Autoregressive Process

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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According to these authors, whenever residual dependence is observed, this correlation must be modeled by an autoregressive process. Different results were found by Ribeiro et al.
From the Durbin-Watson test (DW), the presence of residual autocorrelation was evident for fruit length in the Logistic model and for diameter in the Gompertz model, necessitating the incorporation of the second-order autoregressive process parameters.
Assuming that output gap is autoregressive process, one period ahead forecast may be upward biased in recession and downward biased in boom.
According to Makridakis and Hibon (2000) ARIMA is a combination of 3-parameter model, which consists of Autoregressive process (memory of past events), an integrated process (maintaining and preparing the data fixed and accessible to predict) and moving average (the older the data is the more perfect the prediction will be).
For a stationary time series [x.sub.t] (t = 1, 2, ..., N), autoregressive process produces the following results:
Results are reported in Section 4 where the retrieval of the true causality network from the analytics of time series from an autoregressive process of p = 100 variables is discussed.
An autoregressive process will only be stable if the parameters are within a certain range: for example, if there is only one autoregressive parameter then is must fall within the interval of 1less than xt less than 1.
To eliminate the autoregressive process of the level shift component, the first difference model only depends on the Bernoulli process: [DELTA] [y.sub.t] = [[tau].sub.t] - [[tau].sub.t-1= + [c.sub.t] - [c.sub.t-1] = [c.sub.t] - [c.sub.t-1] + [[delta].sub.t], and passing to the state space form, the measurement and transition equations are obtained, respectively: [DELTA] [y.sub.t] = [c.sub.t] - [c.sub.t-1] + [[delta].sub.t], [c.sub.t] = [phi] [[c.sub.t-1] + [e.sub.t].
We propose a more robust technique to estimate the effective sample size for the case of an autoregressive process of order 1 (AR1), a suitable hypothesis for many time series in meteorology and climate sciences.
To jointly estimate the autoregressive process and its parameters from noisy observations, one of the authors of this paper has recently proposed dual Kalman filters based structure [11, 20].
From the previous subsection, we know that the stochastic process is a kth order Gauss-Markov process and, consequently, an autoregressive process. Under a system theory point of view, an autoregressive process is such that the system has only poles, that is,

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