Expect is usually used when you think a person has a responsibility to do a certain activity, which implies that you hope it will come true.
Someone is expecting something, someone, a package, a certain outcome, etc. and they are somewhat confident that it will happen. If I expect you to join me for lunch, that means that we already made plans to meet up for lunch, and I will be surprised if you don’t show up.
I am expecting the exam result sometime next week. (I am excited for the result, because I did it very well)
I expect to find the room clean by the time I get home. (I hope the room will be clean)
Anticipate is more like you can guess that someone will likely take a certain action, which implies that you already had known it and you were preparing for (and waiting for) the event to happen.
If you anticipate that something will happen, it means that you suspect it MIGHT happen. Anticipation involves a lot more speculation.
The concert on Tuesday is highly anticipated and is discussing widely on social media. (People are very excited for the concert)
I anticipate he will clean the room by the time I get home. (the room will be cleaned probably. I am not surprised if I won’t be cleaned)
Predict implies don’t know what time the event will happen. Generally, it sounds like it’s simply the person’s opinion.
The weather didn’t turn out as rainy as the newspaper article predicted.
Forecast is a subset of prediction, and it’s based on time-series data. So, all forecast are predictions, but not all predictions are forecast. It is usually only for money and weather scenarios. Because correct weather and money predictions base on temporal time-series information.
The company’s sales forecast looks very good.
The forecaster forecasts it will rain this weekend.