Time Series Analysis of Recreational Catch and Effort John Foster ...

Time Series Analysis of
Recreational Catch and Effort
John Foster
Fisheries Statistics Division

Overview
• Data series diagnostics
• ARIMA times series models
• Total effort by state and wave
• Total landings by wave
• Forecasting
2

• Concept
ARIMA Models
• Values in a time series are correlated
• Correlation is a function of time
• Parameters for ARIMA
• p: autoregressive (AR), q: moving average (MA)
• d: difference (I)
• Highly flexible
• Parameterization
• External correlates (tuning series)
• Implementation
• SAS/ETS, proc arima
3

•ARMA (p, q) X
•ARIMA (1,1,1)
•ARIMA (0,2,3)
Model Formulations
( X ) ( )
t
− X
t− 1
= b X
t−1
− X
t−2
+ et
+ a1et
−1
( X − X ) ( )
− 6
= b X
−1
− X
−6
+ e + a6e
−6
t
t
t
= µ +
∑
( X ) ( )
t
− X
t− 1
− X
t−6
− X
t−7
= et
+ a1et
−1
+ a6et
−6
+ a7et
−7
i=
1
t
p
b
i
X
t− i
+
t
+
t
e
t
q
∑
i=
1
a
i
e
t
t−i
4

Effort Models
• Total Effort (angler trips) by Wave, 1990-2009
• Separate models by State: MA, AL, FL
• Untransformed, Log transformed, No correlates
5

Effort Models
• Model Fit:
• Large states better than small states
• Mid Atlantic, NE better than SA, Gulf
• Short series better than long
9

Catch Models
• Total Landings (no. fish) by Wave, 1990-2009
• Coastwide models by species
• Summer flounder, Scup, Striped Bass
• Untransformed, Log and Logit transformed
• No Correlates
10

Full Year Forecast
12

NEW JERSEY
Full Year Forecast
13

Full Year Forecast
15

By Wave Forecast
16

By Wave Forecast
18

• External correlates
Future Development
• Effort
• Weather data: wind, precipitation, storm series
• Economic data: fuel prices, state level gdp
• Management regulations
• Survey metrics
• Optimizing model specifications
19

Time Series Analysis of
Recreational Catch and Effort
John Foster
Fisheries Statistics Division