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.
Thus, the speech signal is modeled as an
autoregressive process of order P, AR(P), according to
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.
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,