A commonly used method of forecasting is the analysis of historical data to discern the trend in demand growth and extend it into the future to forecast demand. Although this method calls for application of statistical techniques it is useful to know its features in a simplified form. If several years' data of fertilizer sales are available and the trend is relatively stable, it is possible to read from past data the current "speed" of demand growth and the extent to which the speed is increasing or decreasing.
Pakistan used to rely upon expert judgement. However, with accumulation of valuable data of past consumption the country has now found demand projections based on time trends to have a far greater degree of accuracy than the multiple regression approach (see below). The trend extension system has been further refined to incorporate the fertilizer price index, irrigation factors and agricultural income. This modified model has been yielding good results. The overall N, P & K forecast is made and individual nutrient demand is derived on the basis of the ratio of the previous four years. Similarly, monthly demand is estimated by the previous three years' mean monthly offtake.
Trend extension is carried out as follows:
Time series data of fertilizer demand, either as fertilizer types or as N P K is listed, by month, for about ten years.
These data are likely to have four major components. The first reflects the "secular trend" which refers to the change occurring persistently over a long time. The second component captures a cyclical movement of demand which most products, including fertilizers, are subject to. Understanding the cyclical variation is useful for short and medium-range forecasts. The third element is the seasonal variation within each year. The fourth component is the disturbance caused by erratic and random events. Through statistical methods the time series data is analysed and broken down into these four components and re-combined to furnish the formula for the forecast.
For example: Country A sold 100,000 tonnes of fertilizer this year. We want to predict next year's sales in August. The time series analysis shows a 10 percent demand growth rate per year. This suggests a demand next year of 110,000 tonnes (100,000 × 1.1). However, a cyclical recession is expected next year according to the time series analysis which has the effect of depressing demand by 10 percent. This means that demand next year is likely to be 99,000 tonnes (110,000 × 0.90). If demand were to be the same each month, the monthly figure will be 8,250 tonnes (99,000/12). However, August is the month of seasonal sales of fertilizer and the seasonal index stands at 1.5. Therefore, August sales may be 12,375 tonnes (8,250 × 1.5). No erratic disturbances are expected. Therefore, the best estimate of August sales is 12,375 tonnes. The seasonal index can be calculated as illustrated in Annex I.
The growth rate is determined by fitting a suitable mathematical equation that approximates the historical trend. For example, the trend can be linear, i.e. a straight line, the degree slope of the straight line indicating the quantity of annual increase in demand. Trends can be quadratic or exponential. Mathematical equations describe the growth rate represented by each of these forms and we choose the equation closest to the historical trend to calculate future demand. A list of mathematical equations and the corresponding growth curves representing different trends are in Annex VIII.
While trend extension (also called extrapolation) is best done by statistical techniques to minimise error a simpler version is to do it graphically. The actual demand over the past years is plotted on a graph and a smooth curve fitted visually. The trend is then projected into the future by extending the path of the historical data. Graphical extension of trend is simpler than projection by mathematical approach. However, graphical extension is subject to errors whereas projecting a trend through a mathematical equation reduces the subjective error.
