Autoregressive Process

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Autoregressive Process

Any process or model that uses past data to predict future data. Technical analysis, for example, is an autoregressive process. See also: Forecasting.
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Processes possessing this property are called compound autoregressive processes (CaR) (see Darolles, Gourieroux, and Jasiak, 2006); they are the discrete time counterparts of the (continuous time) affine processes, which is widely used in finance and insurance (see, e.g., Duffie, Filipovic, and Schachermayer, 2003; Schrager, 2006).
By using (4) we generated 100 multivariate autoregressive processes with known causality structures.
Consider the series generated from two autoregressive processes, which traditionally have been used to test causality analysis tools,
Order Determination for Multivariate Autoregressive Processes using Resampling Methods.
By taking into account time-lagged soil water content, time-lagged soil temperature, autoregressive processes and seasonality, the model provides more-detailed information on the nature of the relationship between [N.sub.2]O and the environmental drivers and the effects of temporal resolution on [N.sub.2]O emissions, obtained from fitting the model with weekly or monthly data.
Among the topics are gradient-based algorithms with applications to signal-recovery problems, graphical models of autoregressive processes, convex analysis for non-negative blind source separation with applications in imaging, robust broadband adaptive beamforming using convex optimization, and cooperative distributed multi- agent optimization.
To examine the nature of various nonlinear estimates, we generated a large number of series from second-order autoregressive processes. The best nonlinear model was compared with the best linear model using in-sample and out-of-sample criteria.
Likelihood ratio statistics for autoregressive processes. Econometrica 1981;49:1057-72.
9B and 9C are not a pair of first-order autoregressive processes due to the dependence of [[Phi].sub.2](t) and [[Phi].sub.3](t) on other variables.
A second approach is to build dynamics into the unobserved factors themselves by modeling them as autoregressive processes.
Johansen's tests for cointegration (1988, 1991, Johansen and Juselius (1990)) are a logical multivariate extension of Dickey-Fuller unit root tests for autoregressive processes. The Johansen tests use the canonical correlation of residuals from a reparameterized model to estimate the space of cointegration vectors and test the dimensions of the space.
Estimation of the above relationship requires specification of the maximum number of lags, [Rho] and [Gamma] (or [Gamma]' and [Rho]' in reverse causality), for the autoregressive processes. As noted by Hsiao (1981), artificial selection of the length of the lags may bias the estimates and induce inefficiency in the inferential procedure.

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