Time-series analysis 



Autoregressive integrated moving average (ARIMA) time-series models were developed to describe 

 the natural fluctuations of potentially impacted species in the MNPS area during the period spanned by 

 our baseline data. Because the model building process and analytical aspects of this technique have been 

 discussed in detail elsewhere (Bireley 1985, 1987; NlJSCo 1985), only a brief review of the methodology 

 follows. 



ARIMA models for each species were fitted only to time-series data from those stations and life 

 history stages where occurrence was high enough to provide reasonable descriptions of natural fluctuations. 

 The data (densities from ichthyoplankton, catches from impingement and seines) were log transformed to 

 reduce skewness and to stabilize variances (Glass et al. 1975), and then averaged over the sampling period 

 specific to each program to ensure that data would be spaced at equal intervals in the final time-series. 

 The sampling periods were a week for impingement and ichthyoplankton data and a month for seine data. 



The deterministic portion of the ARIMA models included explanatory variables much like nonlinear 

 regression models. These variables were cooling-water flow (F), species 'season indicator (S), and periodic 

 components which entered the model as sine or cosine functions of 1 to 6, or 12, 24, 36 ... up to 120 

 months; or combinations of these periods. The stochastic portion of the model described the structure of 

 the model prediction errors using two types of stochastic terms, autoregressive (A) and moving-average 

 (M). Therefore, the general form of the ARIMA models was: 



Zj = Qj[l + sin(tKp) -I- cos(tKp + ....] + [Stochastic terms: A, + M, 4- ....] 



where Z( were the time-series of means of the log transformed data; the subscript (t) was time in days; 

 the multiplier Q of the deterministic portion of the model could be either the flow (F) for impingement 

 models or the season indicator (S) which had a value of zero when a species was known to be absent 

 from the MNPS area and a value of one otherwise (Table 7); and (I) was a constant estimated from the 

 data either as zero or as unity. The periodic component Kp was a constant that converted the time (t) 

 into angular units (radians) of some specified period (p) in months. Some models had more than one 

 pair of sine-cosine terms to accomodate more than one periodic component. 



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