Algorithm AS 311: The Exact Likelihood Function of a Vector Autoregressive Moving Average Model

1997 ◽  
Vol 46 (1) ◽  
pp. 157-171 ◽  
Author(s):  
José Alberto Mauricio
Keyword(s):  
Likelihood Function ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Average Model ◽  
Vector Autoregressive ◽  
Autoregressive Moving Average Model ◽  
Moving Average Model ◽  
Vector Autoregressive Moving Average

Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by VARMA

2020 ◽  
pp. 2150022
Author(s):  
Boping Tian ◽  
Yangchun Zhang ◽  
Wang Zhou
Keyword(s):  
Covariance Matrix ◽  
Moving Average ◽  
Sample Covariance Matrix ◽  
Autoregressive Moving Average ◽  
Average Model ◽  
Largest Eigenvalue ◽  
Vector Autoregressive ◽  
Autoregressive Moving Average Model ◽  
Sample Covariance ◽  
Moving Average Model

In this paper, we derive the Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by the vector autoregressive moving average model when the dimension is comparable to the sample size. This result is applied to make inference on the vector autoregressive moving average model. Simulations are conducted to demonstrate the finite sample performance of our inference.

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