Spot price

Weekly data on the average spot price of salmon is publicly available for 1995 and onwards⁵. I study the period from 2007 week 1 to 2014 week 39 (2007w1-2014w39); see Figure 1. I do not use earlier data so as to match the available time periods of other variables and also since a structural change seems to have occurred in the spot price series around 2006 (Bloznelis, 2016). A fundamental change also occurred between 2013w13 and 2013w14 when the so-called NOS price was replaced by the so-called NASDAQ price. I will now briefly review the differences between the two as described in Fishpool (2014).

NOS survey prices are exporters’ buying prices, i.e. prices paid to salmon farmers. Only representative exporters are included in the survey. The exporter must purchase at least two truck-loads (around 40 metric tons) of salmon per week, on average. The exporter must sell more than half of the total volume as gutted salmon to companies outside its own group. Only between-company sales are reported, where companies do not belong to the same owner. Prices are to be agreed upon on the spot, as opposed to forward contracting. (In practice, the prices are normally agreed upon a few days ahead of delivery rather than on the delivery day; they are nevertheless called spot prices.) With regards to reporting, slaughtering day is the decisive characteristic: the reported transaction is

5 The data can be accessed at https://salmonprice.nasdaqomxtrader.com/public/home?1-1.ILinkListener-loginMenu-downloadIndexHistoryLink and https://salmonprice.nasdaqomxtrader.com/historicalNOSprices.xls

Figure 1 Salmon spot price: original (left), seasonally adjusted (middle), seasonal component (right)

assigned to the week in which slaughtering took place. When published, NOS prices partly reflect the spot market prices as of the last week and partly the last week’s deliveries’ prices pre-agreed on Thursday or Friday the week before.

Meanwhile, NASDAQ survey prices are exporters’ selling prices, i.e. prices received from buyers outside Norway. The NASDAQ survey inclusion conditions are different from those of the NOS survey.

The exporters must sell at least five truck-loads (around 100 metric tons) of salmon per week, on average. Within-group as well as between-group sales may be reported. Only the export to Europe is included, while air-freight export to overseas markets is not. Customs invoice date (as opposed to slaughtering date) determines which week the transaction will be assigned to in the NASDAQ survey.

There is a shorter lag between the actual transactions taking place and the prices being published;

the NASDAQ salmon price is around four to five days old when reported. In sum, the NOS and the NASDAQ prices reflect a slightly different underlying object. Nevertheless, I will use them both (the NOS price for 2007w1-2013w13 and the NASDAQ price for 2013w14-2014w39) as measures of the spot price of salmon.

The difference in the treatment of dates, i.e. how a transaction is assigned to a calendar week, is important when forecasting the salmon price based on historical data. An observation from the NOS series points to a more distant past than one from the NASDAQ series, the difference being around five to six days. That is, if the NOS and the NASDAQ reporting were running simultaneously, the NASDAQ price for 2007w1 would likely match the NOS price for 2007w2 more closely than the NOS price for 2007w1. Therefore, given the last available NOS observation, forecasting one step ahead essentially means forecasting the past; one week ahead of around ten days ago is around three days ago. Meanwhile, forecasting the NASDAQ price one step ahead corresponds to forecasting the future; one week ahead of around four to five days ago is three to two days into the future.

If the NOS/NASDAQ weekly reports were the timeliest source of price information in the salmon spot market, the discrepancy between the two would likely yield different price discovery processes

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Spot price (NOK/kg)

2007 2008 2009 2010 2011 2012 2013 2014 20253035404550

Seasonally adjusted (NOK/kg)

2007 2008 2009 2010 2011 2012 2013 2014 -15-10-5051015

Seasonal component (NOK/kg)

2007 2008 2009 2010 2011 2012 2013 2014

under the NOS reporting than under the NASDAQ reporting; this would need to be taken into account when modelling and forecasting the salmon price. However, it is inconceivable that the market participants do not get timelier price information, e.g. by trading and negotiating prices themselves. This is supported by the observation that the share prices of the salmon farming companies do not seem to react to the weekly NOS and NASDAQ reports. Meanwhile, they do seem to be moved by certain other reports containing timely information, such as the traders’ survey published by the “IntraFish” and TDN every Friday afternoon.

The NOS and the NASDAQ prices were calculated simultaneously for 37 weeks in 2012-2013. The average difference between the NOS and NASDAQ prices was NOK 0.75/kg. I subtract NOK 0.75/kg from the NASDAQ price to be able to concatenate the two series. The same approach was used by the Fish Pool futures and options exchange for adjusting the Fish Pool Index at the time of transition from the NOS to the NASDAQ prices.

In addition to the average spot price, weight-class-specific spot prices are also available. Salmon is divided by fish size into seven weight classes, 1-2 kg, 2-3 kg, 3-4 kg, 4-5 kg, 5-6 kg, 6-7 kg and 7+ kg fish. The weight-class-specific prices lend themselves easily to operations’ management by salmon farmers, processors, and other market participants. However, the distinction between the weight classes is of limited importance in terms of forecasting; the short-term movements in the weight-class-specific prices are highly correlated with the movements in the average price (Bloznelis, 2016).

The correlations between seasonally-adjusted logarithmic returns vary between 0.93 and 0.99 for all the weight classes except for the scarcest class of the small 1-2 kg fish; the correlation for this weight class is still rather high at 0.77 (ibid.). Also, modelling the prices of all the seven weight classes instead of just one translates to increasing the number of dependent variables from one to seven.

This would increase the model complexity and would aggravate the curse of dimensionality.

Therefore, I leave it for future studies. Ultimately, if a need arises to forecast the price of a specific weight class, it could be done by modelling the spread between the weight class of interest and the average price, and adding it to the forecast of the average price.

Seasonality is a key characteristic of salmon production and is due to the seasonality in the supply and demand factors discussed in Chapter 1. The seasonality of supply does not match the seasonality in demand, which produces seasonal patterns in price. Modelling the seasonality for weekly time series is known to be tricky. The seasonal period is long and there is a fractional number of weeks in a year which limits the choice of available techniques and excludes the most popular ones such as dummy variables, seasonal ARIMA model and STL decomposition by Cleveland et al.

(1990). Here I follow an approach proposed by Hyndman (2014) of using a regression with ARMA errors, with Fourier terms as regressors. The number of Fourier terms could be up to 26 pairs for weekly data; however, a parsimonious model may exclude the higher order terms (the ones

generating the high-frequency oscillations) so as to trade off an increase in the model misspecification bias against a decrease in estimation imprecision. This is formalized by choosing between none through 26 pairs of Fourier terms using the corrected Akaike’s information criterion (AICc). The spot price and the export volume exhibit sharp, large movements around Christmas and Easter. I therefore also add four dummy variables to indicate weeks right before and after Christmas and another four for Easter. Note that even though Christmas has a fixed date in the year, that date may belong to different weeks over different years if the weeks are counted from Monday to Sunday.

The Fourier terms together with the Christmas and Easter dummies constitute the seasonal pattern and will be subtracted from the original series, while the remainder will be used for further modelling. The seasonal component and the seasonally-adjusted salmon spot price for the whole period 2007w1-2014w39 are depicted in Figure 1.