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.     

Simultaneous bootstrap for all three parameters in random coefficient autoregressive models

In this paper we consider autoregressive processes with random coefficients and develop bootstrap approaches that asymptotically work for the distribution of estimated autoregressive parameter as well as for the distribution of estimated variances of the innovation noise and the disturbance noise. We discuss how to obtain approximative residuals of the process and how to separate between the innovation and the disturbance noise in order to be able to extend the classical residual bootstrap for autoregressive processes to the situation considered in this paper. Thereafter, we propose a wild bootstrap procedure as a variation of the residual bootstrap that uses estimated densities of the innovation and the disturbance noise to generate bootstrap replicates of the data generating process. The consistency of the bootstrap approaches is established and their performance is illustrated by a simulation study.     

Bootstrap prediction regions for multivariate autoregressive processes

Two new methods for improving prediction regions in the context of vector autoregressive (VAR) models are proposed. These methods, which are based on the bootstrap technique, take into account the uncertainty associated with the estimation of the model order and parameters. In particular, by exploiting an independence property of the prediction error, we will introduce a bootstrap procedure that allows for better estimates of the forecasting distribution, in the sense that the variability of its quantile estimators is substantially reduced, without requiring additional bootstrap replications. The proposed methods have a good performance even if the disturbances distribution is not Gaussian. An application to a real data set is presented.     

A semiparametric approach for modelling multivariate nonlinear time series

In this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada     

Prediction intervals for time series models with trend via sieve bootstrap

This paper discusses method for constructing the prediction intervals for time series model with trend using the sieve bootstrap procedure. Gasser–Müller type of kernel estimator is used for trend estimation and prediction. The boundary modification of the kernel is applied to control the edge effect and to construct the predictor of a trend.     

Data tilting for time series

Summary. We develop a general methodology for tilting time series data. Attention is focused on a large class of regression problems, where errors are expressed through autoregressive processes. The class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression, robust statistical inference and estimation subject to constraints. The method can be viewed as 'empirical likelihood with nuisance parameters'.     

On testing for multivariate ARCH effects in vector time series models

Using a spectral approach, the authors propose tests to detect multivariate ARCH effects in the residuals from a multivariate regression model. The tests are based on a comparison, via a quadratic norm, between the uniform density and a kernel‐based spectral density estimator of the squared residuals and cross products of residuals. The proposed tests are consistent under an arbitrary fixed alternative. The authors present a new application of the test due to Hosking (1980) which is seen to be a special case of their approach involving the truncated uniform kernel. However, they typically obtain more powerful procedures when using a different weighting. The authors consider especially the procedure of Robinson (1991) for choosing the smoothing parameter of the spectral density estimator. They also introduce a generalized version of the test for ARCH effects due to Ling & Li (1997). They investigate the finite‐sample performance of their tests and compare them to existing tests including those of Ling & Li (1997) and the residual‐based diagnostics of Tse (2002).Finally, they present a financial application.     

Predictive inference for linear and multivariate linear models with ma(1) error processes

The prediction distributions of future responses from the linear and multivariate linear models with errors having a first order moving average (MA(1)) process have been derived. First, we obtained the marginal likelihood function for the moving average parameter 6 and from this likelihood function we estimate the maximum likelihood estimates (MLE) of θ. Using the estimated value θ, we have derived the prediction distributions as well as prediction regions for the future responses. An example has been included.     

Multivariate time series prediction using a hybridization of VARMA models and Bayesian networks

In this paper, a new hybrid model of vector autoregressive moving average (VARMA) models and Bayesian networks is proposed to improve the forecasting performance of multivariate time series. In the proposed model, the VARMA model, which is a popular linear model in time series forecasting, is specified to capture the linear characteristics. Then the errors of the VARMA model are clustered into some trends by K-means algorithm with Krzanowski–Lai cluster validity index determining the number of trends, and a Bayesian network is built to learn the relationship between the data and the trend of its corresponding VARMA error. Finally, the estimated values of the VARMA model are compensated by the probabilities of their corresponding VARMA errors belonging to each trend, which are obtained from the Bayesian network. Compared with VARMA models, the experimental results with a simulation study and two multivariate real-world data sets indicate that the proposed model can effectively improve the prediction performance.     

Checks of model adequacy for univariate time series models and their application to econometric relationships

Tests derived from time series analysis play an important role in many empirical studies. These tests are frequently applied to the residuals obtained by fitting an econometric model using some standard estimator. We focus attention here on tests developed for univariate time series models. Various approaches to testing the adequacy of such models are discussed and compared. The validity and sefulness of applying these tests to econometric residuals are then examined and some Monte Carlo evidence is reported.     

Robust multivariate diagnostics for PLSR and application on high dimensional spectrally overlapped drug systems

ABSTRACT

Statistical methods are effectively used in the evaluation of pharmaceutical formulations instead of laborious liquid chromatography. However, signal overlapping, nonlinearity, multicollinearity and presence of outliers deteriorate the performance of statistical methods. The Partial Least Squares Regression (PLSR) is a very popular method in the quantification of high dimensional spectrally overlapped drug formulations. The SIMPLS is the mostly used PLSR algorithm, but it is highly sensitive to outliers that also effect the diagnostics. In this paper, we propose new robust multivariate diagnostics to identify outliers, influential observations and points causing non-normality for a PLSR model. We study performances of the proposed diagnostics on two everyday use highly overlapping drug systems: Paracetamol–Caffeine and Doxylamine Succinate–Pyridoxine Hydrochloride.     

Combining Bayesian method and Kalman smoother for detection additive outlier patches in autoregressive time series

ABSTRACT

This article proposes a development of detecting patches of additive outliers in autoregressive time series models. The procedure improves the existing detection methods via Gibbs sampling. We combine the Bayesian method and the Kalman smoother to present some candidate models of outlier patches and the best model with the minimum Bayesian information criterion (BIC) is selected among them. We propose that this combined Bayesian and Kalman method (CBK) can reduce the masking and swamping effects about detecting patches of additive outliers. The correctness of the method is illustrated by simulated data and then by analyzing a real set of observations.     

A multivariate time series model for the analysis and prediction of carbon monoxide atmospheric concentrations

We use a Bayesian multivariate time series model for the analysis of the dynamics of carbon monoxide atmospheric concentrations. The data are observed at four sites. It is assumed that the logarithm of the observed process can be represented as the sum of unobservable components: a trend, a daily periodicity, a stationary autoregressive signal and an erratic term. Bayesian analysis is performed via Gibbs sampling. In particular, we consider the problem of joint temporal prediction when data are observed at a few sites and it is not possible to fit a complex space–time model. A retrospective analysis of the trend component is also given, which is important in that it explains the evolution of the variability in the observed process.     

Large sample estimation and prediction for explosive growth curve models

Asymptotic distributions of maximum likelihood estimators for the parameters in explosive growth curve models are derived. Limit distributions of prediction errors when the parameters are estimated are also obtained. The growth curve models are viewed as multivariate time-series models, and the usual time-series methods are used for prediction. Estimation constrained by a hypothesis of homogeneity of growth rates is also considered.     

Robust extrapolation designs and weights for biased regression models with heteroscedastic errors

We consider the construction of designs for the extrapolation of regression responses, allowing both for possible heteroscedasticity in the errors and for imprecision in the specification of the response function. We find minimax designs and correspondingly optimal estimation weights in the context of the following problems: (1) for ordinary least squares estimation, determine a design to minimize the maximum value of the integrated mean squared prediction error (IMSPE), with the maximum being evaluated over both types of departure; (2) for weighted least squares estimation, determine both weights and a design to minimize the maximum IMSPE; (3) choose weights and design points to minimize the maximum IMSPE, subject to a side condition of unbiasedness. Solutions to (1) and (2) are given for multiple linear regression with no interactions, a spherical design space and an annular extrapolation space. For (3) the solution is given in complete generality; as one example we consider polynomial regression. Applications to a dose-response problem for bioassays are discussed. Numerical comparisons, including a simulation study, indicate that, as well as being easily implemented, the designs and weights for (3) perform as well as those for (1) and (2) and outperform some common competitors for moderate but undetectable amounts of model bias.     

Multivariate autoregressive extreme value process and its application for modeling the time series properties of the extreme daily asset prices

Abstract

In this article we suggest a new multivariate autoregressive process for modeling time-dependent extreme value distributed observations. The idea behind the approach is to transform the original observations to latent variables that are univariate normally distributed. Then the vector autoregressive DCC model is fitted to the multivariate latent process. The distributional properties of the suggested model are extensively studied. The process parameters are estimated by applying a two-stage estimation procedure. We derive a prediction interval for future values of the suggested process. The results are applied in an empirically study by modeling the behavior of extreme daily stock prices.     

Prediction of transplant-free survival in idiopathic pulmonary fibrosis patients using joint models for event times and mixed multivariate longitudinal data

We implement a joint model for mixed multivariate longitudinal measurements, applied to the prediction of time until lung transplant or death in idiopathic pulmonary fibrosis. Specifically, we formulate a unified Bayesian joint model for the mixed longitudinal responses and time-to-event outcomes. For the longitudinal model of continuous and binary responses, we investigate multivariate generalized linear mixed models using shared random effects. Longitudinal and time-to-event data are assumed to be independent conditional on available covariates and shared parameters. A Markov chain Monte Carlo algorithm, implemented in OpenBUGS, is used for parameter estimation. To illustrate practical considerations in choosing a final model, we fit 37 different candidate models using all possible combinations of random effects and employ a deviance information criterion to select a best-fitting model. We demonstrate the prediction of future event probabilities within a fixed time interval for patients utilizing baseline data, post-baseline longitudinal responses, and the time-to-event outcome. The performance of our joint model is also evaluated in simulation studies.