相关论文: Unit roots in moving averages beyond first order

The first-order moving average model or MA(1) is given by $X_t=Z_t-\theta_0Z_{t-1}$, with independent and identically distributed $\{Z_t\}$. This is arguably the simplest time series model that one can write down. The MA(1) with unit root…

This work presents a Bayesian approach for the estimation of Beta Autoregressive Moving Average ($\beta$ARMA) models. We discuss standard choice for the prior distributions and employ a Hamiltonian Monte Carlo algorithm to sample from the…

A unit root test is proposed for time series with a general nonlinear deterministic trend component. It is shown that asymptotically the pooled OLS estimator of overlapping blocks filters out any trend component that satisfies some…

We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…

This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…

To perform statistical inference for time series, one should be able to assess if they present deterministic or stochastic trends. For univariate analysis one way to detect stochastic trends is to test if the series has unit roots, and for…

The subject of robust estimation in time series is widely discussed in literature. One of the approaches is to use GM-estimation. This method incorporates a broad class of nonparametric estimators which under suitable conditions includes…

We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…

This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…

In this paper we present some new limit theorems for power variation of $k$th order increments of stationary increments L\'evy driven moving averages. In this infill sampling setting, the asymptotic theory gives very surprising results,…

This paper develops a framework for incorporating prior information into sequential multiple testing procedures while maintaining asymptotic optimality. We define a weighted log-likelihood ratio (WLLR) as an additive modification of the…

A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…

This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood…

In this paper, we develop a restricted eigenvalue condition for unit-root non-stationary data and derive its validity under the assumption of independent Gaussian innovations that may be contemporaneously correlated. The method of proof…

When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical…

Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…

This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…

Discrete-time affine processes are widely used in finance and economics and encompass count, positive, and nonnegative-valued processes. This paper develops near-unit-root asymptotic theory for this class of models. Unlike linear AR(1)…

The exact maximum likelihood estimate (MLE) provides a test statistic for the unit root test that is more powerful \citep[p. 577]{Fuller96} than the usual least squares approach. In this paper a new derivation is given for the asymptotic…

This paper deals with unit root issues in time series analysis. It has been known for a long time that unit root tests may be flawed when a series although stationary has a root close to unity. That motivated recent papers dedicated to…