Time Series Modeling - Water Quality Management: Assessment and Interpretation - page 66

The equation of the model is as follow:

Z t =0 : 88 þð 0 : 997Z t 1 0 : 381Z t 2 þ a t Þð 0 : 207Z t 12 þ e t Þ ð 4 : 46 Þ

In this equation, part of ð 0 : 997Z t 1 0 : 381Z t 2 þ a t Þ is non-seasonal auto-

regressive component of the model and ð 0 2076Z t 12 þ e t Þ is its seasonal auto-

regressive component. The standard error is 0.202. Akaike Information Criteria
(AIC) and Schwartz Bayesian Information Criteria (SBC) of the model are less than
other suggested models. The correlation coef

:

cient is 0.53 (Table 4.6 ). The risk is

less than 0.0001 and con dence level p-Value is 0.99 which proves the model to be

excellent (Asadollahfardi et al. 2012 ).

Acidity (pH)

The best developed model for pH parameter was ARMA (2,0,0) (0,0,0) (Fig. 4.5 ).
The equation for acidity is as follows:

Z t =7 : 775 þ 0 : 842Z t 1 0 : 142Z t 2 þ a t ð 4 : 47 Þ

According to comparison methods, standard error of the model is 0.267. The
AIC and the SBC of the model are less than other developed models. The corre-
lation coef

cient is 0.83 which is proper (Table 4.4 ). According to given
assumptions, the amount of risk is less than 0.0297 and a con dence level of

p-Value equals 0.97.

Total Dissolved Solid (TDS)

In Fig. 4 variations of TDS are shown. The best model developed for TDS is an
ARIMA (1,0,1) (0,0,0) with autoregressive order one component and moving
average order one. The equation of the model is as follows:

Z t = 228 : 8 þ 0 : 8Z t 1 þ a t þ 0 : 591a t 1 ð 4 : 48 Þ

The standard error of the model is 29.36 and AIC and SBC are less than other
developed models; the correlation coef cient is 0.91 which is proper (Table 4.4 ).

The amount of the risk is 0.0001 and p-Value is 0.99 which evaluates the model as
excellent.
The characteristics of all the models are shown in Tables 4.4 , 4.5 and 4.6 .It
should be noted that there is no negative value in practice and 95 % confidence
level considered in the calculation has caused the lower limit to be negative. Hence,
negative values should be omitted or replaced by zero.