Online topology estimation for vector autoregressive processes in data networks

2017 ◽  
Author(s):  
Bakht Zaman ◽  
Luis M. Lopez-Ramos ◽  
Daniel Romero ◽  
Baltasar Beferull-Lozano
Keyword(s):  
Data Networks ◽  
Autoregressive Processes ◽  
Vector Autoregressive ◽  
Vector Autoregressive Processes ◽  
Topology Estimation

VECTOR AUTOREGRESSIVE PROCESSES WITH NONLINEAR TIME TRENDS IN COINTEGRATING RELATIONS

2001 ◽  
Vol 5 (4) ◽  
pp. 577-597 ◽  
Author(s):  
Antti Ripatti ◽  
Pentti
Keyword(s):  
Structural Changes ◽  
Asymptotic Theory ◽  
Var Model ◽  
Level Shift ◽  
Autoregressive Processes ◽  
Short Term ◽  
Vector Autoregressive ◽  
Market Rate ◽  
Nonlinear Trends ◽  
Vector Autoregressive Processes

We extend the conventional cointegrated VAR model to allow for general nonlinear deterministic trends. These nonlinear trends can be used to model gradual structural changes in the intercept term of the cointegrating relations. A general asymptotic theory of estimation and statistical inference is reviewed and a diagnostic test for the correct specification of an employed nonlinear trend is developed. The methods are applied to Finnish interest-rate data. A smooth level shift of the logistic form between the own-yield of broad money and the short-term money market rate is found appropriate for these data. The level shift is motivated by the deregulation of issuing certificates of deposit and its inclusion in the model solves the puzzle of the “missing cointegration vector” found in a previous study.

Autoregressive processes in optimization

1988 ◽  
Vol 25 (2) ◽  
pp. 302-312 ◽  
Author(s):  
Tomáš Cipra
Keyword(s):  
Dynamic Structure ◽  
Rates Of Convergence ◽  
Geometric Ergodicity ◽  
Autoregressive Processes ◽  
Stochastic Linear Programming ◽  
Vector Autoregressive ◽  
First Order ◽  
Convergence Of Moments ◽  
Geometric Convergence ◽  
Vector Autoregressive Processes

Vector autoregressive processes of the first order are considered which are non-negative and optimize a linear objective function. These processes may be used in stochastic linear programming with a dynamic structure. By using Tweedie's results from the theory of Markov chains, conditions for geometric rates of convergence to stationarity (i.e. so-called geometric ergodicity) and for existence and geometric convergence of moments of these processes are obtained.

Infinite-Order Cointegrated Vector Autoregressive Processes

1996 ◽  
Vol 12 (5) ◽  
pp. 814-844 ◽  
Author(s):  
Pentti Saikkonen ◽  
HELMUT Lütkepohl
Keyword(s):  
Sample Size ◽  
Error Correction ◽  
Infinite Order ◽  
Asymptotic Properties ◽  
Error Correction Model ◽  
Autoregressive Processes ◽  
Correction Model ◽  
Vector Autoregressive ◽  
Vector Autoregressive Processes ◽  
Linear Restrictions

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the relationships between the variables; therefore, they are important for applied work. Tests for linear restrictions on the coefficients of both the ECM and the pure VAR representation are considered under the present assumptions. It is found that they have limiting x2 distributions. Tests are also derived under the assumption that the number of restrictions goes to infinity with the sample size.

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