Journal of Time Series Analysis最新文献

We develop a statistical inference procedure for the ubiquitous calendar effects in microstructure noise using high frequency data. This is, to the best of our knowledge, the first inference theory ever built for noise calendar effect under the general semi-martingale-plus-noise setup for prices contaminated with non-stationary, endogenous, and serially dependent microstructure noise. We devise a noise-calendar-effect estimator by an appropriately scaled average of high-frequency returns that precede a time of day across a large number of trading days. Feasible central limit theorem for the estimator is established under a joint infill and long-span asymptotics. Monte Carlo simulations corroborate our theoretical findings. An empirical study on the high-frequency data of the e-mini S&P 500 futures and a Chinese stock demonstrates that the noise calendar effect has undergone significant changes over time for the latter, yet remains stable for the former.

We study the estimation problem of the spectral density function for harmonizable non-stationary processes. More precisely, we consider spectrally correlated processes whose spectral measure has the support contained in the union of unknown lines with possibly non-unit slopes. We propose the frequency-smoothed periodogram along the estimated support line as an estimator of the spectral density function. We show the mean-square consistency of the proposed estimator. Additionally, we discuss the estimation of the support line in a specific model with its applications in locating a moving source. Finally, we present simulations confirming the proven results.

Time series containing non-negligible portion of possibly dependent zeros, whereas the remaining observations are positive, are considered. They are regarded as GARCH processes consisting of non-negative values. Our first aim lies in estimation of the omnibus model parameters taking into account the semi-continuous distribution. The hurdle distribution together with dependent zeros cause that the classical GARCH estimation techniques fail. Two different quasi-likelihood approaches are employed. Both estimators are proved to be strongly consistent and asymptotically normal. The second goal consists in the proposed predictions with bootstrap add-ons. The considered class of models can be reformulated as multiplicative error models. The empirical properties are illustrated in a simulation study, which demonstrates computational efficiency of the employed methods. The developed techniques are presented through an actuarial problem concerning insurance claims.

We study statistical inference procedures in coarsened time series through the generalized method of moments. A new model for the coarsened time series via multiple potential outcomes is proposed. It can be naturally extended for inferring multi-variate coarsened time series. We show that this framework generates a general class of estimators. It neatly generalizes the classical Horvitz–Thompson estimator for handling coarsened time series data. Asymptotic properties, including consistency and limiting distribution, of the proposed estimators are investigated. Estimators of the optimal weight matrix and the long-run covariance matrix are also derived. In particular, confidence intervals of the mean function of the potential outcome as a function of coarsening index can be constructed. A real-data application on air quality in the USA is investigated.

The nonlinear autoregressive (NLAR) model plays an important role in modeling and predicting time series. One-step ahead prediction is straightforward using the NLAR model, but the multi-step ahead prediction is cumbersome. For instance, iterating the one-step ahead predictor is a convenient strategy for linear autoregressive (LAR) models, but it is suboptimal under NLAR. In this article, we first propose a simulation and/or bootstrap algorithm to construct optimal point predictors under an $��{�L�}_{�1�}�$ or $��{�L�}_{�2�}�$ loss criterion. In addition, we construct bootstrap prediction intervals in the multi-step ahead prediction problem; in particular, we develop an asymptotically valid quantile prediction interval as well as a pertinent prediction interval for future values. To correct the undercoverage of prediction intervals with finite samples, we further employ predictive – as opposed to fitted – residuals in the bootstrap process. Simulation and empirical studies are also given to substantiate the finite sample performance of our methods.

Spatio-temporal data are often analysed by means of spatial dynamic panel data (SDPD) models. In the last decade, several versions of these models have been proposed, generally based on specific assumptions and estimator properties. We focus on an SDPD model with heterogeneous coefficients both in the spatial and exogeneous regression components. We propose a strategy to identify the specific structure of the SDPD model through a multiple testing procedure that allows to choose between a general version of the model and a nested version derived from the general one by imposing restrictions on the parameters. Our proposal can be used to test the homogeneity of the model parameters as well as the absence of specific components, such as spatial effects, dynamic effects or exogenous regressors. It is also possible to use the proposed testing procedure for the identification of relevant locations. The theoretical results highlight the consistency of the testing procedure in the high-dimensional setup, when the number of spatial units goes to infinity and exceeds the number of time-observations per spatial unit. Further, we also conduct a Monte Carlo simulation study, which gives empirical evidence of the good performance of the testing procedure in finite samples.

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $��ℝ�$. An order-1 autoregressive model in this context is to be understood as a Markov chain, where one specifies a certain structure (regression) for the one-step conditional Fréchet mean with respect to a natural probability metric. We construct and explore different models based on iterated random function systems of optimal transport maps. While the properties and interpretation of these models depend on how they relate to the iterated transport system, they can all be analyzed theoretically in a unified way. We present such a theoretical analysis, including convergence rates, and illustrate our methodology using real and simulated data. Our approach generalizes or extends certain existing models of transportation-based regression and autoregression, and in doing so also provides some additional insights on existing models.

Ridge regression is a popular method for dense least squares regularization. In this article, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed, and a comparison is made with Bayesian ridge-type estimators. The asymptotic distribution and the properties of cross-validation techniques are analyzed. Finally, the estimation of impulse response functions is evaluated with Monte Carlo simulations and ridge regression is compared with a number of similar and competing methods.

We show root-T consistency of the smoothed AIC and smoothed BIC model averaging estimators (sAIC, sBIC) of impulse response coefficients in stationary vector autoregressive models of finite lag order. We also show that there is not one unique way to define the sAIC and sBIC estimators, but that instead there is a whole class of each of these defined by a weight scaling factor that allows the averaging estimator to become more similar to either its model selection counterpart or the equal weights averaging estimator. We also show asymptotic validity of a bootstrap method for estimating the averaging estimators' distributions. Simulations illustrate the benefits of using sAIC instead of AIC estimators.

Central limit theorems (CLTs) for frequency-domain statistics are fundamental tools in frequency-domain analysis. However, for irregularly spaced data, they are still limited. In both the pure increasing domain and the mixed increasing domain asymptotic frameworks, three CLTs of frequency-domain statistics are established for the observations at uniformly distributed sampling locations over a rectangular sampling region. One is for discrete Fourier transforms (DFTs), while the other two pertain to generalized spectral means (GSMs). The asymptotic joint normality and independence of the DFT at any finite number of standard frequencies are derived. Additionally, the asymptotic normalities of two GSMs are set up, with asymptotic variances given in different forms, according to the Gaussian or non-Gaussian model assumption. Three established CLTs are very useful in investigating the sampling properties of many important frequency-domain statistics, such as periodogram, non-negative definite auto-covariance estimator, spectral density estimator, and Whittle likelihood estimator as well.