In this note, we study the forecasting performance ofsome simple models applied to the hog markets in theNordic countries. In terms of accuracy (MSE andMAPE), a simple autoregressive model outperforms thenaive expectations benchmark in some samples, as does avery simple VAR-type model in which lagged piglet pricesare added to the lagged hog prices as RHS variables.Forecasting performance is, however, quite sensitive to thechosen lag structure, and there is reason to doubt whetherthe simple autoregressive model from an economic pointof view yields significantly better results than those of thenaive model. Focusing on directional forecasts, on theother hand, the simple VAR-models perform clearly better.Thus, for producers whose main concern it is whether theprice moves up or down, these models may be quite use-ful. © 1997 John Wiley & Sons, Inc.

Introduction

Hog producers face considerable price volatility. Tosome extent, this volatility is related to seasonal and

fairly regular variations in demand that come as little surprise to those engaged in the business. Still,price fluctuations translate into a significant pricerisk, since the magnitude as well as the direction ofthe period-to-period price changes most often areunknown to the producers.

If prices can be forecast within reasonable confi-dence limits, risk will be reduced. Producers canthen adjust their production volume and, perhapsmore important, they can change their timing as towhen to have hogs ready for delivery. Furthermore,if producers can successfully forecast prices, thiswill reduce costs involved in hedging activities.

Not taking capital investment decisions into ac-count, the planning horizon for a hog finisher spanssome 3–4 months; for a piglet producer 6–7 months,and consequently approximately 9–10 months for aproducer with an integrated upstream production.Once the sow farrowing decision is made, or thepiglets are bought, the die is cast. This note will fo-cus on price uncertainty for hog finishers. Conse-quently, our concern is the hog price risk and thepossibility of making 3–4 months forecasts.

The purpose of this note is to test out the perfor-mance of some simple forecasting models which can

Requests for reprints should be sent to Berth-Arne Bengtsson, De-

partment of Economics, Swedish University of Agricultural Sciences,

Box 7013, S-750 07, UPPSALA, Sweden.

• Ole Gjølberg is with the Department of Economics and Social Sciences at the Agricultural University of Norway.• Berth-Arne Bengtsson is with the Department of Economics at the Swedish University of Agricultural Sciences.

INDUSTRY NOTEForecasting Quarterly Hog Prices:

Simple Autoregressive Models vs. Naive Predictions

•673

•Ole Gjølberg

Berth-Arne Bengtsson

Agribusiness, Vol. 13, No. 6, 673–679 (1997)© 1997 John Wiley & Sons, Inc. CCC 0742-4477/97/060673-07

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easily be applied by individual hog producers. Webelieve that a producer values forecasts along twodimensions. He obviously looks for good predic-tions, preferably forecasts that are of economic value. In addition, most practitioners have a pref-erence for simplicity (i.e., forecasting models thatthey at least conceptually can understand and pos-sibly even run on their own PCs). On this back-ground, we investigate forecasting performancebased on a set of very simple models.

The note is organized as follows. In the next sec-tion we briefly review the standard approach foundin several articles on hog price forecasting. Leaningon this approach, we introduce the assumption thatproducers hold rational expectations when pricingthe piglets. This implies that the piglet price con-tains information regarding the future hog priceand that today’s piglet price therefore is an impor-tant indicator when making forecasts for the hogprice 3–4 months ahead. We then outline the proce-dure for our forecasting experiments, reported inthe subsequent section. Finally, the main conclu-sions are summarized.

Forecasting Models

Several models aimed at forecasting hog prices havebeen presented in the literature. A substantial frac-tion of these models are variations over autoregres-sive and Box–Jenkins type (ARIMA) estimations.There is, however, also a number of econometricmodels involving a set of variables determining sup-ply of and demand for pork, whereas some fore-casts are based upon a combination of forecasts ob-tained through ARIMA models and morecomprehensive econometric models as in, for in-stance, Leuthold et al.,1 Bessler,2 Brandt andBessler,3 and Harris and Leuthold.4 Furthermore,a number of studies explore the forecasting proper-ties of prices from exchanges trading hog or porkfutures as in articles by Elam,5 Fama and French,6

Foote, Williams and Craven,7 Leuthold and Hart-mann,8 and Wilkinson.9 More recently, nonlinearvariants of time series models have been tested outby, for instance, Chavas and Holt,10 including fore-casting with so-called neural networks (Hamm andWade Brorsen11).

There is rather strong evidence that simple ARI-MA models and reduced form econometric specifi-cations yield forecasts that outperform forecastsbased on naive or adaptive expectations or variousexponential smoothings. There is also reported evi-dence that simple combinations of forecasts basedon such models yield even better predictions thaneach model individually.3,12

A popular benchmark for evaluating forecastingperformance is based on naive expectations,

where specifying the expected hog price (the fore-cast) for period t+1 as a weighted sum of the ob-served prices today (t) and n periods into the past,plus an unsystematic component.

Again, the quality of the forecasts could be partic-ularly vulnerable to seasonal variations. If, for in-stance, there is a regular increase in hog prices justbefore Christmas, the forecast based solely on anautoregressive pattern will tend to underestimatethe November–December prices unless the numberof lags in the RHS variable is extended to includeprices one year (or one season) ago. Alternatively,regular price jumps may be accounted for by in-cluding seasonal dummy variables in (2).

Another way of adjusting the forecasts for suchjumps is to include explanatory variables that atthe time they are being observed reflect expectedseasonal or other changes beyond a regular autore-gressive pattern. In hog production one obviouscandidate for such a variable is the piglet price. As-suming that hog finishers hold rational expecta-

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Et(pHt11) 5 pt

H 1 «t11 (1)

i.e., assuming that the expected hog price ( pH ) oneperiod into the future equals today’s hog price plusan unsystematic component («). Obviously, in amarket with trends or also regular seasonal varia-tions, one would not expect such naive forecasts toperform very well. Thus, the naive model serving asa benchmark generally ought to be outperformedby any other model claiming forecasting abilities.

One such alternative model is represented by asimple autoregressive forecast,

n

Et(pHt11) 5 ^ bi pH

t2i 1 «t11 (2)i50

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tions, the price that clears the piglet market shouldreflect expectations regarding the hog price some3–4 months ahead. In other words, the piglet priceshould incorporate relevant information on aggre-gated expectations regarding future supply and de-mand. This is particularly so because of the charac-ter of hog production. Once the piglets are there,knowledge about the total number of piglets con-tains rather exact knowledge about the number offinished hogs 3–4 months ahead. The price thatclears the hog market is, therefore, to a large extentdecided by demand. One would not expect produc-ers to systematically misjudge future demand. Thiswould be incompatible with the notion of rationalexpectations, reflecting an inability to learn fromprevious mistakes, asymmetric information betweenhog producers and distributors or consumers, er-ratic interventions from marketing boards, just toindicate a few possible sources that could con-tribute to such systematic errors.

Given rational expectations, the piglet price oughtto be an unbiased forecast for the future hog pricewith unsystematic errors, conditioned on the ex-pected feed costs during the finishing period.

Data and Procedure

Using the naive model as a benchmark, out-of-sam-ple forecasting performance based on various speci-fications of simple autoregressive models and VAR-models were studied in the four Nordic countries,Denmark, Finland, Norway, and Sweden.

The time span between buying the weaned pigletsand selling the finished hogs is normally 3–4 months.For this reason (and possibly as a matter of conven-tion in economic forecasting) hog prices are usuallyforecast on a quarterly basis, using quarterly obser-vations. We follow this tradition, organizing ourmonthly price observations from the period 1982 to1992 in three data sets in order to get around theoverlapping observation problem. The first (set A)includes observations from January, April, July,and October, the second (set B) comprises observa-tions from February, May, August, and November,whereas the third one (set C) includes data fromMarch, June, September, and December.

The following models were estimated:

where as before pH is the hog price, whereas pP

and pF is the piglet price and the feed price, re-spectively. Each model was run with 1–4 lags in theset of RHS variables. (The complete data set isavailable from the authors upon request.)

The estimation procedure was as follows. Westarted out by estimating each model using observa-tions from the seven years prior to October 1988.Based on the estimation results, an out-of-sampleforecast three months ahead was calculated. Thisprocess was then repeatedly rolled forward, addingone new observation and dropping the first in theestimation before calculating the next three monthsahead out-of-sample forecast, assuming that thehistoric experience forming expectations consistent-ly is based on observations from the seven yearsprior to the date the forecast was being made. Wethus generated three sets of quarterly forecasts(i.e., 48 forecasts for each model and country).

Let us summarize the main preforecasting periodOLS estimation results. The explained variance interms of adjusted R2 is increased when lagged pigletprices and feed prices are included in addition tohog prices as RHS variables (i.e., the explanatorypower of Models III and IV tends to be greater thanthat of Model I). Furthermore, a pattern of first-order autoregressive hog prices is found in almostall countries and data sets. Denmark represents anexception to this, with results indicating that hog

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Model I: ptH 5 a 1O bi pH

t2i 1 «t; i 5 1,2,3,4i

Model II: ptH 5 a 1O gi pP

t2i 1 «t; i 5 1,2,3,4i

Model III: ptH 5 a 1O bi pH

t2ii

1 O gi pPt2i 1 «t; i 5 1,2,3,4

i

Model IV: ptH 5 a 1O bi pH

t2i 1 O gi pPt2i

i i

4

1O wj pFt2j 1 et; i 5 1,2,3,4

j51

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prices follow a more complicated autoregressivepattern. Furthermore, for two of the countries (i.e.,Norway and Denmark) there is a significant serialcorrelation in the residuals of Model I. This, how-ever, disappears when adding piglet and feed pricesas explanatory variables, indicating that Model Irepresents a misspecification. As to the rationalityin the pricing of piglets, the results generate a some-what mixed evidence. Again, Denmark stands outindicating that the piglet price alone does not com-prise information of significant value as to the pre-diction of the hog price three months later. In thecase of Finland, the piglet price appears to be sys-tematically related to subsequent hog prices, al-though with a much longer time span than shouldbe expected on the basis of the normal hog finishingperiod (3–4 months). The estimation results fromthe preforecasting period for Norway and Sweden,on the other hand, strongly fit in with our hypothe-sis that the observed piglet price contains signifi-cant relevant information on the hog price a quar-ter later. In the case of Sweden, we also find thatthe observed feed price is significantly related tothe subsequent hog price.

Forecasting Performance

Accuracy

To be able to compare the naive forecasts acrossdifferent national currencies and price levels,Table I summarizes the naive mean absolute per-centage errors (MAPE) for each data set in eachcountry together with the traditional mean squarederrors (MSE). As can be seen, in the case of Finlandthe naive approach on average would have generat-

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Table I. MSE and MAPE from Naive Forecasts,1988–1992.

Country MSE MAPE

Denmark 16538 8.83Finland 1351 1.79Norway 25179 3.21Sweden 8576 4.89

Table II. MSE and MAPE, Naive Predictions vs. Model I–IV, 1988–1992.

MSELags RHS-variables

MAPELags RHS-variables

Country Model Naive 1 2 3 4 Naive 1 2 3 4

Denmark I 16538 14588 14746 15530 17500 8.83 8.47 8.45 8.60 8.63II 16538 20284 18448 22035 29523 8.83 9.63 8.78 9.57 10.71III 16538 14834 14693 17418 29352 8.83 8.69 8.35 9.27 11.32IV 16538 15514 17280 22112 31715 8.83 9.05 9.66 10.48 12.45

Finland I 1351 1453 1517 1532 1625 1.79 1.80 1.86 1.89 1.96II 1351 6718 6597 6166 5532 1.79 4.15 4.29 4.07 3.75III 1351 2037 2452 2283 2634 1.79 2.08 2.23 2.12 2.36IV 1351 3066 4367 5439 6198 1.79 2.68 3.29 3.30 3.54

Norway I 25179 26886 26046 22681 28865 3.21 3.39 3.36 3.38 4.19II 25179 245206 257924 274603 296628 3.21 13.15 13.36 13.91 14.70III 25179 28059 14956 13268 17025 3.21 3.41 2.39 2.47 2.90IV 25179 48977 24830 24586 30259 3.21 4.95 3.48 3.74 4.07

Sweden I 8576 7714 7361 7734 6908 4.89 4.54 4.37 4.35 4.31II 8576 6212 6218 5907 5045 4.89 4.02 3.97 3.92 3.81III 8576 4982 4670 5102 5032 4.89 3.69 3.57 3.67 3.82IV 8576 5548 5861 7837 8478 4.89 4.03 3.61 4.43 4.77

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ed very small percentage errors, indeed, reflectingthe fact that Finnish hog prices during this periodwere less volatile than those in the other nordiccountries. In the case of Denmark, on the otherhand, such forecasts would have been far less suc-cessful. Then somewhere between the Danish aver-age error of approximately 8.8% and the Finnish1.8%, we find Norway and Sweden with 3.2% and4.9%, respectively.

Focusing on the forecasting performance withineach country separately, Table II presents bothMSEs and MAPEs for each model and country. Themain conclusions can be summarized as follows:

• The naive model performs generally extremely wellcompared to the four competing models. This is par-ticularly so in the case of Finland, where the naivemodel actually is not outperformed by any of themodels.

• The simple autoregressive model (Model I) outper-forms to some extent the naive forecasts. The in-creased accuracy of the autoregressive model is,however, never striking.

• Model III, combining lagged hog prices and laggedpiglet prices, performs clearly better than the naivemodel for Sweden and Norway, and to some extentfor Denmark.

• The forecasting performance is very sensitive to thenumber of lags included in the RHS variables. Gen-erally, it seems that it does not pay to include morethan two (quarterly) lags. In some cases, includingadditional lags is counterproductive in terms offorecasting accuracy.

• Even though we, in a number of the tests, come outwith forecasts that are more accurate than those ofthe naive model, there is reason to question whetherthis holds significant economic value beyond that ofthe naive forecasts. Also, the sensitivity in the re-sults suggests that one should be somewhat carefulwhen “selling” the price forecasts.

Direction

MSEs and MAPEs are hard to interpret in an eco-nomic sense. One may easily demonstrate that accu-rate forecasts in terms of low MSEs may turn out tobe less economically valuable than less exact fore-casts. In many real-life situations, it may be ofgreater value to decisions makers to have an idea

about whether prices will raise or fall, rather thanforecasting the future price with a high degree ofprecision. Let us illustrate. Model A predicts asmall price increase. Model B predicts a strongprice fall. The subsequent price actually decreasesa little. In terms of MSE, Model A does quite well.Still, the decision maker may experience losses fromacting on a price increase forecast and find littlecomfort in the fact that the forecast that turned outto be fairly accurate but substantially wrong.

Table III reports on model performance in termsof predicting the correct direction of price changes.Using the naive model as a benchmark, this simplyimplies that a price increase/fall is assigned a prob-ability of .5. As can be seen, for Norway Models IIIand IV including 2–4 lags in the RHS variables out-perform the naive model significantly. Even moreconvincing are the Swedish results. With just a mi-nor exception, Models II, III, and IV all tend to

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Table III. Percent Correct Directional Forecasts.

Lags RHS

Country Model 1 2 3 4

Denmark I 67 58 52 63II 63 69 65 60III 48 54 48 38IV 56 60 50 48

Finland I 54 48 52 58II 52 50 52 52III 52 44 52 60IV 40 38 38 42

Norway I 29 42 60 58II 38 38 38 38III 48 75 75 69IV 46 67 67 60

Sweden I 63 56 69 71II 77 77 79 75III 77 71 75 73IV 81 71 65 63

Note: Bold figures are significantly greater than 50% at a 5%

level. Given n 5 48, the 90% confidence interval around 50%

is [36;64] using the normal approximation to the binomial

distribution.

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forecast directions significantly better than thenaive model. On the other hand, for Denmark justone model (i.e., Model II) and for Finland none ofthe models come up with better forecasts regardingdirection of price changes than that of tossing a faircoin (i.e. the naive model). Table III furthermoreindicates that the models including lagged pigletprices and lagged feed prices tend to perform betterin terms of forecasting ups or downs than the basicautoregressive model including lagged hog pricesonly (Model I).

The results for Sweden are particularly interestingfrom a practitioner’s point of view because at leastone of the big processors (i.e., Skanek) is offeringhog producers forward piglet pricing arrangements.Producers are given the option to buy piglets forwhich they subsequently pay a weighted average ofthe hog price 13–16 weeks later. Obviously, produc-ers who can systematically predict the direction offuture hog price changes may use this ability prof-itably in their decision of whether to hedge or not(i.e., buy piglets at forward rather than spot prices).

Concluding Remarks

We have evaluated some simple hog price forecast-ing models applied to the Nordic markets.

Forecasting performance studies usually focus onaccuracy, calculating MSEs, MAPEs, or similarmeasures, whereas the naive expectations modelpresents a popular and widely used benchmark inthe evaluations.

In the first part of our study, we follow this ap-proach. Quarterly out-of-sample forecasts weregenerated for the four Nordic countries using astandard autoregressive model as well as some verysimple VAR-models, in which lagged piglet pricesand lagged feed prices were added to the lagged hogprices as explanatory variables.

The out-of-sample experiments gave somewhatmixed results. The naive benchmark model turnedout to yield fairly exact forecasts. In some samples,the autoregressive model clearly outperformed thenaive model, and in a few samples the VAR-typemodels did even better. On the other hand, theforecasting performance in terms of MSEs turnedout to be quite sensitive to the chosen lag structure.

As to forecasting the direction of price changes, onthe other hand, the models appear more convincing(excepting Finland). Particularly for Norway andSweden, the models that include past piglet andfeed prices tend to predict the correct sign of quar-terly hog price changes significantly better than thenaive approach. To many practitioners, good fore-casts on the direction of price changes can be morevaluable than fairly accurate price level predic-tions. This is particularly so in making strategic de-cisions on hedging or timing. In this respect, we findreason for some optimism on behalf of practition-ers’ demand for simple and valuable forecastingmodels.

References

1. R. Leuthold, A. MacCormick, A. Schmitz, and D. Watts,“Forecasting Daily Hog Prices and Quantities: A Study ofAlternative Forecasting Techniques,” Journal of AmericanStatistical Association, 65, 90 (1970).

2. D.A. Bessler, “An Analysis of Dynamic Economic Relation-ships: An Application to the U.S. Hog Market,” CanadianJournal of Agricultural Economics, 32, 109 (1984).

3. J. A. Brandt and D.A. Bessler, “Price Forecasting andEvaluation: An Application in Agriculture,” Journal ofForecasting, 2, 237 (1983).

4. K.S. Harris and R.M. Leuthold, “A Comparison of Alter-native Forecasting Techniques for Livestock Prices: A CaseStudy,” North Central Journal of Agricultural Economics,40 (1985).

5. E.W. Elam, “A Strong Form Test of the Efficient MarketModel Applied to the U.S. Hog Futures Market,” Ph.D.Dissertation, University of Illinois, 1978.

6. E.F. Fama and K.R. French, “Commodity Futures Prices:Some Evidence on Forecast Power, Premiums, and theTheory of Storage,” Journal of Business, 60, 55 (1987).

7. R.J. Foote, R.R. Williams, Jr., and J.A. Craven, Quarter-ly and Shorter-term Price Forecasting Models Relating toCash and Futures Quotations for Pork Bellies, TechnicalBulletin No. 1482, US Dept. Agriculture, Economic Re-search Service, 1973.

8. R.M. Leuthold and P.A. Hartmann, “A Semi-Strong FormEvaluation of the Efficiency of the Hog Futures Market.”American Journal of Agricultural Economics, 61, 482(1979).

9. M. Wilkinson, Futures Prices as Embedded Forecasts: TheCase of Corn and Livestock. Working Paper # CSFM-107,Columbia Business School, New York, 1985.

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10. J. Chavas and M.T. Holt, “On Nonlinear Dynamics: TheCase of the Pork Cycle,” American Journal of AgriculturalEconomics, 73, 819 (1991).

11. L. Hamm and B. Wade Brorsen, “Forecasting QuarterlyHog Prices with Neural Networks,” paper presented at theannual conference of AAEA, Orlando, FL, August 1993.

12. C.W.J. Granger and R. Ramanathan, “Improved Methodsof Combining Forecasts,” Journal of Forecasting, 3, 197(1984).

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