Prista et al: Use of SARIMA models to assess data-poor fisheries 
179 
Table 4 
Prediction intervals of meagre f Argyrosomus regius) landings (May 2007 to April 2008). Point forecasts ( x , ) and 95% boundar- 
ies of the single step (PI SS ,) and multistep (PI msA ) prediction intervals are displayed. The prediction boundaries are given as 
absolute errors ( | | ) and absolute percent errors (APE,) in each monthly forecast step ( h ). In each cell, the left and right values 
represent the lower and upper boundaries, respectively. 
Month 
Step (h) 
K 
Kl 
APE, 
Kl 
APE, 
May-07 
1 
36.4 
19.7-38.4 
54-105 
19.7-38.4 
54-105 
Jun-07 
2 
26.6 
16.2-35.8 
61-135 
17.5-45.0 
66-169 
Jul-07 
3 
26.1 
16.9-40.5 
65-155 
18.8-58.0 
72-222 
Aug- 07 
4 
25.8 
17.3-43.7 
67-169 
19.6-68.8 
76-266 
Sep-07 
5 
31.4 
23.0-68.3 
73-217 
25.9-120.0 
82-382 
Oct-07 
6 
23.0 
17.3-54.7 
75-238 
19.5-103.6 
85-451 
Nov-07 
7 
19.0 
14.3-45.2 
75-238 
16.2-89.7 
85-472 
Dec-07 
8 
6.0 
4.5-14.2 
75-238 
5.1-29.4 
86-491 
Jan-08 
9 
5.7 
4.3-13.5 
75-238 
4.9-28.8 
86-509 
Feb-08 
10 
6.1 
4.6-14.6 
75-238 
5.3-32.2 
87-525 
Mar-08 
11 
6.5 
4.9-15.5 
75-238 
5.7-35.1 
87-539 
Apr-08 
12 
16.3 
12.3-38.7 
75-238 
14.2-89.9 
87-553 
ceding years (represented in the seasonal autoregressive 
term) and, at an intra-annual level, by random environ- 
mental and anthropogenic perturbations occurring on 
the fishery system (represented in the set of nonseasonal 
moving-average terms). 
Model fit and forecast performance 
The univariate SARIMA model presented a good fit to 
the short time series of meagre landings, explaining 
most of its variance and adequately modeling the sea- 
sonality and correlation structure of the data. Similar 
results were obtained in other studies of short and long 
time series: up to 68% (Lloret et al., 2000, series <64 
months), 75% (Saila et al., 1980), 77% (Stergiou et al., 
2003), 84-96% (Stergiou, 1989, 1991; Stergiou et al., 
1997), and 93% (Pajuelo and Lorenzo, 1995). Taken 
together, these results indicate that SARIMA models 
should be adequate for data sets of monthly landings 
in general, and not just those with larger sample sizes. 
Bearing in mind that the minimum series length usu- 
ally stated for SARIMA model fitting is 50 (Pankratz, 
1983; Chatfield, 1996b), such generalized applicability 
may make SARIMA models particularly useful for fish- 
eries with less reliable historical records or where only 
recently landings have been sampled. 
In addition to a good fit, the SARIMA model also pro- 
vided good short-term forecasts of meagre landings. The 
fact that all observed values were located within the 
predicted intervals of the model, and that naive fore- 
casts presented similarly lagged seasonality, indicates 
that the main forecast errors more likely resulted from 
natural variations in the timing of fish migrations and 
fishing seasons (Quero and Vayne, 1987; Prista et al. 2 ) 
or from specifics of SARIMA forecasts and accuracy 
measures (namely, correlation and APE sensitivity to 
near-zero observations) (Hyndman and Koehler, 2006; 
Box et al., 2008) than from model misspecification. At 
the annual level, the 15% error achieved is comparable 
to results previously obtained in larger data sets and 
well within the 10-20% range considered acceptable 
for market-planning and fisheries management (e.g., 
Mendelssohn, 1981; Pajuelo and Lorenzo, 1995; Hanson 
et al., 2006). Additionally, SARIMA forecasts clearly 
outperformed naive forcasting in all accuracy metrics, 
underscoring the large benefits of using these models 
instead of simpler alternatives (Saila et al., 1980; Ster- 
giou, 1991; Stergiou et al., 1997). Considered together 
with the overall good forecasting performance reported 
by Lloret et al. (2000) in their shorter series, these re- 
sults build confidence that SARIMA models are useful 
for forecasting short time series of landings and thus 
can substantially contribute to the planning and man- 
agement of many data-poor fisheries. 
Use of SARIMA models to forecast landings 
of data-poor fisheries 
SARIMA models forecast future landings by directly 
handling the seasonality and autocorrelation structure 
of the data and assuming the continuity over time of 
past time series behavior (Box et al., 2008). These 
models are known to be well adapted to forecast highly 
seasonal and autocorrelated data (Stergiou et al., 1997; 
Georgakarakos et al., 2006). Additionally, some authors 
have reported better SARIMA forecasting performances 
in fisheries with lower interannual variability, namely 
those that target benthic and demersal long-lived spe- 
