5.9. Appendix 2: The Dynamics of Information Smoothing

Information smoothing is so common in the day-to-day operation of business and society that it is worth examining more closely how it really works. Smoothing crops up in forecasts, expectations, perceptions, judgements and in any process of measurement or monitoring.^[] People do not instantly recognise the true conditions within an organisation. People do not change their minds immediately on the receipt of new information. Measurement, reflection and deliberation often take considerable time. Still more time is needed to adjust emotionally to a new situation before beliefs and behaviour change. Smoothing is a versatile way to capture this typical wait-and-see approach. A formulation for information smoothing is shown in Figure 5.35. The smoothing process transforms an input into an observed input over the 'time to form an impression'. The formulation is similar to the average ship rate earlier in the chapter, but the terminology is generalised. In addition, an alternative SMTH1 function is included to demonstrate its precise equivalence to the standard single-stock formulation.

^[] Forecasts and expectations can involve several interlinked smoothing processes in order not only to perceive the value of a given variable, but also to determine its trend. With knowing the trend, it is possible to project the value of the variable at a future point in time (according to the time horizon of the forecast). To find out more about forecasting formulations, examine the model called 'Trend Test' in the CD folder for Chapter 5.

Figure 5.35. Information smoothing

Two simulations are shown in Figure 5.36. They can be recreated by running the model called 'Information Smoothing' in the CD folder for Chapter 5. The top part of the figure shows smoothing of an input (line 1) that begins at 1 000 units per week and increases to 1 100 in week 10. The observed input (line 2) rises gradually from 1000 to 1100 as confidence builds that the one-time change in the input is permanent. Notice that the observed input from the SMTH1 built-in function (line 3) mimics line 2. In fact the numerical values of lines 2 and 3 are identical but the trajectories are deliberately placed on slightly displaced scales so they are both visible. The bottom part of the figure shows smoothing of a random input (line 1).

Figure 5.36. First-order (single stock) smoothing. Top: Smoothing of a step input that increases by 10 per cent. Bottom: Smoothing of a random input with standard deviation of five per cent.

The observed input (line 2) captures the mean value of the input (1000 units per week) but filters-out nearly all the variability. The time to form an impression is eight weeks and this interval is long enough to ensure that week-to-week variations of the input cancel each other out. The shorter the time to form an impression the more variability is observed.