Auto-Regressive (AR) Process

A stationary stochastic process where the current value of the time series is related to the past p values, where p is any integer, is called an AR(p) process. When the current value is related to the previous two values, it is an AR(2) process. An AR(1) process has an infinite memory.
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Kiyani and ranjbari (2001) study the long-run relationship among the Iran's energy, labour and capital factors of agriculture sector using the cointegration and Auto-Regressive Distributed Lag (ARDL) models for estimating the Cobb-Douglas form of production function during the years 1967-1999.
Auto-regressive cross-lagged panel analyses were used to evaluate the relationships between cognitive and functional impairment over time.
Higher-order auto-regressive (AR) models with lags ranging from 1 to 19 were developed, with climatic and non-climatic factors as regressors.
This model will be used in the future research like the predictor for the predictive control of the AMIRA DR300 to improve a basic CARIMA (Controller Auto-Regressive Integrated Moving-Average) linear model.
My colleague Ken Beauchemin took a different route in a recent Commentary and instead of looking only at the behavior of GDP during recoveries he used data on other variables, like the unemployment rate, the inflation rate, and the federal funds rate, from 1959 on and concluded that the current recovery is just slightly below what a vector auto-regressive (VAR) forecast would predict.
Although, in general, non-linear, auto-regressive time series modeling is difficult than linear models, yet with the ANN approach such a restriction does not apply (Garson, G.
Choosing breadth over depth, they survey a wide range of topics, among them maximum likelihood and Bayesian estimation, different types of spatial regression specifications such as the spatial auto-regressive and matrix exponential, applied modeling situations involving different circumstances including origin-destination flows, limited dependent variables, and space-time data samples.
We addressed changes over time via the combined mediation and longitudinal auto-regressive model (see Figure 1).
Before settling on the final model specification in Equations 1, 2, 5, and 6, the study experimented with two and three orders of auto-regressive lags.
These include the nonlinear auto-regressive model (NLAR), the threshold autoregressive model (TAR), smooth transition threshold model (STAR), exponential autoregressive model, and time varying parameter autoregressive model.
We assume, for simplicity, that the time dependence of the u's can be adequately represented by the first order auto-regressive scheme, we write:
The GPC was applied on the control and the CARIMA (Controlled Auto-Regressive Integrated Moving Average) model was chosen for describing the controlled model.