Journal of Time Series Analysis最新文献

This article investigates the consequences of using Singular Spectral Analysis (SSA) to construct a time series bootstrap. The bootstrap replications are obtained via a SSA decomposition obtained using rescaled trajectories (RT-SSA), a procedure that is particularly useful in the analysis of time series that exhibit nonlinear, non-stationary and intermittent or transient behaviour. The theoretical validity of the RT-SSA bootstrap when used to approximate the sampling properties of a general class of statistics is established under regularity conditions that encompass a very broad range of data generating processes. A smeared and a boosted version of the RT-SSA bootstrap are also presented. Practical implementation of the bootstrap is considered and the results are illustrated using stationary, non-stationary and irregular time series examples.

How many factors are there? It is a critical question that researchers and practitioners deal with when estimating factor models. We proposed a new eigenvalue ratio criterion for the number of factors in static approximate factor models. It considers a pooled squared correlation matrix which is defined as a weighted combination of the main observed squared correlation matrices. Theoretical results are given to justify the expected good properties of the criterion, and a Monte Carlo study shows its good finite sample performance in different scenarios, depending on the idiosyncratic error structure and factor strength. We conclude comparing different criteria in a forecasting exercise with macroeconomic data.

This article considers estimation of non-smooth possibly overidentified non-parametric estimating equations models with weakly dependent data. The estimators are based on a kernel smoothed version of the generalized empirical likelihood and the generalized method of moments approaches. The article derives the asymptotic normality of both estimators and shows that the proposed local generalized empirical likelihood estimator is more efficient than the local generalized moment estimator unless a two-step procedure is used. The article also proposes novel tests for the correct specification of the considered model that are shown to have power against local alternatives and are consistent against fixed alternatives. Monte Carlo simulations and an empirical application illustrate the finite sample properties and applicability of the proposed estimators and test statistics.

When we observe a stationary time series with observations missing at periodic time points, we can still estimate its marginal distribution well, but the dependence structure of the time series may not be recoverable at all, or the usual estimators may have much larger variance than in the fully observed case. We show how non-parametric estimators can often be improved by adding unbiased estimators. We focus on a simple setting, first-order Markov chains on a finite state space, and an observation pattern in which a fixed number of consecutive observations is followed by an observation gap of fixed length, say workdays and weekends. The new estimators perform astonishingly well in some cases, as illustrated with simulations. The approach extends to continuous state space and to higher-order Markov chains.

This article introduces a discrete-time fractional stochastic volatility model (FSV) based on fractional Gaussian noise. The new model includes the standard stochastic volatility model as a special case and has the same limit as the fractional integrated stochastic volatility (FISV) model, which is the continuous-time fractional Ornstein–Uhlenbeck process. A simulated maximum likelihood method, which maximizes the time-domain log-likelihood function calculated by the importance sampling technique, and a frequency-domain quasi maximum likelihood method (or quasi Whittle) are employed to estimate the model parameters. Simulation studies suggest that, while both estimation methods can accurately estimate the model, the simulated maximum likelihood method outperforms the quasi Whittle method. As an illustration, we fit the FSV and FISV models with the proposed estimation techniques to the S&P 500 composite index over a sample period spanning 45 years.

Many data sets in biology, medicine, and other biostatistical areas deal with matrix-valued time series. The case of a single univariate time series is very well developed in the literature; and single multi-variate series (i.e., vector time series) though less well studied have also been developed. A class of matrix time series models is introduced for dealing with situations where there are multiple sets of multi-variate time series data. Explicit expressions for a matrix autoregressive model along with its cross-autocorrelation functions are derived. Stationarity conditions are also provided. Least squares estimators and maximum likelihood estimators of the model parameters and their asymptotic properties are derived. Results are illustrated through simulation studies and a real data application.

Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its variations have been widely adopted in the study of financial volatilities, while the extension of GARCH-type models to high-dimensional data is always difficult because of over-parameterization and computational complexity. In this article, we propose a multi-variate GARCH-type model that can simplify the parameterization by utilizing the network structure that can be appropriately specified for certain types of high-dimensional data. The asymmetry in the dynamics of volatilities is also considered as our model adopts a threshold structure. To enable our model to handle data with extremely high dimension, we investigate the near-epoch dependence (NED) of our model, and the asymptotic properties of our quasi-maximum-likelihood-estimator (QMLE) are derived from the limit theorems for NED random fields. Simulations are conducted to test our theoretical results. At last we fit our model to log-returns of four groups of stocks and the results indicate that bad news is not necessarily more influential on volatility if the network effects are considered.

A spectral criterion involving the model parameters is given for the existence and uniqueness of a periodically correlated and seasonal non-negative integer-valued autoregressive process. The structure of the mean and covariance functions of the periodically stationary distribution of the model is derived using its implicit state-space representation. Two infinite series representations for the process, the moving average, and the immigrant generation, are established. Based on the latter representation, a novel and parallelizable simulation method is proposed to generate the process.

In the widely used predictive regression model, any possible serial correlation in innovations leads to estimation bias and statistical inference distortions. Hence, it is important to pretest the existence of such serial correlation. Nevertheless, in the presence of embedded endogeneity, which is a common problem in the predictive regression setting, traditional serial correlation tests such as Box–Pierce (BP) and Ljung–Box (LB) tests are found to perform poorly. Motivated by this, we develop a new portmanteau test in this article as a pretest for serial correlation in predictive regression under possible embedded endogeneity. This test is based on the sample splitting idea and the jackknife empirical likelihood method. The asymptotic distribution of the proposed test has been derived, and the Monte Carlo simulations confirm good finite sample performances. As an illustration, we apply our proposed test in pretesting the serial correlation in predictive regression, where financial variables are used to predict the excess return of S&P 500.