# Predicting forest products price trend: the example of Scots pine in Catalonia

## Description

When deciding on how to estimate future prices, due to influences that are likely to affect a product, we should consider two factors: the expected inflation and the real price change. The rate of real price change allows us to plot a trend line based on time series reflecting existing or past market price, that is, on "facts". Usually, many potential users are not going to use sophisticated forecasting techniques to estimate future prices, preferring to rely on simple approximation techniques. If acceptable time price series is available, then the simplest approach is to evidence a trend line over time that can be extended into the future. This can be done with regression analysis. In working with historical data, we could arrive at a medium-term trend estimate, which excludes the effects of inflation. Although the real price of forest products does not usually vary in an exponential way, the normal practice in investment analyses is often simplified by compounding price using a real price change rate. We can get the annual rate of real price change (r) from a linearized model that allows us to keep the statistical robustness of a linear regression model (with statistics, confidence indicators and tests), but applying the compound rate approach used in mathematics of finance. To do that, the well-known basic formula for compounding Pn=P0 (1+r)^n, where: Pn = estimated price in year n P0= price in year 0 r = annual rate of real price change (the real compound rate) n = number of years from year 0 is transformed into that of a straight line by making a change of variables (linearization). The proposed method is easy to reproduce and seems more orthodox than apply projections made using a simple straight-line model. Even though the straight-line represents an average variation over the years, from a mathematics of finance approach we should discuss price variation in terms of the annual compound rate. In Figure 1, you can see the differences between these approaches. If we have a clear trend in past real prices and the likelihood of a real price variation, we could make future price assumptions. If you agree with this statement and believe that price trend based on historical patterns is a significative information, then you should use r value gotten from the linearized model here proposed to project the price according to the previous compounding equation, where P0 is any real price calculated through the linearized compounding model (Table I). In Catalonia, most of forest products prices have not kept up with inflation and reflect a declining trend. A few others have just barely kept up with inflation. This is means that, despite moderate growth in nominal terms, the real price of almost all Catalan forest products presents a negative trend. For example, Scots pine sawlogs -the most representative harvested species in Catalonia (the 27% of the total volume yearly logged)- have dropped by an average of almost 2% per year since 1980.

## Files

## Steps to reproduce

You should enter current price series (col. B) and the GDP deflator (col. C) data. Then, fit the regression function according to the number of data/years. Please fit the real price change rate compound formula (cell J51); the percent error ranges, MAPEs and their standard deviations too. The real price in 15 years is calculated in cell E58 (E72 for the linearized model). You may change the expected number of years for the estimated price. Regarding this example, the Scots pine sawlogs price series is available at the Catalan Forest Observatory webpage https://www.observatoriforestal.cat/#prod The GDP deflator is calculated by the Spanish Statistical Institute and available on its website: https://www.ine.es/dyngs/INEbase/en/operacion.htm?c=Estadistica_C&cid=1254736177057&menu=resultados&idp=1254735576581