Chapter 15 Statistical models assumptions

In order for a statistical model to work adequately and not to fail, when applied to a data, several assumptions about it should hold. If they do not, then the model might lead to biased or inefficient estimates of parameters and inaccurate forecasts. In this section we discuss the main assumptions, united in three big groups:

1. Model is correctly specified;
2. Residuals are independent and identically distributed (i.i.d.);
3. The explanatory variables are not correlated with anything but the response variable.

We do not aim to explain why the violation of assumptions would lead to the discussed problem, and refer a curious reader to econometrics textbooks (for example Hanck et al., 2022). In many cases, in our discussions in this textbook, we assume that all of these assumptions hold. In some of the cases, we will say explicitly, which are violated and what needs to be done in those situations.

References

• Hanck, C., Arnold, M., Gerber, A., Schmelzer, M., 2022. Introduction to Econometrics with R. https://www.econometrics-with-r.org/index.html (version: 2022-04-17)

The software behind this book. The methods described here are implemented in the greybox package for R and Python, which are free and open source.

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