Chapter 2 Introduction to statistics
Before we move to the discussion of ETS, ARIMA and ADAM, it makes sense to discuss some of the basics statistical terms and what they mean in the context of forecasting. Although, many of them originate from statistics and econometrics, we need to look at them from a different perspective: we are more interested in the forecasting process rather than in the estimation of parameters. Still, if you do not know statistics and econometrics well and want to have a good source on the topic, I would recommend reading an online book by Hanck et al. (2020).
Before we move further, we need to agree what the term “estimator” means, which will be used several times in this chapter:
- Estimate of a parameter is an in sample result of application of a statistical procedure to the data for obtaining some coefficients of a model. The value calculated using the arithmetic mean would be an estimate of the population mean;
- Estimator is the rule for calculating estimates of parameters based on a sample of data. For example, arithmetic mean is an estimator of the population mean. Another example would be method of Ordinary Least Squares, which is a rule for producing estimates of parameters of a regression model and thus an estimator.