Forecasting catfish industry prices using linear and nonlinear methods

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Forecasting catfish industry prices using linear andnonlinear methodsCurtis M. Jolly a , Carel Ligeon b & Nathanael Hishamunda ba Department of Agricultural Economics and Rural Sociology , Auburn University,Alabama Agricultural Experiment Station , Auburn, AL, 36849–5406, USA Phone:334–844–5613 Fax: 334–844–5613 E-mail:b Department of Agricultural Economics and Rural Sociology , Auburn University,Alabama Agricultural Experiment Station , Auburn, AL, 36849–5406, USAPublished online: 13 Nov 2008.

To cite this article: Curtis M. Jolly , Carel Ligeon & Nathanael Hishamunda (1998) Forecasting catfishindustry prices using linear and nonlinear methods, Aquaculture Economics & Management, 2:2, 71-80, DOI:10.1080/13657309809380218

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Forecasting catfish industry prices using linear andnonlinear methods

CURTIS M. JOLLY, CAREL LIGEON & NATHANAEL HISHAMUNDA

Department of Agricultural Economics and Rural Sociology, Auburn University, Alabama Agricultural Experiment Station,Auburn, AL 36849-5406, USA

Abstract

Catfish production has expanded at an increasing ratefrom 1980 to 1994. As production has adjusted overtime so have prices. Catfish farmers and processors areoperating at narrow net margins and knowledge offuture prices and factors influencing prices would behelpful to them in decision making. Theoretical modelssuggest that aquaculture experiences price fluctua-tions which can be analysed by nonlinear models. Inthis paper, autoregressive conditional heteroscedastic(ARCH) models and the generalized autoregressiveconditional heteroscedastic (GARCH) are employedwith ordinary least squares (OLS), unconditional leastsquares (ULS), and maximum likelihood (ML) modelsto forecast prices. These forecasts are compared totraditional OLS model forecasts. AU models had compa-rable statistics (RSME, MAE, R2), but ULS and the MLproduced forecasts with less deviation from the observedvalues. The nonlinear models showed an improvementin price forecasts over the ordinary least squares (OLS)models for prices of whole and frozen catfish.

Keywords: nonlinear models, catfish price forecast

Introduction

Catfish production has become one of the majorgrowth industries in the US agricultural sector. Totalproduction increased from 130 million to over 400million pounds between 1975 and 1993 (Jolly & Clonts1993). The volume of catfish processed in 1993exceeded 459 million pounds and represented a 234%increase since 1983 (USDA 1994; Kinnucan 1995;

Correspondence Prof. Curtis M. Jolly, Department ofAgricultural Economics and Rural Sociology, AgriculturalExperiment Station, Auburn University, Auburn, AL 36849,USA. Tel. 334-844-5613. Fax: 334 8445639. E-mail:[email protected]

Engle & Kouka 1996; Ligeon et al. 1996). In 1997,total quantity of processed catfish is expected tosurpass 500 million pounds, and the total value ofbusiness for the industry is estimated to be over $4billion ( McCall 1997). As production continues, tech-nology and marketing practices of inputs and outputsectors vary over time, and engender changes indemand, supply, and price of marketed catfishproducts.

Traditionally, channel catfish utilised a single batchstocking strategy of uniform-sized fish. Ponds werestocked in March and April and harvested fromSeptember to November of each year. Prices werehence depressed in the Fall (Jolly & Engle 1988; Jolly &Clonts 1993; Tai et al. 1995). Many researchers havefound that these practices affected prices and profitabil-ity. Farmers have attempted to seek alternative strate-gies for mitigating the effects of the traditional produc-tion and marketing practices on prices. Farmers havebegun stocking and harvesting throughout the year(Engle & Pounds 1993). Marketing of fish has beenenhanced by improved storage and processing tech-niques. Though it is believed that these new practiceshave lessened price fluctuations and facilitated theforecasting of prices in the catfish market, littleresearch has been conducted to forecast fish prices. Inthis paper, linear and nonlinear methods of priceanalysis and forecasting are evaluated to determinewhether there is any merit in using more sophisticatedtechniques vs. traditional methods.

Time series analysis of catfish pricesIn the past, decision makers have used ordinary leastsquares (OLS) models in forecasting prices. Forecastswere then improved by the use of a set of linear auto-regressive (AR) models. Autoregressive integratedmoving average (ARIMA) models were consideredsuperior and provided better forecasts (Cicarreli &Narayan 1980; Byers & Peel 1995; Leitch & Tanner1995). Recently, costly attempts have been made to

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72 Forecasting catfish prices • CM. Jolly et al

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pp 71-80

improve the type of forecasts for business decisions byusing a set of nonlinear models to address error distur-bances in time series analysis (Tong 1990; Tiao & Tsay1994).

Some of the techniques used in modelling nonlineartime series include the application of the Autoregres-sive Conditional Heteroscedastic (ARCH) and the Gen-eral Autoregressive Conditional Heteroscedastic(GARCH) models. The traditional regression timeseries models operate under an assumption of constantvariance. The ARCH process introduced by Engle(1982) allows the conditional variance to change overtime as a function of past errors, leaving the uncondi-tional variance constant. The family of GARCH modelsprovides a means of estimating and correcting for thechanging variability of data (Bollerslev 1996). TheGARCH process assumes that the errors, althoughuncorrelated, are not independent, and models theconditional error variance as a function of the pastrealisations of the series (SAS 1993). GARCH has beenapplied to model macroeconomic activities, such asinflation, and interest rates, which experience somevolatility (SAS 1996).

It is common belief that the price of catfish variesseasonally (Nyankori 1991), but with an increasinglong-term trend (Engle & Kouka 1996). However, thecost of production is very sensitive to feed costs as wellas risks due to water quality, disease, parasites, oxygendepletion, winter kill and off-flavour. These factors areimportant in the study of industry prices. Studies oncatfish prices are few, and have indicated that the sea-sonal and cyclical fluctuations in farm, wholesale, andretail prices are minimal. Lambregts et al. (1993)noticed small seasonal variation in demand and pricesin the Texas catfish market. Zidack et al. (1993)accounted for seasonality in their three structuralequations of the catfish industry. Nyankori (1991)used time series analysis to examine price transmissionin the catfish industry and found the existence ofWeigner-Granger causal relationships between farmand wholesale prices of catfish. He stated that the direc-tion of causality in the catfish industry was from farmlevel to the wholesale level for frozen and processedcatfish prices, with a 3-month lag reflecting the well-known partial adjustment process for industry andinstitutional mechanisms. In young industries such ascatfish where margins are narrow and prices arelinked, it is important that industry participants haveaccess to price information to be able to minimise risksassociated to eventual price fluctuations, and toincrease profits. One problem in price forecasting is thechoice of equations.

Model specificationPrevious studies used simultaneous regression modelsin determining price (Kinnucan & Wineholt 1989;Zidack & Hatch 1991; Zidack et al. 1993). In this studythe model form will be:

P¡ = f(T,PFF,QFF)

where:

(1)

Pj = the monthly price of fish product¡ from August1984 to August 1994.

PFF = monthly farm-gate price of whole catfish price,August 1984 to August 1994.

QFF¡ = the quantity offish product¡ during a givenmonth, August 1984 to August 1994.

T = Time trend which represents technological changein production and marketing, August 1984 to August1994.

The product prices studied are processor fresh andfrozen whole and fillet. The explicit format of themodel is:

P¡ = Bo 2PFF + B3QFF + u (2)

where u is the error term.Kinnucan (1995) observed that improved technol-

ogy applied in production resulted in a decline in aver-age output costs over time which resulted in lower realprices, and increased fish consumption. Zidack andHatch have shown decreasing trends in both nominaland real prices of farm-raised catfish from 1980 to1989. If their hypothesis is accepted, the sign of B1

may well be negative. The prices offish at the processorlevel are positively related to the farm price. Hence, asfarm prices increase (ß2 > 0) , the processor prices areexpected to increase. The quantity of fish produced inthe short run, demand remaining constant, is expectedto have a depressing effect on prices. Hence, the coeffi-cient B3 is hypothesised to be negative.

The GARCH models were used to generate the pre-dicted price offish. Results were regressed on time trend,farm price and quantity produced. Three models wereemployed using the GARCH generated prices as depen-dent variables: Ordinary Least Squares (OLS), Uncondi-tional Least Squares (ULS) and Maximum Likelihood(ML). These models were used to make four month fore-casts. The models were evaluated for forecasting pricesusing their root mean square error (RMSE), mean abso-lute error (MAE) and visual observation of their fore-casts, and directional forecast value comparisons.

The GARCH (p,q) regression model is given as:

(3)

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Table 1 Results of alternative models for analysis of fresh and frozen whole catfish prices, US, 1984-94

Model for prices of fresh whole catfish

Standard GARCH

OLS GARCH OLS ULS ML

Model for prices of frozen

Standard

OLS

0.667(10.94)

0.15E-2(8.651)

-

-4.7E-8(-2.459)

1.440(20.80)

0.8603

-

0.050

0.4384

-

GARCH

1.652(6.853)

0.22E-3(0.683)

0.054(999.99)

-

(16.31)

0.9008

-357.18

0.0414

0.4113

-343.96

_

whole catfish

GARCH

OLS

0.792(11.412)

0.14E-2(7.037)

-

-5.38E-8(-2.451)

1.285(4.065)

0.7949

-296.71

0.057

0.4113

-286:13

0.6182

ULS

1.072(7.921)

0.19E-2(1.972)

-

1.03E-8(0.635)

0.72040.754

0.9071

-375.50

0.039

0.1580

-362.28

1.7788

ML

1.052(8.044)

0.18E-2(2.126)

-

9.47E-9(0.580)

0.754(4.321)

0.9071

-375.57

0.039

0.1652

-362.35

1.7638

Intercept

GARCH

QWF

PFARM

R2

AIC

RMSE

MAE

SBC

DW

0.610(7.271)

-0.4E-3(-2.362)

-2.8E-8(-2.368)

1.483(18.44)

0.8533

0.050

0.576

1.553(5.928)

0.001(0.287)

0.676(3.897)

0.917(10.15)

-0.3E-3(-1.885)

0.766(5.978)

-0.31E-3(-0.693)

0.762(6.023)

-0.3E-3(-0.739)

0.8481

-328.1

0.0495

-312.3

-5.9E-8(-4.690)

1.197(13.83)

0.8089

-309.97

0.054

0.598

-299.40

0.9696

-1.16E-8(-0.94)

1.175(7.470)

0.8733

-350.07

0.044

0.4245

-336.85

2.0056

-1.2E-8(-0.988)

1.186(7.675)

0.8733

-350.09

0.044

0.4307

-336.86

1.989

3

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= et-01 ut_i

= V h te t

0sul



pp 71-80

h t=w+

(4)

(5)1=1

where

P t =Xt =b =u t =£j =

h t =

m =

w =

oct =

Yj =

et =

the dependent variable;a vector of explanatory variables;a vector of unknown parameters;the conditional disturbance;unconditional disturbance;GARCH (p,q) conditional variance;order of the autoregressive error model;parameter whose estimate is ARCHp;parameter whose estimate is ARCHj;parameter whose estimate is GARCHJ; anderror in time.

When p = 0, the process reduces to the ARCH(q) pro-cess, and for p = q = 0 is simply white noise.

In this paper the three estimation methods, usedwith the GARCH process, (OLS, ULS and ML) can bedeveloped with missing data. The Yule Walker model isgenerated in the process, but is not examined in thispaper. The estimates of the standard errors calculatedwith the ULS or ML methods take into account jointestimation of the AR and the regression parameters,and may give more accurate standard-error valuesthan YW method. For computational methods of theULS and ML, see SAS ETS User's guide 1993.

DataData on farm-gate prices, processor prices of wholefresh and frozen catfish, processor prices of fresh andfrozen catfish fillet, the monthly quantity of fresh andfrozen processed fish fillet were collected from variousissues of Aquaculture Outlook and Situation Report(USDA 1984); Aquaculture and Situation Report(USDA 1994); and Aquaculture Outlook, Supplemen-tal Report 1995 (USDA 1995). It is important here toput more emphasis on recent past than distant past toobtain meaningful comparison. By using the price datafor the months of years 1986 to mid-1994 and modelresults, we can make some valuable comparisons withthe actual price data for the later months of 1994.

Results

The OLS model estimate for fresh whole catfish showedthat time trend and quantity of whole fish wereinversely related to price of fresh whole catfish, but farm

price was positively related to price of whole dressed fishat the retail level (Table 1). All variables were signifi-cant at the a = 0.05 level. The R2 of the model was 0.85which means that 85% of the variation of the depen-dent variable was explained by the variation of the inde-pendent variables. The RMSE was reasonably low(0.05) and the MAE was 0.576. The small RSME andMAE indicate good model predictive value.

OLS price models of whole frozen catfish producedsimilar results to that of fresh. The time trend was posi-tively related to price. All coefficients were significantat the a = 0.05. The variation of the explanatory vari-ables explained 86% of the variation of the dependentvariable. The RMSE was 0.05.

Models for price of fresh and frozen fillet generatedidentical R2 of 0.88 (Table 2). All coefficients for themodels had similar signs and were significant at thea = 0.05. The RMSE was 0.46 which was similar to theother models.

The GARCH models for whole fresh and frozen fishare seen in Table 1. The results showed an RMSE equalto 0.04. The Schwartz, Bayesian Criterion (SBC) of- 312.31 and the Akaike's Information Criterion (AIC)of- 328.1 were obtained. The lower the AIC and theSBC, the better the fit of the model. The GARCH1 is sig-nificant at the a = 0.05, and therefore, appropriate foruse in the OLS, ULS and the ML models.

The OLS model for fresh whole catfish, with thepredicted price from the GARCH 1, showed that thecoefficients for farm price (PFARM) and quantity ofwhole fish (QWF) were significant at the a = 0.5 level(Table 1). The R2 was 0.80. The MAE was 0.059 andan RMSE of 0.05. The D.W. was 0.97 which is an indi-cation of serial correlation, but is not a problem in fore-casting since the parameters are still unbiased.

ULS model results showed that only farm price posi-tively affected the price of whole fresh fish. The MAEwas 0.42, the RMSE was 0.04, and the SBC and AICwere, respectively, - 336.85 and - 350.07. The D.W.equalled 2.0 which means that serial correlation wasnot a problem. TheR2 was 0.87, meaning that themodel had high explanatory power.

The ML model produced similar results to the ULSmodel in terms of signs of coefficients, MAE and RMSE.The D.W. was 1.99, the SBC and AIC were - 336.86,and - 350.09, respectively. The total R2 of 0.87 is ameasure of how well the next value of prices can bepredicted using the structural part of the model and thepast value of the residual. Since autorelation is not aproblem, the R2 and the total R2 are equal (SAS 1993).Hence, it can be said that the transformed model hashigh predictive properties.


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CM. Jolly et al • Forecasting catfish prices 75

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76 Forecasting catfish prices • C. M. }olly et al

For frozen whole catfish, the G ARCH 1 was signifi-cant at the a = 0.05 and was thus used to generate pre-dicted prices of frozen whole catfish. The RMSE was0.041, the SBC w a s - 343.96, AIC- 357.18. The totalR2 was 0.90.

The OLS model had all coefficients significant ata = 0.05. All variables showed positive variation withprice, but the trend. A positive time trend means thatprices are increasing over time which is inconsistentwith the statement made by Kinnucan (1995). Theprice of processed fish may be increasing in time sinceprocessed fish have a longer shelf live than nonpro-cessed. Here the seller is better able to control supplyand thus can influence price. RMSE was 0.05, the AIC- 296.7 and the SBC was 286.13. The D.W. was 0.62and the total R2 was 0.79.

The ULS had results almost identical to the OLS.Time trend significantly influenced price. The samewas true with the ML. The other statistics are seen inTable 1.

For the fillet frozen result of the G ARCH process wassignificant and was used as the dependent variable.The OLS model showed that all coefficients were posi-tive and significant at a = 0.05, but price of fish wasinversely influenced by the quantity offish. The RMSE

was 0.06 and the MAE 0.32 (Table 2). All models werecharacterized by high total R2, relatively low MAEsand RSMEs. The quantity of fish did not affect price inthe UL and ML models, but the farm price affected theprices of fillet. This phenomenon was expected since fil-let shelf life was lengthened with the introduction ofimproved processing technology, and the supply hasbecome more controllable.

ForecastingThe AIC, SBC and the R2 showed that the traditionalOLS and the models developed from the GARCH pro-cedure had good fit. The low MAE, RMSE indicatethat all equations were good forecast models. There islittle difference in the RSME and MAE of the modelsderived from the GARCH. The ULS and ML derivedfrom GARCH process seemed to have lower RMSEthan the traditional OLS models. Though all modelsproduced almost similar statistics, when comparingthe 4 months forecast with that observed during thesame period (Table 3), the ULS and ML models devi-ated less from the forecasts than the OLS model,derived from traditional procedure and from theGARCH. The deviations for all models were alwaysless for the earlier years than the future years which

Table 3 Observed and forecast prices for whole and fillet fresh and frozen catfish and percent difference, August to November 1994



vp 71-80

OLS FORECAST

Aug.Sept.Oct.Nov.

GARCHAug.Sept.Oct.Nov.

GARCHAug.Sept.Oct.Nov.

GARCH

Aug.Sept.Oct.Nov.

Observed

Whole

Fresh

1.721.721.721.70

(Ib)

Frozen

2.062.062.062.02

OLS FORECAST1.721.721.721.70

2.062.062.062.02

ULS FORECAST1.721.721.721.70

2.062.062.062.02

ML FORECAST

1.721.721.721.70

2.062.062.062.02

Fillet (Ib)

Fresh

2.932.932.932.91

2.932.932.932.91

2.932.932.932.91

2.932.932.932.91

Frozen

2.902.872.872.88

2.902.872.872.88

2.902.872.872.88

2.902.872.872.88

Predicted

Whole

Fresh

1.651.631.621.60

1.671.651.631.61

1.681.661.631.60

1.681.661.631.61

(Ib)

Frozen

1.901.891.881.87

1.941.921.891.87

1.961.931.901.87

1.961.931.901.87

Fillet

Fresh

1.661.641.621.60

2.862.832.802.77

2.872.842.812.77

2.872.842.812.77

(Ib)

Frozen

2.792.772.762.74

2.842.822.802.77

2.882.852.822.79

2.872.852.822.79

Percent difference

Whole (%)

Fresh

4.075.235.815.88

2.914.075.235.29

2.333.495.235.88

2.333.495.235.29

Frozen

7.778.258.747.43

5.836.808.257.43

4.856.317.777.43

4.856.317.777.43

Fillet (%>

Fresh

43.3444.0344.7145.02

2.393.414.444.81

2.053.074.104.81

2.053.074.104.81

Frozen

3.793.483.834.86

2.071.742.443.82

0.690.701.743.13

1.030.701.743.13


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C. M. Jolly et al • Forecasting catfish prices 77

may mean that for any model developed for the cat-fish industry, the forecast must be frequentlyupdated. With such rapid deterioration of forecastover time, the forecasts for the catfish industry maybe for the short-run only. Since the forecasts werealways lower than the observed, the models tended tounderestimate prices.

The graphs in Figs 1-4 show that predicted valuesmoved with the observed over time. From visual obser-vation there seemed to be only minor differences in theforecasts for the models, and all models show the same

downturns in prices, but the downturns were slightlyless with the GARCH process models. Similar behaviourof observed and predicted prices of whole frozen, freshand frozen fillet prices were expected and it was notnecessary to display all of them graphically.

Discussion

Results of this study show that some improvement canbe obtained from forecasting using the GARCH pro-

Sept-92 Jan.-93 May «3 Sep. «3 Jan.'94 May's* Sep. ̂ Jan.'95

Fig. 1 Forecasting of price ofwhole fresh catfish usingtraditional OLS model

PWF = Price whole fresh catfish PPWF = Predicted price of whole fresh catfish

Price 1.8

1.75

1.7

1.65

1.6

1.55

1.5

1.45

1.4

1.35

1.3Sepf92 Jan.'93 May'93 Sep.'93 Jan.'94 May'94 Sep.'94 Jan.'95

TimePWF = Price whole fresh catfish PPWF = Predicted price of whole fresh catfish

PWF

rI /PPPWF/ iIIft

1 /II1/

Ail

'\Forecast

\%

Fig. 2 Forecasting of price ofwhole fresh catfish using a pricecombination of GARCH and OLSmodel



pp 71-80

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78 Forecasting catfish prices • C. M. Jolly et al

\Forecast

Fig. 3 Forecasting of price ofwhole fresh catfish using a pricecombination of G ARCH andunlimited least square model

Sept'92 Jan.'93 May'93 Sep.'93 Jan.'94 May TO Sep.'94 Jan.'85

TimePWF = Price whole fresh catfish PPWF = Predicted price of whole fresh catfish

cess, but the improvement is minimal. The traditionalmodels produced low RSME, MAE and high R? values.The traditional OLS model has one advantage in thatit is easy to develop. However, the statistics producedfrom the application of the G ARCH procedure help inimproving model forecasts. The RMSEs were slightlyhigher than that derived from the GARCH proce-dure. The RMSEs and the MAEs from all GARCHderived models were similar. Leitch & Tanner (1995)

concluded that there was no real value in using theerrors to judge forecasting models. They thoughtthat forecasters are mistaken when using the size oferror in judging models because the conventionalerror criteria do not appropriately capture the pur-pose of the forecasts. They argued that the RMSE,MAE and the Theil U-statistic had little to do with theprofitability of the forecasts. Tiao and Tsay seemed tobelieve that there was some benefit in using higher



pp 71-80

Price 1.8)1.75

1.7

1.65

1.6

1.55

1.5

1.45

1.4

1.35

1.3

PWF ,

Fig. 4 Forecasting of price ofwhole fresh catfish using a pricecombination of GARCH andmaximum likelihood model

\Forecast

Sept "92 Jan.'93 May'93 Sep. "93 Jan. "94 MayW Sep.W Jan.'95

Time

PWF = Price whole fresh catfish PPWF = Predicted price of whole fresh catfish

© 1998Blackwell Science Ltd

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CM. Jolly et al • Forecasting catfish prices 79

nonlinear adaptive models. They concluded that ifone accepts the premise that any model is, at best, anapproximation, then, the parameter estimationshould be treated more in the context of the use forwhich the model is to be put rather than as an end initself. If we accept this premise, we would most likelyaccept the ULS and ML models derived from theG ARCH over the traditional OLS, and the OLSderived from the GARCH since their forecasts devi-ated less from the observed prices.

It is important to note that for the fresh and frozenwhole catfish the quantity of fish was significant inexplaining price when OLS was used, but not signifi-cant when the ULS and ML models were used.Though the variable was negatively related to price,it was barely significant when the OLS model wasemployed, and insignificant in the ULS and ML mod-els. On the other hand, for the fresh and frozen filletmodels, the variable technology was positivelyrelated to price in all models which may imply thatthere is a price benefit associated to the use of tech-nology in the processing of fillet catfish. The quantityof fish was only significant when the OLS model wasused. Again, farm price was positively related to theprice of fillet catfish. Hence, it is possible to concludethat for whole frozen and fresh catfish, farm gateprice can be used to forecast the retail price, whereasfor fillet catfish, both the farm gate price and technol-ogy would have to be utilised in the forecast of theprice of catfish fillet.

There is not much difference in model forecast andthe type of model used may be determined by the fore-caster's knowledge of the models. For greater precisionin forecast the ML and ULS models would be preferred.However, since in most cases the price at the farm levelsignificantly influenced the price at the retail level,decision makers may well use simple forecasts of farmprices to estimate the retail level price. It is assumedhere that the structure of the industry and catfishmarket remain unchanged.

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Forecasting catfish industry prices using linear and nonlinear methods

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