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A company is developing a new product and wants an accurate estimate of the investment's ROI. For that the money in-flows and out-flows for the project have to be forecasted. And to develop those forecasts, the resulting product's life cycle must first be forecasted.

In this chapter, we are considering a real company. The company was in the process of developing a new product – a special purpose computer. In June of a year, the company wished to predict the product's future life cycle before the product had been fully developed. The product would be introduced into the market in January of the following year. However, to predict the locus of a product's future life cycle before the product has been fully developed is known to be very difficult.

This chapter presents a method for predicting a new brand's life cycle trajectory from its beginning to its end before the brand is introduced into the markets. The chapter also presents a combination of two methods to use current information to revise the entire predicted trajectory so it comes closer and closer to the true life cycle trajectory. The true trajectory is not known till the product is pulled from the market. The two methods are the Delphi method and Kalman filtering tracking method.

The company, which this application originates with, and the problem we discuss are real. However, we are prepared to identify neither the company nor the product. This chapter discusses the approach, but the data and the time scale have been masked, so that no identification from the data is possible.

This chapter describes the method we use to predict the demand for a new brand over its entire future life cycle before the brand is introduced into the market. The forecast is a prior forecast prepared at time t−1 using all the data that is available up till time t−1. Additional information about the future in the form of advance orders becomes available at time t. The advance orders contain the customers' plans for future purchases. They contain therefore a forecast for future demand. This chapter discusses how at time t−1 the prior forecast of, and the estimate of the locus of, a new brand's life cycle (based on information up to t−1) for the future periods t+1, t+2, …,t+k are developed. The chapter discusses how at time t when advance orders become available for the future periods t+1, t+2, …,t+k the prior forecast is updated for the length of the life cycle with this new information. These updates are made using Kalman's filter. Using this method we have been able to obtain good estimates of the locus of the life cycle of new brands. We have also been able to predict the turning points in the brand's life cycle six months before it occurs. The chapter shows a method for developing sequentially improved forecasts.

Assume that we generate forecasts from a model y=cx+d+. “c” and “d” are placement parameters estimated from observations on x and y, and is the residual.

If the residual is observed to be symmetric about the mode, it is usually assumed to be distributed by the Gaussian family of functions. If the residual is skew to the left of the mode, or to the right of the mode, it cannot be assumed to be normally distributed. A family of functions will then have to be found which will correctly represent the observed skew values for . The analyst has to search for a family on a case-by-case basis, trying one family of functions first, then another, till one is found which fits the observed non-symmetric -values correctly. This chapter aims to eliminate this time consuming estimation process. The chapter introduces a family of functions. The family is capable of taking any skew or symmetric locus by varying its placement parameters. The family will simplify the effort to correctly measure the densities of because the estimation problem is reduced to fitting only one function to the data if it is symmetric or skew.

This chapter shows how the forecasting and the planning functions in a supply chain can be organized so they will yield optimal forecasts for an entire supply chain. We achieve this result by replacing the process of generating forecasts with that of making optimal coordinated supply chain decisions. The ideal performance for a supply chain is to have the flows of materials perfectly synchronized with the demand rate for the finished product that the chain produces. When the equality is achieved, we have a pure “demand pull” supply chain. This ideal is difficult to achieve because forecasting and decision making in supply chains are typically decentralized and forecasting and planning uncoordinated. Creating a competitive advantage for the finished product requires achieving the ideal. The opposite, not achieving the ideal, leads to uncoordinated forecasts and decisions that trigger unintended buildup of inventories, lost sales and the bullwhip effects, slowness and high costs.

This chapter shows how (1) we can achieve the ideal synchronous supply chain flows by using temporal linear programs; (2) then, we guide each individual supply chain member company in developing his optimal operations plan to guide him in executing his part in the supply chain plan. The result from the two factors: the entire supply chain will achieve the ideal flow rates.

Assume that we generate forecasts from a model y=cx+d+ξ. The constants “c” and “d” are placement parameters estimated from observations on x and y, and ξ is the residual error variable.

Our objective is to develop a method for accurately measuring and evaluating the risk profile of a forecasted variable y. To do so, it is necessary to first obtain an accurate representation of the histogram of a forecasting model's residual errors. That is not always so easy because the histogram of the residual ξ may be symmetric, or it may be skewed to either the left of or to the right of its mode. We introduce the probability density function (PDF) family of functions because it is versatile enough to fit any residual's locus be it skewed to the left, symmetric about the mean, or skewed to the right. When we have measured the residual's density, we show how to correctly calculate the risk profile of the forecasted variable y from the density of the residual using the PPD function. We achieve the desired and accurate risk profile for y that we seek. We conclude the chapter by discussing how a universally followed paradigm leads to misstating the risk profile and to wrongheaded decisions by too freely using the symmetric Gauss–normal function instead of the PPD function. We expect that this chapter will open up many new avenues of progress for econometricians.