Recently it has become clear that many technologies follow a generalized version of Moore's law, i.e. costs tend to drop exponentially, at different rates that depend on the technology. Here we formulate Moore's law as a time series model and apply it to historical data on 53 technologies. Under the simple assumption of a correlated geometric random walk we derive a closed form expression approximating the distribution of forecast errors as a function of time. Based on hind-casting experiments we show that it is possible to collapse the forecast errors for many different technologies at many time horizons onto the same universal distribution. As a practical demonstration we make distributional forecasts at different time horizons for solar photovoltaic modules, and show how our method can be used to estimate the probability that a given technology will outperform another technology at a given point in the future.
