178 
Fishery Bulletin 109(2) 
Table 3 
Forecasts of meagre ( Argyrosomus regius) landings (May 2007 to April 2008). Observed landings (x h ), forecasted landings (x,), 
monthly forecast errors (e h ), monthly absolute percent error (APE,,), mean error (ME), and mean absolute percent error (MAPE) 
are displayed for the two naive models (NM1 and NM2) and the seasonal autoregressive integrated moving-average model 
(SAR). Annual root mean-square error of the mean-centered transformed data (RMSE) and annual percent error (PE) for NM1, 
NM2 and SAR were 0.261 and 30.2%, 0.285 and 38.9%, and 0.234 and 15.4%, respectively. 
Month 
Step ( h ) 
Obs ( x h ) 
Forecasts (x,) 
Forecast errors ( e , ) 
APE, 
NM1 
NM2 
SAR 
NM1 
NM2 
SAR 
NM1 
NM2 
SAR 
May-07 
1 
37.1 
29.9 
21.0 
36.4 
-7.2 
-16.1 
-0.7 
19.4 
43.5 
1.8 
Jun-07 
2 
41.5 
27.2 
18.1 
26.6 
-14.3 
-23.4 
-14.9 
34.4 
56.5 
35.8 
Jul-07 
3 
23.0 
17.9 
14.7 
26.1 
-5.2 
-8.3 
+3.1 
22.4 
36.2 
13.3 
Aug- 07 
4 
15.7 
25.9 
18.4 
25.8 
+10.2 
+2.8 
+10.1 
65.3 
17.6 
64.7 
Sep-07 
5 
20.8 
24.2 
26.3 
31.4 
+3.4 
+5.5 
+10.6 
16.3 
26.2 
51.1 
Oct-07 
6 
30.6 
15.3 
21.9 
23.0 
-15.2 
-8.7 
-7.6 
49.8 
28.5 
24.9 
Nov-07 
7 
32.9 
10.2 
13.3 
19.0 
-22.7 
-19.6 
-13.9 
69.0 
59.5 
42.2 
Dec-07 
8 
16.1 
6.8 
6.8 
6.0 
-9.3 
-9.2 
-10.1 
57.7 
57.5 
62.8 
Jan-08 
9 
7.5 
5.0 
4.8 
5.7 
-2.5 
-2.7 
-1.8 
32.8 
35.7 
24.5 
Feb- 08 
10 
3.2 
5.4 
5.2 
6.1 
+2.1 
+2.0 
+2.9 
66.6 
61.9 
90.7 
Mar-08 
11 
8.0 
5.8 
4.1 
6.5 
-2.2 
-3.9 
-1.5 
27.3 
48.6 
19.0 
Apr- 08 
12 
34.1 
15.2 
10.8 
16.3 
-18.9 
-23.4 
-17.9 
55.5 
68.4 
52.4 
Mean 
1:12 
22.5 
15.7 
13.8 
19.1 
-6.8 
-8.8 
-3.5 
43.1 
45.0 
40.3 
Sum 
1:12 
270.5 
188.8 
165.4 
228.9 
-81.7 
-105.1 
-41.6 
— 
— 
— 
As with SARIMA forecasts, naive model predictions 
also lagged observed values by one or two months. How- 
ever, the SARIMA forecasts registered the best perfor- 
mance in all accuracy measures, resulting in a 10% to 
18% reduction in RMSE, 49% to 60% reduction in ME, 
6% to 10% reduction in MAPE, and =15% reduction 
in PE (Table 3). The coefficient of persistence of the 
SARIMA model was also better (P=0.46) than the one 
registered by NM1 ( P= 0. 23 ) and NM2 (P=0.03). 
Monitoring of fisheries 
During the hold-out period, observed landings remained 
entirely within the 95% prediction intervals of the 
SARIMA forecasts (Fig. 3), indicating that the observed 
forecast errors were within the range of values expected 
from random variability. Consequently the time series for 
meagre landings may be described as having remained 
in-control during the forecasting period. The Pis were 
symmetrical in the log-transformed scale (Fig. 3, A and 
C), but asymmetrical in the original scale of the data 
(Fig. 3, B and D). This pattern was expected from predic- 
tions of log-transformed data and indicates that sudden 
increases in monthly landings (positive forecast errors) 
are considered “more acceptable” than sudden decreases 
(negative forecast errors). Individual forecast errors that 
could have signaled an alarm ranged from 4.3 to 23.0 
t (negative errors) to 13.5-68.3 t (positive errors). In 
relative terms, alarms would have been triggered by a 
higher than 54-75% drop, or by a higher than 105-238% 
increase, in monthly landings (Table 4). Compared to 
monthly Pis, multistep Pis were wider as a result of the 
increasing number of comparisons performed (Table 4). 
Even so, it is noticeable that such widening took place 
mainly on their upper boundary, and only a 12% increase 
was observed on their lower boundary. 
Discussion 
Interpretation of the models 
Univariate SARIMA models based on landings do not 
have explanatory variables, but several studies have 
found the mathematical formulation in the models to 
correlate well with fish life history and fleet dynamics 
(Stergiou, 1990b; Stergiou et al., 1997; Lloret et al., 
2000). In Europe, adult and juvenile meagre are thought 
to perform spring— summer migrations to major estuar- 
ies, remaining there until mid-summer (adults) and 
autumn (juveniles). These migrations are well known to 
local fishermen that actively target the meagre schools 
while they reside in estuarine grounds (Quero and 
Vayne, 1987; Prista et al. 2 ). Such interactions between 
fish migrations and directed fishing effort are likely the 
cause of the strong seasonal component of the SARIMA 
model because target effort tends to intensify the natu- 
ral seasonal signal generated by fish migrating through 
a fishery (Lloret et al., 2000; Prista et al. 2008). In the 
case of central Portugal, such intensification is likely 
modulated at an interannual level by the expectations 
created for local fishermen by catches obtained in pre- 
