I think in general you're right, but with a some exceptions. Like say it depends on what part of economy we are talking about. If inflation, GDP numbers and so on, then those move slower. But stock market can react pretty quickly it seems. For example it can react to getting a hint of a possibly changing regulatory environments. A crashing or rapidly rising stock market will affect the economy quite a bit, especially if it is sustained long enough.
War can change things, disasters, foreign economic threats (say a trade war with a major superpower). Those can have rapid effects as well.
Well, disasters and foreign economic threats aren't due to a politician's policy, and the regulatory environment usually doesn't change straight away (that requires legislation, not just a policy manifesto). War is a rare event as well, and it doesn't necessarily affect the wider economy - the war in Iraq and Afghanistan hasn't affected the US economy much, which quite happily went through a boom time in the early years of the war, then crashed for reasons unrelated to the war. Of course, the economy of Iraq got soundly fucked by war, but that wasn't due to the economic policies of the politician in charge.
The war had enormous implications for the economy. Commodity prices were driven extremely high due to investor uncertainty about the Middle East oil supply. It got so bad that Congress had to pressure traders to stop hoarding massive amounts of crude oil in the hopes that the supply would be disrupted and the price would escalate. These commodity price rises fueled speculation into other asset classes, such as housing and loans.
As always there were some short-term positive Keynesian stimulative effects by increased government spending, but a massive run-up of the deficit did increase the cost of servicing the national debt, which might otherwise have been directed into productive enterprises, rather than the wasteful Iraq war which achieved negative progress.
War can change things, disasters, foreign economic threats (say a trade war with a major superpower). Those can have rapid effects as well.