[[PHI].sub.p]([B.sup.S])--represents the seasonal autoregressive
component of order p;
Let us now complete the model specification by proposing an appropriate exogenous dynamics for the dynamic frailty process, called (first-order) autoregressive
gamma process (ARG).
Thus, the autoregressive
model, estimated for the variation of the IPCA, via regression, is: [[??].sub.t] = 0.19 + 0.60 [y.sub.t-1]
where [X.sub.t] = data series, [a.sub.t] = random error (with mean zero and variance [[sigma].sup.2]), B = backward shift operator, [phi] = coefficient non-seasonal autoregressive
, [theta] = coefficient non-seasonal moving average, [PHI] = coefficient seasonal autoregressive
, [THETA] = coefficient seasonal moving average, [[DELTA].sup.d] = difference operator, with d order of differencing, and [[DELTA].sup.D.sub.s] = seasonal difference operator, with D seasonal order of differencing and s length of the seasonal period.
From this Figure, we observe that the streamflow series have a periodic behavior in the mean and variance and in this case, general periodic autoregressive
models are usually assumed in the analysis of the time series data (Modal & Wasimi, 2006).
First, although we used a fully cross-lagged panel design and controlled for autoregressive
effects, the nonexperimental study design means that we cannot derive conclusions about the causal relationships between loneliness and GPIU.
Therefore, the adjustment quality evaluators highlight the superiority of the Logistic model with second order autoregressive
errors to describe the pear fruit length increase.
Limited by the length of the paper, Table 2 merely lists the quantile vector autoregressive
regression model results at representative quantiles (25%, 50%, and 75%, p=3).
Two famous econometricians formulated the strategy of forecasting a times series called the Box-Jenkins method named after the statisticians George Box and Gwilym Jenkins,  this method applies autoregressive
moving average (ARMA) or autoregressive
integrated moving average (ARIMA) models to find the best fit of a time-series model to past values of a time series.
Third, assuming that output gap is autoregressive
process, one period ahead forecast may be upward biased in recession and downward biased in boom.