S-ARMA Model and Wold Decomposition for Covariance Stationary Interval-Valued Time Series Processes

Covariance Matrix Estimation for Stationary Time Series

We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911) 351–376...

Discrete-valued ARMA processes

This paper presents a unified framework of stationary ARMA processes for discrete-valued time series based on Pegram’s [Pegram, G.G.S., 1980. An autoregressive model for multilag markov chains. J. Appl. Probab. 17, 350–362] mixing operator. Such a stochastic operator appears to be more flexible than the currently popular thinning operator to construct Box and Jenkins’ type stationary ARMAproces...

Holt’s exponential smoothing model for interval-valued time series

Interval-valued time series are interval-valued data that are collected in a chronological sequence through time. This paper adapts an approach to forecasting interval valued-time series based on Holt’s exponential smoothing method. In the adapted Holt’s method for interval-valued time series, the smoothing parameters are estimated by using techniques for non-linear optimization problems with b...

MCMC for Integer Valued ARMA Processes

The Classical statistical inference for integer valued time-series has primarily been restricted to the integer valued autoregressive (INAR) process. Markov chain Monte Carlo (MCMC) methods have been shown to be a useful tool in many branches of statistics and is particularly well suited to integer valued time-series where statistical inference is greatly assisted by data augmentation. Thus in ...

Supplement to “ Covariance Matrix Estimation for Stationary Time Series ”