Difference between forecast, estimation, projection, prediction?

Question

Could someone explain me the difference between those terms. For me all of them are somehow synonymous. Thanks in advance!

Answer 1

Language is often inexact, but in terms of how I've seen the words used in mathematics and statistics:

• Approximation happens when you have a value, or a function, that is difficult to calculate, and so you replace it with a simpler calculation. In more rigorous contexts, this usually includes some exploration of the error involved. For example, using $\pi = \frac{22}{7}$ is an approximation with an error of about 0.04%. Approximations often relate to asymptotic behaviours, i.e. an approximation for a function is often expressed in relation to how the error behaves in some kind of limit.

• Estimation happens when you have a quantity you can't measure directly, but you can use a random mechanism to guess its value. For example, I roll a die 100 times and I get 20 rolls of 1, so I estimate that it has a 20% probability of rolling a 1, with a standard deviation of 4%.

• Forecasting and prediction are, to me, the same thing. They both involve having a sequence of data, and building a model based on that data to predict something about a future data point. For example, I can look at the price of Bitcoin over the past year, and if I assume it follows a certain pattern then I expect that its value tomorrow is going to be 2% higher than its value today.