Viewed over the whole available history of fiat money in Sweden, high levels of inflation have been present only over a short time span. It is only in the last two decades the seventies and the eighties that inflation has been high, at an average of eight percent on an annual basis. Based on consumer price data from 1830 to 1970, by contrast, the average inflation rate has been about two percent. In January 1993, the governing board of the Riksbank announced an inflation target of two percent as target for monetary policy. In the period after this announcment inflation has come down to its pre 1970 level. This poses difficulty for forecasting inflation, since the 1970-92 period represents a sizable part of the available and reliable macro data. In particular, forecasts based on linear models have the property that they tend to revert back to their unconditional means. Since the mean has been high, linear models thus tend to produce implausibly high forecasts that do not take into account the new monetary regime with an inflation target, nor the new legislative independence of the Riksbank.inflation state. It is then possible to use data from 1970-1992 and yet produce plausible forecasts one to two years ahead. The forecasts incorporate the risk of switching back to high inflation, but are not dominated by this risk the way linear models are. Nor is this risk ignored altogether, such as with the introduction of a dummy variable for the shift in the level of inflation.