# Difference between forecasting model, forecasting method and forecasting function

I am new to the field of Business Analytics. Can anyone distinguish between forecasting model, forecasting method and forecasting function? According to the book forecasting function is is an equation for calculating the forecasts over the forecast horizon. Then it provides the example for forecasting method as $$F_t =b_0 + b_1 t$$ and model as $$Y_t = \beta_0 + \beta_1 t + \varepsilon_t$$

I can't understand any difference between these equations, because they all seem to be the equations with time as dependent variable and some constants. What is the difference in these equations that makes these three terms different?

• Which book is this? Is there any more context in the book that might be helpful? We have to guess what some of these symbols mean. – The Laconic Sep 22 '18 at 18:14
• The forecasting model does not need to be the linear regression, which means that (a) the forecasting function does not need to be linear ($x=at+b$) and that (b) the forecasting method does not need to be minimizing the square of the error. – AlainD Sep 23 '18 at 14:19

The equation $$Y_t = \beta_0 + \beta_1 t + \varepsilon_t$$ is a mathematical model of how the data, $$Y_t$$, are composed. It is of course not true but might be useful. It says there is some baseline (intercept) of $$\beta_0$$ and as $$t$$ increases, $$Y_t$$ is linearly increasing at rate $$\beta_1$$. However, our data contain error, hence the $$\varepsilon_t$$ to account for stochastic variability around $$\beta_0 + \beta_1 t$$. In some contexts, $$\beta_1$$ might be considered the trend.
The equation $$F_t = b_0 + b_1 t$$ is a formula to forecast. Because the noise (error) itself is not really forecastable, this only includes terms for properties of the time-series that we estimate from the mathematical model.
• Also, there's some difference between $\beta$ and $b$ that needs to be addressed. I presume the former is the true parameter and the latter is an estimate, but without more context, who knows... – The Laconic Sep 22 '18 at 18:12