Monetary Policy, Money Supply And Price Inflation
There are several reasons why there is such a time lag, but the most important one is that most prices tend to be quite sticky and so will not respond immediately to changes in the money supply. A few prices, most notably fuel prices, are almost completely flexible and will for that reason respond almost immediately to money supply changes, but for most other prices, the response will be lagged. The reason is that first of all, because of inventories and forwards/futures contracts, it will take a while before most firms notice higher costs. And because they know many customers will be upset over price increases and that competitors might wait, they will often wait to pass on cost increases. As I've explained before, it is well-known that exporters usually in the short run adopt a pricing to market strategy, where they wait before they raise price and instead absorb cost increases through reduced margins. Eventually, however, when companies realize that exchange rate movements are permanent, they will adjust prices, causing a lagged effect on price inflation.
In this context I would also like to link to another graph, from Spencer at the Angry Bear blog, showing a very strong negative correlation between bond yields and money supply velocity. Money supply velocity is as you might know defined as money supply relative to GDP, or in this case personal income. As bond yields represent the opportunity cost of holding money, we would expect a negative correlation between interest rates and the demand for holding money. Higher demand for holding money is in turn associated with money supply velocity. If we see historically when money supply growth has been highest we can also see that it is during periods of aggressive interest rate cuts, such as in 1983, 2001 and now that money supply growth has been highest.
As there is a immediate link between monetary policy changes and money supply growth, and a lagged link between money supply growth and price inflation, it also follows that there is a lagged link between monetary policy changes and price inflation.
That in turn has two implications, one for current economic forecasting and one for economic policy. The economic forecasting effect, as Daniel pointed out, is that even if money supply growth slows, price inflation will remain high for a while. The economic policy effect is that price inflation targeting is very difficult to implement in practice. Policy makers only know about current inflation, but their influence on that is very small. They can however influence future price inflation, but as they don't know how high it would have been if they didn't make any policy moves, they could just as well end up pushing inflation further away from the target as closer to it (Although arguably, as this post demonstrates, if central banks starts paying attention to the lagged effect between money supply and price inflation, their forecasts would probably improve. But except for Austrians and the dwindling number of Monetarists, few pay attention to money supply today).