NOAA Technical Memorandum NMFS-AFSC-305

Methods for the Alaska Groundfish 

First-Wholesale Price Projections:

Section 6 of the Economic Status of 

the Groundfish Fisheries Off Alaska

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

Alaska Fisheries Science Center

September 2015

by

B. E.. Fissel

doi:xxxxxxxxxxxxxxxxxx
NOAA Technical Memorandum NMFS

The National Marine Fisheries Service's Alaska Fisheries Science Center uses 

the NOAA Technical Memorandum series to issue informal scientific and 

technical publications when complete formal review and editorial processing 

are not appropriate or feasible. Documents within this series reflect sound 

professional work and may be referenced in the formal scientific and technical 

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the Northwest Fisheries Science Center.

This document should be cited as follows:

Fissel, B. E. 2015. Methods for the Alaska groundfish first-wholesale 

price projections: Section 6 of the Economic Status of the Groundfish

Fisheries off Alaska. U.S. Dep. Commer., NOAA Tech. Memo. NMFSAFSC-305, 39 p. doi: XXXXXXXXXXXXX.

Document available: http://www.afsc.noaa.gov/Publications/AFSC TM/NOAA-TM-AFSC-305.pdf.

Reference in this document to trade names does not imply endorsement by 

the National Marine Fisheries Service, NOAA.
September 2015

NOAA Technical Memorandum NMFS-AFSC-305

by

B. E. Fissel

Methods for the Alaska Groundfish 

First-Wholesale Price Projections:

Section 6 of the Economic Status of the 

Groundfish Fisheries Off Alaska

Alaska Fisheries Science Center

7600 Sand Point Way NE

Seattle, WA 98115

www.afsc.noaa.gov

U.S. DEPARTMENT OF COMMERCE

Penny. S. Pritzker, Secretary

National Oceanic and Atmospheric Administration

 Kathryn D. Sullivan, Under Secretary and Administrator

National Marine Fisheries Service

Eileen Sobeck, Assistant Administrator for Fisheries 

doi:10.7289/V5PZ56T3
This document is available to the public through: 

National Technical Information Service 

U.S. Department of Commerce 

5285 Port Royal Road 

Springfield, VA 22161 

www.ntis.gov 
Abstract

For a significant portion of the year there is a temporal lag in officially reported

first-wholesale prices. This lag occurs because the prices are derived from the Commercial

Operators Annual Report which is not available until after data processing and validation

of the data in August of each year. The result is a data lag that grows to roughly a

year and a half (e.g., prior to August 2014 the most recent available official prices

were from 2012). To provide information on the current state of fisheries markets,

now-casting is used to estimate 2014 first-wholesale prices from corresponding export

prices which are available at a shorter time lag. Now-casting provided fairly accurate

predictions and displayed rather modest prediction error with most of the confidence

bounds within 5-10% of the price. In addition, time series models are used to project

first-wholesale prices for 2015-2018. Resampling methods are used estimate a prediction

density of potential future prices. Confidence bounds are calculated from the prediction

density to give the probability that the prices will fall within a certain range. Prediction

densities also provide information on the expected volatility of prices. As prices are

projected past the current year the confidence bounds grow reflecting increasing

uncertainty further out in the future. An empirical example to projecting the prices

of pollock goods illustrates the methods. The full results of this research are published

in the Status Report for the Groundfish Fisheries Off Alaska, 2014, provided to the

North Pacific Fishery Management Council.

iii

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Overview of First-wholesale Price Projection Methods . . . . . . . . . . 2

Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

First-Wholesale Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Export Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Modeling and Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Price Stationarity and Return Calculations . . . . . . . . . . . . . . . . . . . 7

Methods for Now-casting First-wholesale Returns Using Export Data . . . . 8

Methods for Projecting First-wholesale Returns for Future Years . . . . . . . 10

ARMA Time Series Models . . . . . . . . . . . . . . . . . . . . . . . . . 11

Exponential Smoothing Time Series Models . . . . . . . . . . . . . . . . 12

Volatility Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Wholesale Price Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Residual Pooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Return Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Forecast Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Calculating Price Projection Confidence Bounds . . . . . . . . . . . . . . . . 22

Empirical Illustration of Price Projection Methods to Pollock Surimi, Fillets

and Roe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Citations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Coefficient Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

v

Introduction

The Stock Assessment and Fishery Evaluation Report for the Groundfish Fisheries

of the Gulf of Alaska and Bering Sea/Aleutian Island Area: Economic Status of the

Groundfish Fisheries Off Alaska, 2013 (Economic SAFE) provides first-wholesale

prices for the groundfish products produced by U.S. North Pacific fisheries (Table 26,

Fissel et al. (2014)). These prices are derived from production and revenue data

collected from processors in the Commercial Operators Annual Report (COAR).

Because of the COAR’s submission deadline, data processing, and validation of the

data from the report are not completed until July of the following year. Thus, at

the time of the Economic SAFE’s writing (October), the most recent pricing data

available are for the previous year. For example, in October 2014 the most recent

first-wholesale price data are for the calendar year 2013. Furthermore, because the

report is annual, this remains the most recent data for much of the following year

(2015 in the previous example). Price projections of first-wholesale products (Section 6,

Fissel et al. (2014)) are published in the Economic SAFE to provide recent information

on the state of the North Pacific fishing industry. Current prices (i.e., coresponding

to the year the Economic SAFE’s is written; 2014 in the previous example) are estimated

(“now-cast”) using corresponding export prices. Furthermore, first-wholesale prices

are forecast out over the next 4 years (2015 to 2018 in the previous example). The

projections give a probabilistic characterization of the range of future prices.

This report describes the methodology applied in projecting pound prices for

Alaska fisheries first-wholesale products. The purpose of this document is to provide

a concise description of the data and methods used to create price projections for

first-wholesale North Pacific groundfish products. The description provided is intended

to be sufficient for the reader to evaluate and reproduce the methods. A numbering

modeling methods were used to provide accurate robust estimates. A complete treatment

of the statistical theory and estimation strategies can be found by following the

references.
The procedure used for constructing the price projections is summarized in the

following section. Subsequent sections describes the first-wholesale and export data

used for in the analysis,the estimation procedures of the time series models. This

is follow by a discussion of the Monte Carlo simulation procedure that was used to

obtain confidence bounds for pound prices and forecast combination.

The focus of this report is on modeling methods, however, an empirical illustration

of the forecast methods have been provided in the final section of this report. The

first-wholesale price projections for all products can be found in the Section 6 of the

Economic SAFE (Fissel et al. (2014)) along with a brief description of the product

markets for context and an informal evaluation of price projections based on news

media reports.

Forecasting methods may be revised in the future which incorporate new data or

improved methods.

Overview of First-wholesale Price Projection Methods

The methods for now-casting the current year’s prices are distinctly different

than the methods used to estimate future prices. Current year prices were now-cast

using export prices which are available with a minimal time lag of up to 3 months.

The regression relationship between export prices and first-wholesale prices was

fairly strong for most products. Therefore, now-casts were made with fairly high

precision, particularly in comparison to the projections of future prices. Only a small

component of the future first-wholesale prices was forecastable, a feature that is

common in price forecasts for commodities Chevallier and Ilepo (2013). Price projections

were primarily made using models that estimate long-run returns and deviations

from their long-run value. Estimates were made more robust by using a suite of

canonical time series models to capture different aspects of the time series signal.

The primary suite of models used were within the class of autoregressive moving

average (ARMA) time series models (Hamilton 1994). Two exponential smoothing

models were also used, however, these tended to contribute little to the price projections

2
(Hyndman and Athanasopoulos 2013). Changes in price return volatility over time

were also modeled as Generalized Autoregressive Conditional Heteroskedasticity

(GARCH) processes. Confidence bounds for the estimated models were constructed

using residual resampling methods. Simulations created a probabilistic distribution

of potential returns that are consistent with historical deviations from the models.

Price projections from the suite of models were then combined using weights that

were determined by model fit. Prices were calculated from returns and statistics such

as the mean and percentiles for confidence bounds were calculated from the forecast

distribution

Data

The species and products for which price projections are made approximately

correspond with the prices in Table 26 of the Economic SAFE (Fissel et al. (2014)).

With the notable exception that estimates are made for all Alaska, and no distinction

is made between at-sea and shoreside prices. For products where prices between the

at-sea and shoreside sectors differ, then discrepancy is typically attributed to product

quality or other production differences that are constant fairly constant over time.

Because of this a forecast of the product price and be used to impute the sector

specific product prices. Furthermore, export data which make no distinction between

sectors, hence, aggregating over sectors aligns the product definition closer to the

corresponding export product definition.

First-Wholesale Data

The first-wholesale product pound prices (hereafter prices) projected in this analysis

were based on the published prices in Table 26 of the Economic SAFE (Fissel et al.

(2014)).1 The prices were based on the Commercial Operators Annual Reports, see

footnotes on Table 26 of the Economic SAFE (Fissel et al. (2014)) for further source

1The data as published in Table 26 of the Economic SAFE is

rounded however more detailed data can be obtained in csv format at:

http://www.afsc.noaa.gov/REFM/Socioeconomics/SAFE/CSV groundfish/table26 data.csv .

3
details. Price data extend from 1992 to 2013. Prices are stratified by three factors:

species, product type, and inshore/off-shore sector. For this analysis a product is

defined by the two characteristics: species and product type (e.g., pollock fillet).

Sector prices were aggregated by taking an average over inshore and offshore prices

weighted by product quantity.

Many of the products listed in Table 26 of the Economic SAFE are produced

in relatively small quantities, to reduce the set of forecasts to set of products for

which there is a significant market some products were aggregated. Specifically, any

product whose average annual share of value for a given species was less than 10%

was reclassified to the ”other products” product type. Exceptions to the product

aggregation rule were: pollock fillets and pollock deep-skin fillets were not reclassified;

most non-head and gut flatfish product types were reclassified as ”other products”;

and ”rex sole other products” was only present in four non-contiguous years and was

removed. Furthermore, all products from the species ”deep-water flatfish”, ”Kamchatka

flounder”, ”other flatfish”, and ”other species” were removed from the analysis. These

species were dropped because either the times series was not sufficiently long to

make reasonable predictive estimates or the product definition was too ambiguous

or highly aggregated to understand what product market was being estimated. The

final list of products for which prices projections were made can be found on Table 1

along with abriged product names that are used in tables to conserve space.

Table 1.– First-wholesale North Pacific groundfish product and abbreviations.

Long product name Product

pollock surimi PLCK Suri

pollock roe PLCK Roe

pollock fillet PLCK Flt

pollock deep-skin fillet PLCK DsFlt

pollock other products PLCK Other

Pacific cod fillet PCOD Flt

Pacific cod head and gut PCOD H&G

4
Pacific cod other products PCOD Other

sablefish head and gut SABL H&G

yellowfin (BSAI) head and gut YLWS H&G

rock sole (BSAI) head and gut with roe RCKS H&GwR

rock sole (BSAI) head and gut RCKS H&G

Greenland turbot (BSAI) head and gut GLDT H&G

arrowtooth head and gut ARTH H&G

flathead sole head and gut FLTS H&G

rex sole (GOA) whole fish REXS Whole

shallow-water flatfish (GOA) fillet SHAL Flt

Atka mackerel head and gut AMAK H&G

rockfish head and gut RCKF H&G

Export Data

Data on U.S. exports of fisheries products were used to ‘now-cast’ recent first-wholesale

prices (see the following section for nowcasting). Export data are collected on a

monthly basis by the Foreign Trade Division of the U.S. Census Bureau and is typically

available at a 2 to 3 month lag. The comparatively recent export data are used to

predict the current annual price. The analysis used the monthly export quantities

and revenues by product type, U.S. city of origin and export destination for January 1992

- August 2014.2. The product definitions for export data are different from the first-wholesale

product definitions. The following is a list of the export product definitions considered

in the analysis grouped by species or species complex:

• Pollock: ”GROUNDFISH POLLOCK ALASKA FILLET FROZEN”, ”GROUNDFISH

POLLOCK ALASKA ROE FROZEN”, ”GROUNDFISH POLLOCK ALASKA

SURIMI”, ”GROUNDFISH POLLOCK NSPF MINCED FROZEN”, ”GROUNDFISH

2These data are available at:

http://www.st.nmfs.noaa.gov/commercial-fisheries/foreign-trade/applications/monthly-product-bycountryassociation

5
POLLOCK ALASKA FROZEN”, ”GROUNDFISH POLLOCK ALASKA MEAT

FROZEN”

• Cod: ”GROUNDFISH COD NSPF FILLET FROZEN”, ”GROUNDFISH COD

NSPF FROZEN”, ”GROUNDFISH COD NSPF FRESH”, ”GROUNDFISH

COD NSPF SALTED”, ”GROUNDFISH COD NSPF DRIED”, ”GROUNDFISH

COD NSPF MINCED FROZEN”, ”GROUNDFISH COD NSPF MINCED

FROZEN > 6.8KG”

• Sablefish: ”SABLEFISH FROZEN”, and ”SABLEFISH FRESH”

• Flatfish: ”FLATFISH SOLE YELLOWFIN FROZEN”, ”FLATFISH NSPF

FILLET FROZEN”, ”FLATFISH NSPF FILLET FRESH”, ”FLATFISH SOLE

ROCK FROZEN”, ”FLATFISH PLAICE FRESH”, ”FLATFISH PLAICE FROZEN”,

”FLATFISH NSPF FRESH”, ”FLATFISH NSPF FROZEN”, ”FLATFISH TURBOT

GREENLAND FROZEN”

• Atka mackerel: ”ATKA MACKEREL FROZEN”

• Rockfish: ”GROUNDFISH OCEAN PERCH PACIFIC FROZEN”

Some export product definitions were combined into a single series by summing

quantities and revenues. Data for the export product ”GROUNDFISH COD NSPF

MINCED FROZEN > 6.8KG” were aggregated with ”GROUNDFISH COD NSPF

MINCED FROZEN”. Data defined as ”FLATFISH NSPF FILLET FROZEN” were

aggregated with ”FLATFISH NSPF FROZEN”. Data defined as ”FLATFISH NSPF

FILLET FRESH” were aggregated with ”FLATFISH NSPF FRESH”. Finally, data

defined as ”FLATFISH PLAICE FRESH” were aggregated with ”FLATFISH PLAICE

FROZEN”. Furthermore, not all export product defined above were used. For example,

the product ”GROUNDFISH POLLOCK NSPF MINCED FROZEN” was dropped

because data were only present in 1991. In general, any time series containing less

than 10 years was not used in the analysis. Similarly, the time series for export products

”GROUNDFISH POLLOCK ALASKA FROZEN” and ”GROUNDFISH POLLOCK

ALASKA MEAT FROZEN”began in 2010 and 2012, respectively, and were not used.

6
A few of the export time series has a gap of few years in the middle of the time series

and where this occurred missing years were imputed at the average product price

returns. Alternative imputation methods were explored and yielded similar results.

Export data were further constrained to exports originating from Washington and/or

Alaska. An analysis of alternative point-of-origin constraints indicated that in-sample

predictions of first-wholesale prices improved when export data were restricted to

these states.

The monthly export quantities and revenues were aggregated by summing over

the months within a year. If the months of the current year being predicted (e.g.,

2014) did not yet span the full year, then only the months with export data available

in the ‘current’ year were summed in each year. For example, if in 2014 export data

were only available through September, then export prices for all years were calculated

using only data through September in every year. This is because the objective of

analysis is predicting current first-wholesale prices using (potentially) partially available

export data. Quantities in the export data are denoted in kilos which can be converted

to pounds using a factor of 2.20462 (2.20462*kilos≈pounds). Export prices were

calculated as dividing export revenues (denoted in U.S.$) by quantities.3

Modeling and Estimation

Price Stationarity and Return Calculations

Price projections were estimated on annual returns rather than prices. Financial

time series analysis is typically conducted on asset returns. The primary reason is

that statistical tests on raw asset prices generally indicate the presence of a stochastic

trend known as a unit root. Unless accounted for, stochastic trends can create statistical

difficulties such as falsely identified (spurious) relationships between prices which

are actually unrelated (see Chapter 18, Hamilton (1994) for details on unit roots).4

The presence of unit roots were confirmed in first-wholesale prices data using the

3Subsequent regression analysis would not be affected if prices were left as dollars per kilo because the

conversion factor is constant.

4See Chapter 5, Chevallier and Ilepo (2013) for a general discussion of unit roots in commodity prices.

7
Augmented Dick-Fuller and Philips-Perron unit root tests. Because unit roots are so

ubiquitous in financial time series the results of the unit root tests are not presented

here. Unit roots can be filtered by calculating returns. Returns were calculated as

rt = ln(pt) − ln(pt−1), where rt and pt represent returns and prices, respectively,

at time t and ln() is the natural logarithm. Unit root tests conducted on the return

series rejected the presence of a unit root indicating that the time series were stationary

and suitable for canonical time series methods.

Methods for Now-casting First-wholesale Returns Using Export Data

Now-casting is the prediction of a variable for a time period that has partially or

completely occurred, but for which data are not yet available. Now-casting is widely

used by agencies for the timely reporting critical economic data for which there is

some reporting lag in the underlying data. For example, now-casting is used by the

Bureau of Economic Analysis to estimate recent quarters of U.S. Gross Domestic

Product. Subsequent revisions to GDP are the largely the result of new data becoming

available (Banbura et al. 2013).

Now-casting is used to estimate average annual first-wholesale returns for groundfish

products in 2014 which, at the time the Economic SAFE is written, had only partially

occurred. Predictions were made using U.S. export returns for groundfish products

for which data are available with a minimal time lag. The relationship between export

returns and first-wholesale returns is modeled through linear regression, which when

used in a now-casting framework is sometimes referred to as a “bridge” regression.

Analysis of the time series profile of first-wholesale production quantities and

export quantities for a given species (or species and product type where product type

definition roughly matched) generally showed a distinct break in the relationship in

the year 1998. From 1998 on first-wholesale production and exports were roughly

proportional while earlier years export quantities tended to be significantly smaller

and the relationship was more erratic. Furthermore, inclusion of pre-1998 data generally

8
reduced predictability. Because of this, now-cast models were fit and prediction of

recent returns were made based on post-1997 data.

For each product that was now-cast, all export variables matching the first-wholesale

species, or species complex, were tested. These matches correspond with the groupings

in the itemized list in the previous section titled ‘Export Data’.5 Variable selection

was based on the Akaike and Bayesian Information Criterions. Model residuals were

tested for heteroskedasticity and autocorrelation. Residual autocorrelation was tested

using the Breuch-Godfrey test up to 3 lags and results indicated that residuals were

independent. However, many models exhibited at least some heteroskedasticity both

visually and as determined by a Breusch-Pagan test. Furthermore, visual analysis of

series and model residual indicated the occasional presence of outliers. To mitigate

the potential leverage from heteroskedasticity and outliers, models were fit using

the robust linear estimation method of iterated re-weighted least squares. For the

product ‘Atka mackerel head and gut’ iterated re-weighted least squares failed to

converge and models were estimated by ordinary least squares. Table 2 presents the

regression model specifications.

Specific parameter estimates are not provided in this report. The unadjusted

R-squared has been calculated to provide some indication of how well the export

models perform relative to the mean. However, R-squared was not used in model

selection and the properties of R-squared in a robust linear estimation and Ordinary

Least Squares (OLS) frameworks may not coincide. Thus, the R-squared statistic

should be viewed only as a statistic comparing the fitted and the mean deviations

and not as a measure of goodness-of-fit.

Now-casted returns were used in the subsequent price projection models. The

now-casted price is calculated by inverting the return calculation with a log-normal

adjustment to account for the estimation randomness:

pi,2013 ∗ exp(ˇri,2014 + ˇσ

2

i,2014/2) = ˇpi,2014, (1)

5A limited number of cross-species variables were attempted but they weren’t found to increase

predictability significantly. Thus cross-species variables were excluded from the models based on these

trials, the limited observations and the large number of possible combinations if all variables were tested.

9
Table 2.– Now-cast model specifications.

Product Variables R-Squared

PLCK Suri SURIMI, DV 08-09, DV PRE-2K 0.54

PLCK Roe ROE, DV 07-10 0.64

PLCK Flt FILLET, DV PRE-01 0.23

PLCK DsFlt FILLET, DV PRE-01 0.01

PLCK Other FILLET 0.02

PCOD Flt FILLET, NSPF FROZEN, DRIED, DV 03 0.60

PCOD H&G NSPF FROZEN, DRIED, FRESH 0.47

PCOD Other NSPF FROZEN, FRESH, SALTED, MINCED,

DV PRE-01

0.65

SABL H&G FROZEN, FRESH 0.33

YLWS H&G SOLE YELLOWFIN,

(SOLE YELLOWFIN)*(DV PRE-07), PLAICE

0.14

RCKS H&GwR SOLE ROCK, PLAICE, NSPF FRESH 0.32

RCKS H&G SOLE ROCK, SOLE YELLOWFIN, PLAICE 0.42

GLDT H&G TURBOT GREENLAND 0.21

ARTH H&G TURBOT GREENLAND, NSPF FROZEN,

SOLE ROCK

0.10

FLTS H&G TURBOT GREENLAND, SOLE ROCK, DV 06,

SOLE YELLOWFIN, NSPF FROZEN

0.36

REXS Whole NSPF FROZEN, PLAICE, DV 05&11 0.69

SHAL Flt NSPF FROZEN, SOLE ROCK, NSPF FRESH, DV 04-05 0.76

AMAK H&G FROZEN 0.12

RCKF H&G FROZEN 0.00

‘DV YY’ is a dummy variable for the indicated years.

where exp(x) = e

x

is the exponential function, ˇri,t (ˇpi,t) is the now-casted return

(price) of product i and ˇσ

2

i,t is the prediction error from the regression.

Methods for Projecting First-wholesale Returns for Future Years

Time series forecasting models are not generally a structural model of a data

generating process. Rather, forecasting models construct a parsimonious parametric

structure that captures features of the series’ evolution over time (e.g., if I observe

yt today can I expect to observe yt+1 = ρyt tomorrow on average?). Different models

can capture different features of the dynamics of time series’. Furthermore, the forecast

performance of these different models can be improved by combining the forecasts

from the individual models (Timmermann 2006).

10
The forecast procedures used here follow this approach of forecasting with multiple

parsimonious models then combining the forecasts. Forecasts were made using two

classes of models:1) ARMA models and 2) exponential smoothing models (ETS).

Models were combined using weights determined by their forecast performance as

measured by a small-sample-adjusted Akaike Information Criterion (AICc) (Burnham

and Anderson 2002). The following sections describe the classes of forecast models.

ARMA Time Series Models

The autoregressive moving-average (ARMA) model is the work-horse of time

series analysis. The ARMA models captures linear dependence between future and

earlier observations of both the observed returns and the error process. The ARMA(p, q)

model of returns, rt, posits the following dynamic relationship:

rt+1 = α +

X

p

i=1

ρirt+1−i +

X

q

j=1

φjεt+1−j + εt+1, (2)

where p is the number of autoregressive (AR) terms and q is the number of moving-average

(MA) terms. The residuals {εt} were assumed to be a white-noise process with mean

of zero, a finite variance, and is uncorrelated with all other realizations. The parameters

of the autoregressive component, ρi, capture the dependence between rt+1 and previous

observed returns, rt+1−i, i > 1. The parameters of the moving-average component,

φj capture the dependence between the return rt+1 and previous errors, εt−1. Trends

in the context of ARMA models were considered by including functions of time directly

in Equation 2 (e.g., γ1t + γ2t

2

....). Time trends were not supported empirically and

were not included in any of the final ARMA models. All ARMA models included a

constant.

Parameter estimation of ARMA(p, q) models can be carried out using the Kalman

filter procedure. The Kalman filter is a recursive procedure to calculate maximum

likelihood estimates of all of the ARMA model’s parameters (see Chapter 13, Hamilton

(1994)). For a given p and q, estimated parameters, ˆρi i = 0, ..., p and φˆ

j j = 0, ..., q,

11
and residuals ˆεs s = 1, ..., t forecasts of rt+1 were made from Equation 2 as

rˆt+1 = ˆα +

X

p

i=0

ρˆirt−i +

X

q

j=0

φˆ

jεˆt−j . (3)

Return forecasts ARMA(p, q) models were estimated for orders 0 ≤ p ≤ 3,

0 ≤ q ≤ 3. Because of the limited number of observations and to preserve degrees of

freedom in estimation, the set of ARMA models were further restricted to p + q ≤ 3.

The AICc are well defined model selection statistics for ARMA models. Table 9

presents the estimated model model coefficients and AICc statistics.

Exponential Smoothing Time Series Models

The exponential smoothing (ETS) approach models a dynamic process as a weighted

average of past observations with weights that decay exponentially. The discussion

of these models closely follows Hyndman and Athanasopoulos (2013). ETS models

decompose time series into a state space where the decay and drift are modeled

as explicit but unobserved states. Forecasts were made using a simple exponential

smoothing model and an exponential smoothing trend model.

The simple exponential smoothing model has a single parameter, α which controls

the decay of the weights from the most recent observation. It posits the following

model written in state-space form:

rt+1 = lt + εt+1 (4)

lt+1 = lt + αεt+1, (5)

where 0 < α < 1 and εt+1  ̃ iid N(0, σ2). The latent state ltis referred to as the

level. Recursive substitution of equations above expresses rt+1 in terms of previous

values:

rt+1 =

X

t−1

i=0

α(1 − α)

i

rt−i + (1 − α)

t

l0 + εt+1, (6)

12
showing it is exponential smoother from initial state “l0” where larger values of α

give comparatively greater weight to recent observations. The forecast of rt+1 can be

expressed as a weighted average of the previous observation and its expected value,

Et(rt+1) = αrt + (1 − α)Et−1(rt).

The exponential smoothing trend model augments Equation 4 with a trend positing

the following time series structure:

rt+1 = lt + bt + εt+1 (7)

lt+1 = lt + bt + αεt+1 (8)

bt+1 = bt + αβεt+1, (9)

where 0 < α < 1 and β is a smoothing parameter. Time series with smaller values of

β have a trend component with less variation on average, thus resulting in a smoother

trend and observations. This model reduces to the previous case of simple exponential

smoothing (Equation 4) when β = 0 and b0 = 0. Equation 7 can be rewritten as

rt+1 =

X

t−1

i=0

α(1 − α)

i

rt−i + (1 − α)

i

bt−i + (1 − α)

t

(l0 + b0) + εt+1. (10)

Smaller values of α again give greater weight to more recent observations. The addition

of the trend btincorporates the slope of rt as a predictor (Hyndman and Athanasopoulos

2013). The exponential state space trend is different from the time deterministic

trends in ARMA models where trend refers to a variable that is an explicit function

of time t.

The forecast of the trend exponential smoothing model can be expressed as the

weighted average of the previous observation and its expected value plus the trend:

Et(rt+1) = αrt + (1 − α)Et−1(rt) + bt.

Due to their recursive structure, exponential smoothing models must be estimated

using maximum likelihood. The AICc are well defined model selection statistics for

exponential smoothing models. Table 10 lists the estimated model coefficients and

AICc statistics.

13
Volatility Estimation

Volatility characterizes the spread of the distribution of the random innovations

to a time series. Volatility can be time-varying, which if neglected can distort the

spread of the forecast distribution by over- or underestimation of the variance. One

particular time-varying feature frequently displayed is the tendency for periods of

high (low) volatility to be followed by another period of high (low) volatility which is

known a volatility persistence. Volatility persistence is a typical feature of commodity

prices (Chevallier and Ilepo 2013) and is one which is also displayed by some of the

returns of first-wholesale fisheries products.

Neglecting to account for time varying volatility can result in forecasts with too

much or too little volatility in the forecast distribution depending on the current

state of volatility. A standard method for accounting for volatility persistence is to

estimate a Generalized Autoregressive Conditional Heteroskedasticity (GARCH)

model. Specifically, this analysis estimates a GARCH(1,1) model for the volatility.

The GARCH(1,1) model can be written as

σ

2

t = γ0 + γ1ε

2

t−1 + γ2σ

2

t−1 + ut

. (11)

Similar to the ARMA(p,q) model the (1,1) in GARCH(1,1) refers to the number

of lagged squared residual, ε

2

, and squared volatility, σ

2

, terms used in the model.

Note that the true volatility σ is unobserved. The model is estimated using ˆεt from

the estimated ARMA and ETS models. Specifically, for each species-product and

each model estimated The GARCH(1,1) model is fit to each of the estimated models

presented above.

The GARCH model implies a long-run equilibrium volatility. The long-run volatility

of the GARCH(1,1) model can be computed directly from the estimated coefficients

as

σ

2

long−run =

γ0

1 − γ1 − γ2

. (12)

14
GARCH models were estimated using maximum likelihood and convergence of

the models is know to be difficult. Convergence is further complicated by the limited

number of observations. Alternative search algorithms were used, data were rescaled,

and different initial conditions were attempted to facilitate convergence. When convergence

failed the canonical constant volatility of the ARMA model was used. If multiple

convergence points were found after trying these alternatives then the model that

minimized the Bayes Information Criterion (BIC) was chosen. Finally, the implied

estimated long-run volatility (Eq.12) was examined relative to the distribution of

the squared residuals and if the long-run volatility was above the 95th quantile or

below the 5th quantile then it was treated as if the model had converged at a bad

point and again the canonical constant volatility of the ARMA model was used for

the price projections.6

In addition to producing volatility forecasts, the fitted GARCH volatilities were

used to normalize residuals from the fitted ARMA models prior to resampling in the

subsequent simulations. GARCH normalized residuals were calculated as follows: let

εˆm,i,t be the residual and ˆσm,i,t the estimated volatility for product i (e.g., pollock

surimi) from model m ∈ M where M = {1, 2, . . .} indexes the forecasting models

(e.g., ARMA(1,1)). The residual is normalized by the estimated volatility (Equation 11),

ε ̈m,i,t =

εˆm,i,t

σˆm,i,t

.

Wholesale Price Simulations

The objective of simulating the prices rather than relying on standard distribution

theory is to produce accurate prediction densities for calculating confidence bounds.

The residuals from the fisheries returns have features that aren’t consistent with a

normally distributed error process. Abnormally distributed errors are characteristic

of financial time series (Chevallier and Ilepo 2013). Large errors of three standard

deviations or more are too common. Roughly 20% of the normalized residual series

6For some of the estimated models the coefficient on lagged volatility γ2 was significant and large.

However results varied across products significantly. Some parameters were sufficiently large to suggest

an IGARCH model however these were not considered, though they may be tested in the future.

15
have an excess kurtosis observed greater than one and the maximum excess kurtosis

is approximately 5.5. If confidence bounds were based on the canonical assumption

of normally distributed errors they would be too small and fail to contain future

realized returns with the correct probability.

Accurate confidence bounds were produced using a Monte Carlo simulation of the

time series models that randomly sample hypothetical residuals from an empirical

distribution and treats them as realized errors which are propagated through the

estimated time series models. The empirical distributions were constructed from

the residuals of the corresponding estimated models normalize by the volatilities.

Because the time series were relatively short the empirical distribution of residuals

for a single time series is not sufficiently rich to characterize the true error distribution

and may be subject to small sample bias from extreme events. The empirical distributions

were made more robust by pooling normalized residuals across products for a given

model type. The procedures for residual pooling and return simulation are described

in the following sections.

Residual Pooling

For each model and product the 22 residuals across time from the regression

alone were not rich enough to characterize an empirical distribution. Especially,

one potentially subject to extreme events. To see this, consider the case where an

‘abnormally’ large deviation that occurs with probability 0.01 and was observed in

one of the sample years. However, with only 22 under the empirical distribution this

‘abnormal’ event has a 1

22 = 0.045 chance of being draw, thus over representing the

‘abnormal’ event. Residuals pooling can alleviate this problem by using combining

the residuals from the other product regressions into a single empirical distribution

for a given model, {ε ̈m,i,t}|M=m. A sufficient condition validating the pooling is that

the normalized residuals are identically distributed, F( ̈εm,i,t) = F( ̈εm,j,s) for all

products i, j, times s, t and a fixed model m. Equality of distributions across products

16
was supported by Kolmogorov-Smirnov tests.7 Table 3 presents the proportion of

test statistics that reject the null of equal distributions at the 5% significance level is

slightly 5% supporting the assumption that the distributions were equal.

Table 3.– Proportion of tests rejecting the null of equal distributions at 5% significance.

ARMA(0,0) ARMA(0,1) ARMA(0,2) ARMA(0,3) ARMA(1,0) ARMA(1,1)

0.039 0.033 0.044 0.035 0.032 0.036

ARMA(1,2) ARMA(2,0) ARMA(2,1) ARMA(3,0) ETS(AAN) ETS(ANN)

0.043 0.040 0.046 0.038 0.030 0.040

Return Simulation

Return were simulated for the years 2015-2018. Returns were simulated by randomly

sampling from the pooled residual distribution and plugging these samples into the

fitted models. The pooled residual distributions were ordered and indexed prior to

random sampling so that residuals for the same product and time were used when

forecasts were subsequently combined. Thus, for a randomly sampled index ι and

models m and m0,  ̈εm,i,t(ι) and  ̈εm0

,i,t(ι) were sampled normalized residual from the

same product i and same time t but different models. The index ι is a randomly

sampled number from 1, 2, ..., V where V is the number of products times the number

of observations. Let ι(t) be the randomly drawn index (e.g., ι(2015)) so that  ̈εm(ι(t))

is a randomly sampled normalized residual that will be used to simulate year t. The

volatility corrected sampled residual for product i, and model m is ε

∗

m,i,t =  ̈εm(ι(t)) ∗

σm,i,t, where σm,i,t is the fitted GARCH(1,1) volatility. Thus, ˆεm,i,t and ε

∗

m,i,t are the

in-sample residual and randomly sampled residuals; ri,t and ˆrm,i,t are the observed

and fitted (or simulated) returns and ˆfm,i is the fitted model. Informally, residual

pooling is justified under the assumtion that a deviation (suitably normalized) that

occurred in one product market, could have actually occurred in any other product

market.

The following algorithm was used to simulate returns.

7Alternative distribution tests such as the and Anderson-Darling K-sample tests were also

implemented with similar results.

17
1. Randomly draw four indices for the simulated years: ι(2015), ι(2016), ι(2017)

and ι(2018).

2. From the model m pooled residuals and the randomly drawn indices construct

the volatility corrected residuals (as described above): ε

∗

m,i,2015, ε

∗

m,i,2016, ε

∗

m,i,2017,,

ε

∗

m,i,2018.

3. Iteratively calculate the following equations for the fitted model m and product

i:

rˆm,i,2015 = ˆfm,i(ri,2014, ri,2013, ..., εm,i,2014, εm,i,2013, ...) + ε

∗

m,i,2015 (13)

rˆm,i,2016 = ˆfm,i(ˆrm,i,2015, ri,2014, ..., ε∗

m,i,2015, εm,i,2014, ...) + ε

∗

m,i,2016 (14)

rˆm,i,2017 = ˆfm,i(ˆrm,i,2016, rˆm,i,2015, ..., ε∗

m,i,2016, ε∗m,i,2015, ...) + ε

∗

m,i,2017 (15)

rˆm,i,2018 = ˆfm,i(ˆrm,i,2017, rˆm,i,2016, ..., ε∗

m,i,2017, ε∗m,i,2016, ...) + ε

∗

m,i,2018 (16)

4. Repeat steps 2 and 3 for all models m ∈ M.

5. Repeat steps 1-4 10,000 times.

6. Repeat steps 1-5 for each product i ∈ I.

Forecast Combination

Forecast combination is a method for aggregating multiple forecasts from a set

of models, typically using an average or weighted average. Forecast combination

frequently improves forecast ability by permitting simultaneous use of many models

that capture different features of the dynamic process.

The AICc goodness-of-fit statistics of the ARMA and ETS models that were used

here generally fall within a small range as displayed by the clustering in Figure 1.

This indicates that no single model significantly outperforms other models.8 The

limited number of observations prevent the use of a hold-out sample to construct a

more robust forecast criterion for out-of-sample goodness-of-fit (e.g., through cross

8Smaller AICc values indicate better model fit.

18
validation). Criterion, such as AICc, that account for model complexity are preferred

to other in-sample measure of fit such as Mean Squared Error (Burnham and Anderson

2002).

Pacific cod head and gut

pollock fillet

pollock surimi

sablefish head and gut

yellowfin (BSAI) head and gut

190 200 210 220

AICc

Product

Figure 1.– AICc statistics of key products.

To account for the relative goodness-of-fit of the competing models, AICc weights

were used for the weighted average of the forecast models. Weights were calculated

by comparing the AICc statistic of each model relative the minimum AICc statistic

(i.e., the model with the best fit):

ωm,i =

exp(−0.5 ∗ (AICm,i − AICmin,i))

PM

k=1 exp(−0.5 ∗ (AICk,i − AICmin,i))

, (17)

where AICm,i is the AICc statistic of model m and product i; AICmin = minm(AICm,i).

Empirical forecasting research has found that forecast combination using a simple

average ( 1

N

forecast combination) generally performs very well and sometimes performs

better than weighted averages based on forecast ability or model fit (Timmermann

2006). In practice, this empirical result is accounted for by shrinking the model-fit

weights (Eq. 17) towards the simple average 1

N

. A shrinkage factor of 0.5 is used and

the limited number of observations hinder the tuning of an optimal shrinkage factor.

Trials with alternative factors local to 0.5 yielded qualitatively similar forecast results,

19
ω

∗

m,i = 0.5 ∗ ωm,i + 0.5 ∗ 1/N. (18)

The ARMA(0,0) (random walk), MA(1), MA(2), and AR(1) models tend to fit

best and account for 51% of the weight on average (Table 4).9

Each of the 10,000 return projections were combined using a weighted average of

the projected returns (Eq. 13) with the model weights in Equation 18,

rˆ

∗

i,t =

X

M

m=1

ω

∗

m,i ∗ rˆm,i,t. (19)

9ARMA(0,1)=MA(1), ARMA(0,2)=MA(2) and ARMA(1,0)=AR(1)

20
Table 4.– Forecast combinations model weights.

Product ARMA.0.0. ARMA.1.0. ARMA.2.0. ARMA.3.0. ARMA.0.1. ARMA.1.1. ARMA.2.1. ARMA.0.2. ARMA.1.2. ARMA.0.3. EPLCK Suri 0.056 0.106 0.057 0.048 0.075 0.056 0.044 0.292 0.090 0.091 0PLCK Roe 0.045 0.043 0.342 0.105 0.044 0.043 0.106 0.084 0.051 0.054 0PLCK Flt 0.177 0.079 0.121 0.090 0.085 0.070 0.068 0.108 0.056 0.054 0PLCK DsFlt 0.290 0.112 0.057 0.044 0.111 0.057 0.044 0.057 0.044 0.047 0PLCK Other 0.043 0.056 0.053 0.044 0.341 0.108 0.054 0.108 0.054 0.054 0PCOD Flt 0.201 0.088 0.065 0.046 0.096 0.110 0.058 0.124 0.059 0.059 0PCOD H&G 0.290 0.108 0.060 0.047 0.109 0.076 0.049 0.062 0.049 0.051 0PCOD Other 0.141 0.068 0.138 0.059 0.076 0.067 0.061 0.169 0.065 0.065 0SABL H&G 0.164 0.073 0.059 0.045 0.074 0.094 0.066 0.193 0.070 0.070 0YLWS H&G 0.294 0.109 0.058 0.045 0.110 0.081 0.050 0.059 0.050 0.045 0RCKS H&GwR 0.105 0.063 0.049 0.071 0.131 0.133 0.073 0.153 0.063 0.071 0RCKS H&G 0.063 0.189 0.074 0.051 0.200 0.077 0.061 0.084 0.050 0.066 0GLDT H&G 0.057 0.052 0.054 0.045 0.242 0.118 0.060 0.137 0.087 0.064 0ARTH H&G 0.042 0.045 0.057 0.048 0.314 0.114 0.060 0.121 0.058 0.059 0FLTS H&G 0.202 0.117 0.062 0.058 0.119 0.059 0.104 0.061 0.050 0.074 0REXS Whole 0.194 0.083 0.074 0.053 0.088 0.057 0.076 0.141 0.063 0.068 0SHAL Flt 0.177 0.111 0.076 0.048 0.144 0.107 0.048 0.090 0.054 0.053 0AMAK H&G 0.283 0.109 0.068 0.056 0.113 0.062 0.048 0.065 0.046 0.050 0RCKF H&G 0.230 0.099 0.079 0.057 0.107 0.082 0.053 0.092 0.055 0.050 0

21
Calculating Price Projection Confidence Bounds

Prices were calculated by inverting the calculation made for returns (see the

section titled Price Stationarity and Return Calculations). Simulated future returns

were used to constructed simulated prices by starting from the calculated now-cast

price ˇpi,2014 and using predicted returns to calculate the t+ 1 price: pi,t ∗exp(ˆri,t+1) =

pˆi,t+1. Iterating this calculation forward produces prices for the years 2015 to 2018.

Prices were calculated for each fo the 10,000 simulated combined forecasts. The

result is a distribution of simulated projected prices.

Confidence bounds for prices were obtained by calculating quantiles of the forecast

distributions. Calculations were made for the 5%, 10%, 20%, 30%, 50%, 70%, 80%,

90%, and 95% quantiles. Intervals can be obtained by using the corresponding confidence

bounds. For example, a 90% confidence interval can be constructed from the 5% and

95% confidence bounds.

Empirical Illustration of Price Projection Methods to Pollock Surimi, Fillets

and Roe

The following empirical example illustrates the results of applying the previously

described methods to pollock surimi, pollock fillets (excluding deep-skin fillets), and

pollock roe. With a catch of 1.37 million metric tons (t) in 2013 the North Pacific

pollock fishery is the largest fishery by volume in the United States. The first-wholesale

revenue totaled $1.33 billion in 2013 making it the highest value groundfish fishery in

Alaska (Fissel et al. 2014). Surimi, fillets and roe are primary product types made

from pollock and accounted for 28.4%, 28.1% and 8.7% of the total first-wholesale

value from pollock in 2013. Table 5 summarizes the realized first-wholesale prices

from 2011 to 2013 and price projections for 2014 to 2016. The summary data provided

for the years 2014 to 2016 are the expected price (mean) and 90% confidence bounds.

Tables 6, 7, and 8 provide a finer breakdown of the prediction densities. Confidence

bounds give the probability that the price will fall within the bound. Thus, for the

5% bound, 5% of the simulated prices were less than the given value. Similarly, for

22
Table 5.– Pollock surimi, fillet and roe price projection summary.

Product Stat. 2011 2012 2013 2014 2015 2016

PLCK Suri mean 1.281 1.422 1.005 1.044 0.98 0.998

PLCK Suri CI 90 [1.03,1.06] [0.89,1.08] [0.9,1.12]

PLCK Flt mean 1.5 1.469 1.354 1.351 1.409 1.418

PLCK Flt CI 90 [1.33,1.37] [1.31,1.52] [1.29,1.56]

PLCK Roe mean 3.595 4.226 3.253 2.675 2.901 3.109

PLCK Roe CI 90 [2.63,2.72] [2.67,3.17] [2.71,3.58]

the 95% bound, 95% of the simulated prices were less (and 5% were greater). Hence,

the region between the 5% and 95% bounds can be interpreted as the 90% confidence

bound. Smaller confidence bounds indicate less uncertainty in the projections. Figures 2,

3, and 4 display the mean predicted price and 90%, 80%, 60% and 40% confidence

intervals corresponding to the confidence bounds in the tables.

Figure 2.– Pollock surimi price projections and confidence bounds.

23
Table 6.– Projected mean, probability bounds of first-wholesale pollock surimi prices.

Lower Upper

5% 10% 20% 30% Mean Median 70% 80% 90% 95%

2014 1.00 1.01 1.02 1.03 1.04 1.04 1.06 1.07 1.08 1.09

2015 0.71 0.76 0.83 0.89 0.98 0.98 1.08 1.15 1.24 1.34

2016 0.69 0.76 0.84 0.90 1.00 1.01 1.12 1.19 1.30 1.42

2017 0.61 0.68 0.78 0.86 0.99 0.99 1.15 1.25 1.42 1.59

2018 0.55 0.63 0.74 0.83 0.98 0.99 1.18 1.30 1.52 1.73

At the ’Lower’ and ’Upper’ bounds x% of the simulated prices were less. The confidence bounds are the

regions between the ’Upper’ and ’Lower’ bounds.

Pollock surimi return volatility projections

Hist. Avg. 2015 2016 2017 2018 Long-run

20.61 20.60 20.60 20.60 20.60 20.60

24
Figure 3.– Pollock fillet price projections and confidence bounds.

Table 7.– Projected mean, probability bounds of first-wholesale pollock fillet prices.

Lower Upper

5% 10% 20% 30% Mean Median 70% 80% 90% 95%

2014 1.30 1.31 1.32 1.33 1.35 1.35 1.37 1.38 1.40 1.41

2015 1.11 1.17 1.25 1.31 1.41 1.42 1.52 1.59 1.68 1.78

2016 1.03 1.11 1.21 1.29 1.42 1.42 1.56 1.66 1.81 1.95

2017 1.00 1.08 1.20 1.28 1.43 1.43 1.61 1.72 1.89 2.04

2018 0.98 1.07 1.19 1.29 1.45 1.46 1.65 1.77 1.97 2.15

At the ’Lower’ and ’Upper’ bounds x% of the simulated prices were less. The confidence bounds are the

regions between the ’Upper’ and ’Lower’ bounds.

Pollock fillet return volatility projections

Hist. Avg. 2015 2016 2017 2018 Long-run

14.84 14.84 14.84 14.84 14.84 14.84

25
Figure 4.– Pollock roe price projections and confidence bounds.

Table 8.– Projected mean, probability bounds of first-wholesale pollock roe prices.

Lower Upper

5% 10% 20% 30% Mean Median 70% 80% 90% 95%

2014 2.53 2.56 2.60 2.63 2.67 2.67 2.72 2.75 2.79 2.82

2015 2.17 2.33 2.53 2.67 2.90 2.92 3.17 3.34 3.55 3.81

2016 1.99 2.21 2.49 2.71 3.11 3.11 3.58 3.87 4.33 4.83

2017 1.77 1.97 2.25 2.48 2.89 2.89 3.37 3.69 4.20 4.71

2018 1.57 1.78 2.05 2.27 2.67 2.68 3.15 3.47 3.97 4.43

At the ’Lower’ and ’Upper’ bounds x% of the simulated prices were less. The confidence bounds are the

regions between the ’Upper’ and ’Lower’ bounds.

Pollock roe return volatility projections

Hist. Avg. 2015 2016 2017 2018 Long-run

20.10 17.69 20.32 19.91 20.28 20.22

The now-cast price projections for the year 2014 displays a modest degree of

variation with the 90% confidence bounds within approximately 1.5% of the projected

price. The accuracy of the now-cast predictions is a reflection of the fact that the

majority of these products are exported, thus export prices are a strong predictor of

first-wholesale prices.

As prices are projected past 2014 the confidence bounds grow reflecting increased

uncertainty further out in the future. Price projections for the years 2015 to 2018

26
typically display some degree of mean reversion as prices attempt to stabilize the

equilibrium trends estimated by the ARMA and ETS models. The mean price projection

for surimi is fairly stable however there is considerable uncertainty as displayed by

the wide confidence bounds (Fig. 2). While the estimated volatility for surimi is

substantial it is expected to remain constant over 2015 to 2018 (Tables 6). Fillet

price projection shows a slight upward trend in the mean (Fig. 3) and are slightly

less volatile relative to surimi (Table 7). The mean price projection for roe is more

erratic which is likely a reflection that the precipitous decline since 2005 has left the

current price far from the estimated steady state (Fig. 4). Furthermore, the recent

volatility is expected to persist as predicted to increase roe volatility is predicted to

increase over 2015 to 2018 (Fig. 8).

Conclusions

This report describes the methodology applied in projecting annual prices of

Alaska fisheries first-wholesale products in the Stock Assessment and Fishery Evaluation

Report for the Groundfish Fisheries of the Gulf of Alaska and Bering Sea/Aleutian

Island Area: Economic Status of the Groundfish Fisheries Off Alaska, 2013 Fissel

et al. (2014). The data and methods described are intended to be sufficient for the

reader to evaluate and reproduce the methods.

An empirical illustration of the forecast methods has been included to show how

the described methods were applied. Now-casts for the year 2014 were made with

fairly high precision because of the availability of contemporaneous data related to

the product markets for which predictions are being made. Price projections for the

years 2015 to 2018 contain considerably more uncertainty, however; the predictive

densities retrospectively are consistent in the sense that they accurately reflect historically

deviation from the models. Quantiles of the predictive distribution are shown to give

a probabilistic characterization of the range of future prices. Thus, the methods and

resultant price projections give policymakers, researchers, and the public accurate,

27
contemporaneous first-wholesale price information and realistic bounds for the range

of future prices.

The Economics and Social Sciences Research Program at the Alaska Fisheries

Science Center plans to continue to include price projections as a component of the

annual Economic SAFE. As forecasting methods are improved in the future or new

data elements are incorporated, these methods may be revised. Any new methods

will be published in future technical documents.

28
Citations

Banbura, M., D. Giannone, M. Modugno, and L. Reichlin. 2013. Now-casting and

the real-time data flow. In G. Elliott and A. Timmermann (editors), Handbook of

economic forecasting, volume 2A. North-Holland.

Burnham, K. P. and D. R. Anderson. 2002. Model selection and multimodel

inference: a practical information-theoretic approach. Springer.

Chevallier, J. and F. Ilepo. 2013. The Economics of Commodity Markets. John

Wiley & Sons.

Fissel, B., M. Dalton, R. Felthoven, B. Garber-Yonts, A. Haynie, A. Himes-Cornell,

S. Kasperski, J. Lee, D. Lew, and C. Seung. 2014. Stock assessment and fishery

evaluation report for the groundfish fisheries of the Gulf of Alaska and Bering

Sea/Aleutian Island area: Economic status of the groundfish fisheries off Alaska,

2013. North Pacific Fishery Management Council. P.O. Box 103136, Anchorage,

AK.

Hamilton, J. 1994. Time Series Analysis. Princeton University Press, Princeton, NJ.

Hyndman, R. and G. Athanasopoulos. 2013. Forecasting: principles and practice.

http://otexts.org/fpp/. Accessed on Feb. 2014.

Timmermann, A. 2006. Forecast combinations. In G. Elliott, C. Granger,

and A. Timmermann (editors), Handbook of Economic Forecasting, volume 1.

North-Holland.

29

Coefficient Tables

Table 9.– ARMA model AICc and coefficients.

product model AICc intercept ar1 ar2 ar3 ma1 ma2 ma3

PLCK Suri ARMA(0,3) 210.62 -1.45 -0.79 0.91 0.10

PLCK Suri ARMA(1,0) 210.24 -0.67 -0.54

PLCK Suri ARMA(2,0) 213.10 -0.50 -0.58 -0.08

PLCK Suri ARMA(3,0) 214.66 -1.08 -0.60 0.10 0.33

PLCK Suri ARMA(0,0) 213.21 -1.70

PLCK Suri ARMA(1,1) 213.15 -0.58 -0.49 -0.07

PLCK Suri ARMA(2,1) 216.49 -0.78 -0.06 0.28 -0.47

PLCK Suri ARMA(0,2) 207.45 -1.24 -0.86 1.00

PLCK Suri ARMA(0,1) 211.53 -0.36 -0.43

PLCK Suri ARMA(1,2) 210.63 -1.45 0.10 -0.89 1.00

PLCK Roe ARMA(0,2) 205.98 -2.36 -0.26 -0.74

PLCK Roe ARMA(1,2) 209.00 -2.40 0.14 -0.30 -0.69

PLCK Roe ARMA(0,3) 208.34 -2.47 0.05 -0.70 -0.35

PLCK Roe ARMA(2,1) 205.05 -2.37 0.14 -0.68 -0.18

PLCK Roe ARMA(2,0) 202.06 -2.32 0.05 -0.68

PLCK Roe ARMA(3,0) 205.08 -2.36 -0.03 -0.68 -0.11

PLCK Roe ARMA(0,0) 210.97 -3.02

PLCK Roe ARMA(1,0) 213.60 -3.06 0.04

PLCK Roe ARMA(0,1) 211.82 -3.18 0.53

PLCK Roe ARMA(1,1) 213.36 -2.97 -0.35 0.72

PLCK Flt ARMA(1,0) 192.07 0.67 -0.07

PLCK Flt ARMA(2,0) 190.49 1.22 -0.11 -0.45

PLCK Flt ARMA(1,1) 192.51 1.74 0.64 -1.00

PLCK Flt ARMA(2,1) 192.58 1.18 -0.36 -0.50 0.32

PLCK Flt ARMA(3,0) 191.37 0.89 0.03 -0.41 0.33

31
PLCK Flt ARMA(0,1) 191.77 0.92 -0.23

PLCK Flt ARMA(0,0) 189.52 0.57

PLCK Flt ARMA(0,3) 194.15 0.61 0.02 -0.27 0.40

PLCK Flt ARMA(0,2) 190.83 2.15 -0.23 -0.77

PLCK Flt ARMA(1,2) 193.77 2.00 0.23 -0.37 -0.63

PLCK DsFlt ARMA(1,0) 159.21 1.91 -0.12

PLCK DsFlt ARMA(0,3) 164.32 2.08 -0.42 -0.20 -0.39

PLCK DsFlt ARMA(1,1) 162.23 1.91 -0.42 0.30

PLCK DsFlt ARMA(2,1) 165.70 1.91 -0.21 0.05 0.11

PLCK DsFlt ARMA(0,2) 162.20 1.91 -0.09 0.10

PLCK DsFlt ARMA(0,0) 156.75 1.92

PLCK DsFlt ARMA(0,1) 159.24 1.91 -0.10

PLCK DsFlt ARMA(2,0) 162.20 1.91 -0.11 0.07

PLCK DsFlt ARMA(1,2) 165.67 1.91 -0.20 0.10 0.08

PLCK DsFlt ARMA(3,0) 165.66 1.91 -0.11 0.06 -0.04

PLCK Other ARMA(2,1) 196.44 5.43 -0.03 0.05 -1.00

PLCK Other ARMA(1,1) 193.18 5.44 -0.03 -1.00

PLCK Other ARMA(0,3) 196.40 5.42 -1.03 0.12 -0.09

PLCK Other ARMA(0,2) 193.19 5.44 -1.03 0.03

PLCK Other ARMA(0,1) 190.25 5.43 -1.00

PLCK Other ARMA(0,0) 200.51 4.47

PLCK Other ARMA(1,0) 196.26 4.80 -0.52

PLCK Other ARMA(2,0) 196.81 4.99 -0.70 -0.32

PLCK Other ARMA(1,2) 196.49 5.44 -0.38 -0.65 -0.35

PLCK Other ARMA(3,0) 200.09 5.01 -0.72 -0.35 -0.04

PCOD Flt ARMA(1,0) 191.07 1.82 -0.11

PCOD Flt ARMA(2,0) 192.43 2.05 -0.14 -0.26

PCOD Flt ARMA(3,0) 195.64 2.09 -0.16 -0.27 -0.06

PCOD Flt ARMA(0,0) 188.66 1.76

32
PCOD Flt ARMA(1,1) 190.24 2.79 0.53 -1.00

PCOD Flt ARMA(2,1) 192.98 2.92 0.59 -0.16 -1.00

PCOD Flt ARMA(0,2) 189.87 2.98 -0.46 -0.54

PCOD Flt ARMA(0,1) 190.78 1.94 -0.23

PCOD Flt ARMA(0,3) 192.93 2.93 -0.41 -0.48 -0.10

PCOD Flt ARMA(1,2) 192.86 2.90 0.24 -0.64 -0.36

PCOD H&G ARMA(1,1) 200.09 2.26 0.72 -1.00

PCOD H&G ARMA(2,1) 203.12 2.53 0.78 -0.12 -1.00

PCOD H&G ARMA(0,1) 198.79 1.21 -0.07

PCOD H&G ARMA(0,0) 196.22 1.17

PCOD H&G ARMA(1,0) 198.82 1.19 -0.05

PCOD H&G ARMA(2,0) 201.35 1.40 -0.06 -0.14

PCOD H&G ARMA(3,0) 203.64 1.84 -0.10 -0.17 -0.22

PCOD H&G ARMA(1,2) 203.15 2.47 0.62 -0.85 -0.15

PCOD H&G ARMA(0,3) 202.61 2.89 -0.23 -0.30 -0.47

PCOD H&G ARMA(0,2) 201.11 1.67 -0.13 -0.18

PCOD Other ARMA(0,3) 196.72 0.09 0.13 -0.53 0.01

PCOD Other ARMA(0,2) 193.41 0.11 0.14 -0.54

PCOD Other ARMA(1,2) 196.72 0.10 -0.01 0.15 -0.53

PCOD Other ARMA(0,0) 194.00 -0.81

PCOD Other ARMA(1,0) 196.59 -0.89 0.06

PCOD Other ARMA(2,0) 193.96 0.02 0.06 -0.48

PCOD Other ARMA(3,0) 197.27 0.02 0.06 -0.48 0.00

PCOD Other ARMA(0,1) 196.08 -1.06 0.37

PCOD Other ARMA(1,1) 196.61 -0.86 -0.49 0.85

PCOD Other ARMA(2,1) 197.04 -0.20 -0.36 -0.43 0.54

SABL H&G ARMA(0,0) 184.96 3.47

SABL H&G ARMA(1,0) 187.61 3.48 -0.03

SABL H&G ARMA(2,0) 188.73 3.63 -0.03 -0.29

33
SABL H&G ARMA(3,0) 191.89 3.73 -0.06 -0.31 -0.10

SABL H&G ARMA(0,1) 187.59 3.49 -0.06

SABL H&G ARMA(1,1) 186.56 3.77 0.54 -1.00

SABL H&G ARMA(2,1) 187.98 3.83 0.65 -0.29 -1.00

SABL H&G ARMA(0,2) 184.42 3.82 -0.32 -0.68

SABL H&G ARMA(1,2) 187.67 3.81 0.09 -0.38 -0.62

SABL H&G ARMA(0,3) 187.69 3.82 -0.30 -0.66 -0.05

YLWS H&G ARMA(3,0) 190.91 1.49 -0.07 -0.11 -0.11

YLWS H&G ARMA(0,1) 185.13 1.28 -0.07

YLWS H&G ARMA(1,1) 186.17 2.06 0.72 -1.00

YLWS H&G ARMA(2,1) 189.28 2.20 0.78 -0.10 -1.00

YLWS H&G ARMA(0,2) 187.82 1.42 -0.08 -0.11

YLWS H&G ARMA(1,2) 189.30 2.18 0.65 -0.88 -0.12

YLWS H&G ARMA(0,3) 190.88 1.69 -0.10 -0.14 -0.13

YLWS H&G ARMA(1,0) 185.14 1.27 -0.05

YLWS H&G ARMA(2,0) 187.89 1.37 -0.06 -0.10

YLWS H&G ARMA(0,0) 182.54 1.27

RCKS H&GwR ARMA(2,0) 203.99 -2.61 -0.17 -0.25

RCKS H&GwR ARMA(0,3) 201.25 -2.40 -0.45 -0.23 -0.32

RCKS H&GwR ARMA(1,1) 199.06 -2.32 0.37 -1.00

RCKS H&GwR ARMA(2,1) 201.14 -2.30 0.43 -0.24 -1.00

RCKS H&GwR ARMA(3,0) 201.27 -2.74 -0.27 -0.24 -0.58

RCKS H&GwR ARMA(0,1) 199.16 -2.22 -1.00

RCKS H&GwR ARMA(0,0) 199.90 -2.91

RCKS H&GwR ARMA(1,0) 202.00 -2.75 -0.16

RCKS H&GwR ARMA(0,2) 198.66 -2.30 -0.62 -0.38

RCKS H&GwR ARMA(1,2) 201.85 -2.32 0.15 -0.73 -0.27

RCKS H&G ARMA(1,2) 212.10 0.66 -0.84 0.22 -0.37

RCKS H&G ARMA(0,3) 210.01 1.37 -0.78 0.14 -0.36

34
RCKS H&G ARMA(0,0) 210.49 -0.16

RCKS H&G ARMA(1,0) 206.56 0.21 -0.51

RCKS H&G ARMA(0,2) 209.01 1.63 -0.84 -0.16

RCKS H&G ARMA(3,0) 212.01 0.48 -0.53 -0.14 -0.20

RCKS H&G ARMA(0,1) 206.41 0.84 -0.61

RCKS H&G ARMA(1,1) 209.36 0.70 -0.09 -0.52

RCKS H&G ARMA(2,0) 209.51 0.24 -0.52 -0.02

RCKS H&G ARMA(2,1) 210.42 1.25 0.23 0.26 -1.00

GLDT H&G ARMA(1,0) 216.88 2.90 -0.28

GLDT H&G ARMA(2,0) 216.36 3.19 -0.38 -0.38

GLDT H&G ARMA(3,0) 219.27 3.20 -0.44 -0.43 -0.14

GLDT H&G ARMA(0,0) 216.05 3.06

GLDT H&G ARMA(1,1) 212.79 2.74 0.22 -1.00

GLDT H&G ARMA(2,1) 215.50 2.74 0.24 -0.16 -1.00

GLDT H&G ARMA(0,2) 212.34 2.76 -0.69 -0.31

GLDT H&G ARMA(0,1) 210.91 2.71 -1.00

GLDT H&G ARMA(0,3) 215.17 2.77 -0.72 -0.46 0.18

GLDT H&G ARMA(1,2) 213.76 2.81 -0.59 0.00 -1.00

ARTH H&G ARMA(1,1) 221.90 5.02 -0.13 -1.00

ARTH H&G ARMA(2,1) 224.55 5.13 -0.18 -0.19 -1.00

ARTH H&G ARMA(0,1) 219.32 5.01 -1.00

ARTH H&G ARMA(0,0) 231.66 4.80

ARTH H&G ARMA(1,0) 228.04 3.94 -0.51

ARTH H&G ARMA(2,0) 225.05 5.27 -0.73 -0.59

ARTH H&G ARMA(3,0) 226.83 5.31 -0.88 -0.74 -0.34

ARTH H&G ARMA(1,2) 224.84 5.07 0.35 -1.55 0.55

ARTH H&G ARMA(0,3) 224.68 5.10 -1.17 0.04 0.14

ARTH H&G ARMA(0,2) 221.73 5.04 -1.19 0.19

FLTS H&G ARMA(2,0) 190.22 3.01 0.27 -0.14

35
FLTS H&G ARMA(0,3) 189.21 2.83 -0.13 -0.41 -0.46

FLTS H&G ARMA(1,1) 190.51 3.12 0.11 0.14

FLTS H&G ARMA(2,1) 187.87 2.67 0.98 -0.46 -1.00

FLTS H&G ARMA(3,0) 190.52 2.76 0.23 -0.01 -0.37

FLTS H&G ARMA(0,1) 187.59 3.13 0.23

FLTS H&G ARMA(0,0) 186.17 3.35

FLTS H&G ARMA(1,0) 187.64 3.17 0.23

FLTS H&G ARMA(0,2) 190.28 3.09 0.31 0.16

FLTS H&G ARMA(1,2) 191.91 2.96 -0.95 1.35 0.47

REXS Whole ARMA(0,1) 178.68 1.77 0.19

REXS Whole ARMA(1,1) 180.84 1.79 -0.72 1.00

REXS Whole ARMA(0,3) 179.62 0.20 -0.21 -0.48 -0.32

REXS Whole ARMA(2,1) 179.09 -0.08 0.71 -0.44 -1.00

REXS Whole ARMA(3,0) 181.25 0.87 -0.02 -0.36 -0.27

REXS Whole ARMA(0,2) 177.07 0.08 -0.33 -0.67

REXS Whole ARMA(0,0) 176.34 1.60

REXS Whole ARMA(1,0) 178.90 1.70 0.09

REXS Whole ARMA(2,0) 179.32 1.13 0.09 -0.37

REXS Whole ARMA(1,2) 180.05 0.19 0.25 -0.50 -0.50

SHAL Flt ARMA(1,2) 199.18 -1.05 0.49 -0.99 -0.01

SHAL Flt ARMA(1,0) 195.80 -1.63 -0.24

SHAL Flt ARMA(2,0) 197.16 -1.51 -0.32 -0.28

SHAL Flt ARMA(3,0) 200.46 -1.51 -0.33 -0.28 -0.02

SHAL Flt ARMA(0,3) 199.20 -0.33 -0.52 0.26 0.64

SHAL Flt ARMA(0,0) 194.52 -1.65

SHAL Flt ARMA(1,1) 195.87 -1.05 0.49 -1.00

SHAL Flt ARMA(0,2) 196.49 -0.94 -0.57 -0.43

SHAL Flt ARMA(0,1) 195.02 -1.57 -0.36

SHAL Flt ARMA(2,1) 200.46 -1.51 -0.30 -0.27 -0.02

36
AMAK H&G ARMA(0,2) 215.66 3.22 -0.16 -0.15

AMAK H&G ARMA(0,3) 217.59 3.59 0.11 -0.19 -0.40

AMAK H&G ARMA(2,0) 215.48 3.32 -0.10 -0.24

AMAK H&G ARMA(1,2) 218.91 3.23 0.14 -0.28 -0.13

AMAK H&G ARMA(0,0) 211.13 2.90

AMAK H&G ARMA(1,0) 213.64 2.89 -0.08

AMAK H&G ARMA(2,1) 218.30 3.40 0.16 -0.25 -0.29

AMAK H&G ARMA(3,0) 216.64 3.46 -0.17 -0.25 -0.32

AMAK H&G ARMA(0,1) 213.52 2.92 -0.15

AMAK H&G ARMA(1,1) 215.98 3.11 0.40 -0.58

RCKF H&G ARMA(1,0) 202.70 0.35 0.12

RCKF H&G ARMA(1,1) 203.30 0.72 -0.65 1.00

RCKF H&G ARMA(2,0) 203.48 0.96 0.16 -0.32

RCKF H&G ARMA(3,0) 205.17 1.20 0.08 -0.28 -0.28

RCKF H&G ARMA(0,1) 202.42 0.40 0.21

RCKF H&G ARMA(0,3) 206.35 1.38 0.05 -0.38 -0.11

RCKF H&G ARMA(2,1) 205.69 1.24 0.53 -0.39 -0.44

RCKF H&G ARMA(0,2) 202.88 1.78 0.25 -0.75

RCKF H&G ARMA(1,2) 205.44 1.75 0.52 -0.56 -0.44

RCKF H&G ARMA(0,0) 200.34 0.41

37
Table 10.– ETS model AICc and coefficients.

product model AICc alpha beta l b

PLCK Suri ETS(AAN) 226.42 0.05 0.05 -16.40 3.85

PLCK Suri ETS(ANN) 218.81 0.00 -1.69

PLCK Roe ETS(ANN) 216.57 0.00 -3.06

PLCK Roe ETS(AAN) 221.87 0.00 0.00 3.16 -0.55

PLCK Flt ETS(ANN) 195.12 0.00 0.57

PLCK Flt ETS(AAN) 203.49 0.00 0.00 -7.48 1.87

PLCK DsFlt ETS(AAN) 166.03 0.00 0.00 3.94 -0.16

PLCK DsFlt ETS(ANN) 159.95 0.00 1.92

PLCK Other ETS(AAN) 211.81 0.00 0.00 2.01 0.25

PLCK Other ETS(ANN) 206.11 0.00 4.47

PCOD Flt ETS(AAN) 202.89 0.05 0.05 -3.83 1.82

PCOD Flt ETS(ANN) 194.26 0.00 1.76

PCOD H&G ETS(ANN) 201.82 0.00 1.17

PCOD H&G ETS(AAN) 207.17 0.00 0.00 2.57 -0.23

PCOD Other ETS(ANN) 199.61 0.00 -0.81

PCOD Other ETS(AAN) 205.47 0.02 0.00 0.63 -0.18

SABL H&G ETS(ANN) 190.56 0.00 3.49

SABL H&G ETS(AAN) 196.08 0.00 0.00 8.31 -0.38

YLWS H&G ETS(ANN) 188.15 0.00 1.26

YLWS H&G ETS(AAN) 197.00 0.03 0.03 0.72 1.38

RCKS H&GwR ETS(AAN) 211.22 0.00 0.00 -2.60 -0.04

RCKS H&GwR ETS(ANN) 205.51 0.00 -2.91

RCKS H&G ETS(AAN) 222.00 0.00 0.00 -7.39 0.51

RCKS H&G ETS(ANN) 216.09 0.00 -0.17

GLDT H&G ETS(ANN) 221.65 0.00 3.06

GLDT H&G ETS(AAN) 227.74 0.00 0.00 10.82 -0.51

ARTH H&G ETS(AAN) 242.87 0.00 0.00 15.38 -0.83

38
ARTH H&G ETS(ANN) 237.26 0.00 4.79

FLTS H&G ETS(AAN) 197.55 0.00 0.00 4.06 0.03

FLTS H&G ETS(ANN) 191.78 0.00 3.36

REXS Whole ETS(ANN) 180.71 0.00 1.61

REXS Whole ETS(AAN) 186.59 0.00 0.00 7.21 -0.40

SHAL Flt ETS(AAN) 205.45 0.00 0.00 0.66 -0.25

SHAL Flt ETS(ANN) 200.12 0.00 -1.66

AMAK H&G ETS(AAN) 220.42 0.00 0.00 -13.84 1.41

AMAK H&G ETS(ANN) 216.73 0.00 2.89

RCKF H&G ETS(AAN) 211.52 0.00 0.00 -8.89 0.73

RCKF H&G ETS(ANN) 205.95 0.00 0.41

39

RECENT TECHNICAL MEMORANDUMS

Copies of this and other NOAA Technical Memorandums are available from the 

National Technical Information Service, 5285 Port Royal Road, Springfield, VA 22167 

(web site: www.ntis.gov). Paper and electronic (.pdf) copies vary in price. 

AFSC304 HIMES-CORNELL, A. 2015. Industry perceptions of measures to affect access to quota shares, active 

participation, and lease rates in the Bering Sea and Aleutian Islands crab fisheries. U.S. Dep. 

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performance review of the 2014 North Pacific Groundfish and Halibut Observer Program, 55 p. NTIS 

number pending.

301 ALLEN, B. M., and R. P. ANGLISS. 2015. Alaska marine mammal stock assessments, 2014, 304 p.

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300 HELKER, V. T., B. M. ALLEN, and L. A. JEMISON. 2015. Human-caused injury and mortality of 

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299 LEW, D. K., G. SAMPSON, A. HIMES-CORNELL, J. LEE, and B. GARBER-YONTS. 

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2013, 134 p. NTIS No. PB2015-104937.

298 PRESCOTT, M. M., and M. ZIMMERMANN. 2015. Smooth sheet bathymetry of Norton Sound, 23 p.

NTIS No. PB2015-104936. 

297 VON SZALAY, P. G. 2015. The impact of sample size reduction on the precision of biomass estimates 

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296 STONE, R. L., D. STEVENSON, and S. BROOKE. 2015. Assessment of a pilot study to collect coral 

bycatch data from the Alaska commercial fishing fleet, 45 p. NTIS No. PB2015-104935. 

295 DALY, B. J., C. E. ARMISTEAD, and R. J. FOY. 2015. The 2013 eastern Bering Sea continental shelf 

bottom trawl survey: Results for commercial crab species, 165 p. NTIS No. PB2015-104934. 

294 FOWLER, C. W., and L. K. JOHNSON. 2015. Reality-based marine protected areas for the eastern 

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293 JOHNSON, S. W., A. D. NEFF, and M. R. LINDEBERG. 2015. A handy field guide to the nearshore 

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292 WHITTLE, J. A., S. C. VULSTEK, C. M. KONDZELA, and J. R. GUYON. 2015. Genetic stock 

composition analysis of chum salmon bycatch from the 2013 Bering Sea walleye pollock trawl fishery, 

50 p. NTIS No. PB2015-104931. 

291 GUYON, J. R., C. M. GUTHRIE III, A. R. MUNRO, J. JASPER, and W. D. TEMPLIN. 2015. Genetic 

stock composition analysis of the Chinook salmon bycatch in the Gulf of Alaska walleye pollock (Gadus 

chalcogrammus) trawl fisheries, 26 p. NTIS number pending.

290 GUTHRIE, C. M. III, HV. T. NGUYEN, and J. R. GUYON. 2015. Genetic stock composition analysis of 

the Chinook salmon bycatch from the 2013 Bering Sea walleye pollock (Gadus chalcogrammus) trawl 

fishery, 21 p. NTIS number pending.