in areas ranging from effect of traffic congestion on accident rates to the analysis of trends in gastric cancer mortality. In this paper, we propose efficient estimators for the regression coefficients of the spatial conditional autoregressive model, when uncertain auxiliary information is available about these coefficients. We provide efficiency comparisons of the proposed estimators based on asymptotic risk analysis and Monte Carlo simulations. We apply the proposed methods to real data on Boston housing prices and illustrate how a bootstrapping approach can be employed to compute prediction errors of the estimators.     

A nonparametric test of conditional autoregressive heteroscedasticity for threshold autoregressive models

Threshold autoregressive models are widely used in time‐series applications. When building or using such a model, it is important to know whether conditional heteroscedasticity exists. The authors propose a nonparametric test of this hypothesis. They develop the large‐sample theory of a test of nonlinear conditional heteroscedasticity adapted to nonlinear autoregressive models and study its finite‐sample properties through simulations. They also provide percentage points for carrying out this test, which is found to have very good power overall.     

On diagnostic checking of the autoregressive conditional intensity model

The autoregressive conditional intensity model proposed by Russell (1998) is a promising option for fitting multivariate high frequency irregularly spaced data. The authors acknowledge the validity of this model by showing the independence of its generalized residuals, a crucial assumption of the model formulation not readily recognized by researchers. The authors derive the large‐sample distribution of the autocorrelations of the generalized residual series and use it to construct a goodness‐of‐fit test for the model. Empirical results compare the performance of their test with other off‐the‐shelf tests such as the Ljung–Box test. They illustrate the use of their test with transaction records of the HSBC stock.     

时变三因子模型风险系数的动态研究

由Fama和French提出的三因子模型能够较好地解释股票的收益率风险溢价。文章以状态空间模型为框架,将风险因子系数作为状态变量,市场风险溢价作为观测变量,构建时变三因子模型来应对股票市场价格的时变特征。研究结果显示,利用卡尔曼滤波来估计时变风险因子系数,增强了估计结果的准确性与连贯性;风险因子系数变化规律与中国A股市场政策和环境影响相吻合,消除非理性噪声后的时变三因子模型更具有解释力度。     

Volatility forecasting of financial time series using wavelet based exponential generalized autoregressive conditional heteroscedasticity model

Abstract

An improved forecasting model by merging two different computational models in predicting future volatility was proposed. The model integrates wavelet and EGARCH model where the pre-processing activity based on wavelet transform is performed with de-noising technique to eliminate noise in observed signal. The denoised signal is then feed into EGARCH model to forecast the volatility. The predictive capability of the proposed model is compared with the existing EGARCH model. The results show that the hybrid model has increased the accuracy of forecasting future volatility.     

Departure from independence and stationarity in a handball match

This paper analyses direct and indirect forms of dependence in the probability of scoring in a handball match, taking into account the mutual influence of both playing teams. Non-identical distribution (i.d.) and non-stationarity, which are commonly observed in sport games, are studied through the specification of time-varying parameters.

The model accounts for the binary character of the dependent variable, and for unobserved heterogeneity. The parameter dynamics is specified by a first-order auto-regressive process.

Data from the Handball World Championships 2001–2005 show that the dynamics of handball violate both independence and i.d., in some cases having a non-stationary behaviour.     

On a mixture autoregressive model

We generalize the Gaussian mixture transition distribution (GMTD) model introduced by Le and co-workers to the mixture autoregressive (MAR) model for the modelling of non-linear time series. The models consist of a mixture of K stationary or non-stationary AR components. The advantages of the MAR model over the GMTD model include a more full range of shape changing predictive distributions and the ability to handle cycles and conditional heteroscedasticity in the time series. The stationarity conditions and autocorrelation function are derived. The estimation is easily done via a simple EM algorithm and the model selection problem is addressed. The shape changing feature of the conditional distributions makes these models capable of modelling time series with multimodal conditional distributions and with heteroscedasticity. The models are applied to two real data sets and compared with other competing models. The MAR models appear to capture features of the data better than other competing models do.     

Bootstrap of the linear correlation model

In the linear correlation model one observes an i.i.d. sequence (Xi, F$), i^l, of {p + l)-variate random vectors satisfying Yi=Xif}+ei. In this paper, we show the validity of the bootstrap for the LSE of p under minimal moment assumptions, answering a question posed by D. FREEDMAK     

Threshold negative binomial autoregressive model

This article studies an observation-driven model for time series of counts, which allows for overdispersion and negative serial dependence in the observations. The observations are supposed to follow a negative binomial distribution conditioned on past information with the form of thresh old models, which generates a two-regime structure on the basis of the magnitude of the lagged observations. We use the weak dependence approach to establish the stationarity and ergodicity, and the inference for regression parameters are obtained by the quasi-likelihood. Moreover, asymptotic properties of both quasi-maximum likelihood estimators and the threshold estimator are established, respectively. Simulation studies are considered and so are two applications, one of which is the trading volume of a stock and another is the number of major earthquakes.     

On a mixture vector autoregressive model

The authors show how to extend univariate mixture autoregressive models to a multivariate time series context. Similar to the univariate case, the multivariate model consists of a mixture of stationary or nonstationary autoregressive components. The authors give the first and second order stationarity conditions for a multivariate case up to order 2. They also derive the second order stationarity condition for the univariate mixture model up to arbitrary order. They describe an EM algorithm for estimation, as well as a diagnostic checking procedure. They study the performance of their method via simulations and include a real application.     

Bootstrap procedures in a spatial-temporal model

Two bootstrap procedures are introduced into the hybrid of the backfitting algorithm and the Cochrane–Orcutt procedure in the estimation of a spatial-temporal model. The use of time blocks of consecutive observations in resampling steps proved to be optimal in terms of stability and efficiency of estimates. Between iterations, there were minimal changes in the empirical distributions of the parameter estimates associated with the covariate and temporal effects indicating convergence of the algorithm. Crop yield data are used to illustrate the proposed methods.

The simulation study indicated that prediction error from the fitted model (estimated from either Method 1 or Method 2) is very low. Also, the prediction error is relatively robust to the number of spatial units and the number of time points.     

Bayesian estimation for first-order autoregressive model with explanatory variables

In this article, we develop a Bayesian analysis in autoregressive model with explanatory variables. When σ² is known, we consider a normal prior and give the Bayesian estimator for the regression coefficients of the model. For the case σ² is unknown, another Bayesian estimator is given for all unknown parameters under a conjugate prior. Bayesian model selection problem is also being considered under the double-exponential priors. By the convergence of ρ-mixing sequence, the consistency and asymptotic normality of the Bayesian estimators of the regression coefficients are proved. Simulation results indicate that our Bayesian estimators are not strongly dependent on the priors, and are robust.     

A new algorithm for maximum likelihood estimation in normal scale-mixture generalized autoregressive conditional heteroskedastic models

In this paper, we propose a new generalized autoregressive conditional heteroskedastic (GARCH) model using infinite normal scale-mixtures which can suitably avoid order selection problems in the application of finite normal scale-mixtures. We discuss its theoretical properties and develop a two-stage algorithm for the maximum likelihood estimator to estimate the mixing distribution non-parametric maximum likelihood estimator (NPMLE) as well as GARCH parameters (two-stage MLE). For the estimation of a mixing distribution, we employ a fast computational algorithm proposed by Wang [On fast computation of the non-parametric maximum likelihood estimate of a mixing distribution. J R Stat Soc Ser B. 2007;69:185–198] under the gradient characterization of the non-parametric mixture likelihood. The GARCH parameters are then estimated either using the expectation-mazimization algorithm or general optimization scheme. In addition, we propose a new forecasting algorithm of value-at-risk (VaR) using the two-stage MLE and the NPMLE. Through a simulation study and real data analysis, we compare the performance of the two-stage MLE with the existing ones including quasi-maximum likelihood estimator based on the standard normal density and the finite normal mixture quasi maximum estimated-likelihood estimator (cf. Lee S, Lee T. Inference for Box–Cox transformed threshold GARCH models with nuisance parameters. Scand J Stat. 2012;39:568–589) in terms of the relative efficiency and accuracy of VaR forecasting.     

Conditional heteroscedasticity test for Poisson autoregressive model

In this article, the problem of interest is testing the conditional heteroscedasticity of Poisson autoregressive model. We construct a non parametric test statistic based on empirical likelihood method. The asymptotic distribution of the proposed statistic is derived and its finite-sample property is examined through Monte Carlo simulations. The simulation results show that the proposed method is good for practical use.