A prognostication is a prediction about the future. If you make gloomy prognostications about how much traffic there will be on the way home, you'll be pleasantly surprised to find the drive fast and easy.
Use the noun prognostication when someone's making a forecast or a guess about upcoming events. Your prognostication about whether or not it will rain tomorrow might lead to your family's picnic being cancelled. Another way to use the word is to mean a sign or portent: "I hope that black cat isn't a prognostication of bad luck!" The Latin root, prognostica, means "sign to forecast weather," and it comes from the Greek prognostikos, "foreknowing."