Journal of Time Series Analysis最新文献

Independent Component Analysis (ICA) is a popular tool used for blind source separation and has found application in fields such as financial time series, signal processing, feature extraction, and brain imaging. Inspired by modeling a macroeconomic time series that has components with heavy tails, we consider the ICA problem with an infinite variance source. Many of the ICA procedures require the existence of a finite second or even fourth moment. Distance covariance is a measure of dependence that has become an increasingly popular choice as an objective function in the ICA setting. Unfortunately, the standard weight function used in distance covariance requires a finite variance assumption when applied in the ICA framework. The objective of this paper is to derive consistency when using the distance covariance applied to the infinite variance case. Extensions to the ICA model with noise, which has a direct application to time series models when testing independence of residuals based on their estimated counterparts, are also considered.

State-space models are widely used by statisticians because they allow a useful interpretation of some components of interest. Their efficient estimation, as well as the computation of forecasts or nonlinear functions of the observables, depends crucially on the correct specification of the error terms. Gaussianity is a common assumption explicitly used in the Kalman filter recursion, but departing from Gaussianity is of particular interest in fields such as finance, where there is a need for leptokurtic and/or asymmetric distributions to capture some features of the data. We introduce an approach based on the characteristic function or Laplace transform of the observed process and show that, for a large class of state-space models (with finite second-order moments and non-zero higher-order cumulants), it is possible to recover the cumulants of the structural shocks and the measurement errors from the cumulants and cross-cumulants of the observed process and the first-order parameters. This allows the statistician to design specification tests related to the properties of the structural shocks or measurement errors, separately or jointly, or of the data generating process (DGP) of the observed time series. In a non-Gaussian framework, we design a test for the property that the DGP of the observed time series is a state-space model with different shocks versus an ARMA DGP with only a single innovation process, but with the same second-order properties. We illustrate the size and power properties of this test applied to a simple stochastic volatility model.

Block resampling methods provide useful nonparametric inference with time series by applying data blocks to capture dependence and develop distributional approximations for statistics. Among such methods, the block bootstrap (BB) and subsampling (SS) represent distinct approaches, where SS has advantages over bootstrap in more general applicability and computation, though bootstrap, when viable, can be more accurate. Recently, convolved subsampling (CS) has emerged as a hybrid method between SS and BB, though its accuracy has remained an open question, and its performance depends intricately on the choice of two tuning parameters (i.e., block length and convolution level). This paper establishes the formal accuracy properties of CS for a broad class of smooth-model statistics and time processes, showing that CS can be second-order correct like the BB, offering improvements over SS or normal approximations. However, the success of CS can depend heavily on the convolution level chosen and on how the CS approximation is centered or de-biased. Indeed, without such consideration, CS can even become invalid. In developing accuracy properties, this work also provides important guideposts for the convolution level needed to implement the CS. Numerical evidence suggests the method achieves good coverage accuracy and compares favorably with other block resampling approaches.

This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters is based on second-order properties of the count and underlying Gaussian time series, yielding estimators of the underlying covariance matrices for which standard principal component analysis applies. Theoretical consistency results are established for the proposed estimation, building on certain concentration results for the models of the type considered. They also involve the memory of the latent Gaussian process, quantified through a spectral gap, shown to be suitably bounded as the model dimension increases, which is of independent interest. In addition, novel cross-validation schemes are suggested for model selection. The forecasting is carried out through a particle-based sequential Monte Carlo, leveraging Kalman filtering techniques. A simulation study and an application are also considered.