scholarly journals Prediction intervals and regions for multivariate time series models with sieve bootstrap

2018 ◽  
Vol 38 (2) ◽  
pp. 317-357
Author(s):  
Maciej Kawecki ◽  
Roman Różański ◽  
Grzegorz Chłapiński ◽  
Marcin Hławka ◽  
Krzysztof Jamróz ◽  
...  
Keyword(s):  
Time Series ◽  
Simulation Study ◽  
Linear Time ◽  
Multivariate Time Series ◽  
Prediction Intervals ◽  
Time Series Models ◽  
Bootstrap Procedure ◽  
Sieve Bootstrap ◽  
Prediction Regions ◽  
Theoretical Results

In the paper, the construction of unconditional bootstrap prediction intervals and regions for some class of second order stationary multivariate linear time series models is considered. Our approach uses the sieve bootstrap procedure introduced by Kreiss 1992 and Bühlmann 1997. Basic theoretical results concerning consistency of the bootstrap replications and the bootstrap prediction regions are proved. We present a simulation study comparing the proposed bootstrap methods with the Box–Jenkins approach.

scholarly journals The Influence of Covariance Hankel Matrix Dimension on Algorithms for VARMA Models

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Estimation Method ◽  
Hankel Matrix ◽  
Time Series Models ◽  
Minimal Dimension ◽  
Theoretical Results ◽  
Statistical Results

Some methods for estimating VARMA models, and Multivariate Time Series Models in general, rely on the use of a Hankel matrix. Some authors suggest taking a larger dimension than theoretically necessary for this matrix. If the data sample is populous enough and the Hankel matrix dimension is unnecessarily large, this may result in an unnecessary number of computations, as well as in worse numerical and statistical results. We provide some theoretical results to know which is the Hankel matrix with the lowest dimension that is theoretically necessary and illustrate, with several simulated VARMA models, that using a dimension of the Hankel matrix greater than the theoretical minimal dimension proposed as valid does not necessarily lead to improved estimates. Although we use two algorithms, our main contributions are independent of the estimation method considered. We note that our paper does not include any comparisons between different algorithms for estimating VARMA models, as this is not our aim.

Recent Theoretical Results for Time Series Models with GARCH Errors

2002 ◽  
Vol 16 (3) ◽  
pp. 245-269 ◽  
Author(s):  
W. K. Li ◽  
Shiqing Ling ◽  
Michael McAleer
Keyword(s):  
Time Series ◽  
Time Series Models ◽  
Theoretical Results

scholarly journals The Hyvärinen scoring rule in Gaussian linear time series models

2021 ◽  
Vol 212 ◽  
pp. 126-140
Author(s):  
Silvia Columbu ◽  
Valentina Mameli ◽  
Monica Musio ◽  
Philip Dawid
Keyword(s):  
Time Series ◽  
Linear Time ◽  
Time Series Models ◽  
Scoring Rule
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