Forecasting with Smith Charts

Forecasting the memory market can be quite daunting unless you use the appropriate tools, then it becomes enormously simple.  Many of my clients ask The Memory Guy how it is that I am able to come up with such consistently-acurate forecasts in a seemingly-unpredictable market.  My answer is always that I use the Smith Chart.  This chart is a nomogram, presented in an angular/logarithmic format (as opposed to the semi-logarithmic format that I often use in this blog) which was originally devised to help antenna designers determine the effects of impedance and standing waves.  It has its basis in wave theory.  Its relation to regular cycles leads it to immediate use in predicting the cycles of the memory market, or semiconductors, or for any other cyclical market.  Here’s how it is done.

The first thing to do is to determine the frequency of the industry’s cycles.  These cycles can be observed in the chart below, which shows both DRAM and NAND flash revenues since 1991.

The big peaks occur roughly every 5 years on average, so the base frequency is about 157 micro Hertz, or μHz.

It helps to have a frequency analysis of the actual shapes of the waves, and that can be done relatively easily by taking the values from one peak to the next and arranging them in a matrix, with the revenue for each peak-to-peak curve constituting a single row in the matrix.  Since the intervals are of different durations, these lines need to be centered below one another.  What do you do with the cells that aren’t filled when you do this?  That’s easy.  By applying Boltzman’s Constant to these cells you create a neutral ground for the calculations to continue.

To avoid edge effects each row must be multiplied by a sinc function.  This assures that the next step includes no sampling aliases.  This multiplication must be applied both vertically and horizontally through the matrix.  This bears some resemblance to the algorithms applied in computational lithography.

After the data has been groomed we determine the weighted frequency of the cycles, which can be achieved easily enough by performing a Laplace transform on each row.  Those who prefer can use a Hadamard transform, with appropriate compensation.

The resultant matrix is then easily transposed to create a set of dimensions that can be applied to the Smith chart.

Although much of the above work can be done with a calculator or in an Excel, spreadsheet, I prefer to calculate it with pencil and paper.  It makes the numbers seem more real.  Although I have tried to use mental arithmetic, it’s a little too challenging to keep all the numbers in my head.

Introduction to the Smith Chart

The Smith chart is an amazing tool.  It dissolves complex equations into simple sketches that, once drawn onto the chart, can determine the answers to the enormous complexities of antenna designs.

The chart is beautifully symmetric, with the capacitive reactance component or inductive susceptibility accounting for the lower half of the nomogram, while inductive reactance component or capacitive susceptibility is accounted for in the upper half.  For forecasting these would naturally be proxies for the components of economic versus temporal stability.  The circles around the outside of the chart can be used for any of three things: the resistance or conductance component, the wavelengths toward the signal generator or toward the load, or the angle of reflection and transmission coefficient.  For forecasting DRAM these obviously will be translated to the partial derivative of the dollar value of the average transistor over the node migration.

Along the bottom is a separate and very useful little linear nomogram that I will show how to use in a future post.  In the world of RF this is used to determine the Radially-Scaled Parameters: The SWR (the Standing Wave Ratio) both toward the load and toward the generator, attenuation, standing wave loss coefficient, reflection & return losses, and the transmission & reflection coefficients.  I am sure that readers will recognize the parallels between these and common forecast methods, and that I need not further explain.

The Forecast Process

The following series of pictures illustrates the process for a single column of the forecast matrix.  (You can click on any of the charts to view an enlarged rendition.)  First a point is drawn to indicate the current year and state of the present economy.  This shows as a red dot in the first figure.

 

In the second frame one column of matrix values is plotted onto the chart.  This entire process must be repeated for each column of the matrix.  At the end of the line a series of concentric circles is used to help center the blowback arrow that is drawn in the following figure.  The accuracy of this arrow is imperative!  Standard methods can be used for this process.  Next the peak of the column values is located (called out here with a green circle), and a line is drawn between that peak and the tip of the blowback arrow.  Use a protractor to measure the angle between the two and calculate the inverse hyperbolic arc-cotangent.

There you have it!  The process is not at all difficult, but it seems to be as rarely used as it is simple.

Wrap-Up

This same approach can be used to generate forecasts of any duration (we usually  forecast 30 years out) and to any resolution.  Our forecasts are annual, but I have heard of one researcher who used this method to predict minute-by-minute oil futures prices over a 3-year window.   Unfortunately, this researcher was institutionalized shortly thereafter and the forecast has not been kept up-to-date.

In summary, it becomes a relatively trivial exercise to produce accurate forecasts when the appropriate tools are used, and the Smith Chart helps enormously to simplify the process.

Objective Analysis is investigating ways to use the 3D Smith chart to further this success, but this exercise might not be completed until the next April 1st, when we expect to have further amazing revelations.