Time series

I have some questions, please.

1- Why nonlinear time series models?
2- What are the limitations of linear time series models?
3- What key features in data cannot be captured by linear time series models?
4- What diagnostic tools (visual or statistical) suggest incompatibility of a linear model with the data?

Can you help me to found the answers to these questions?


TS Contributor
Q1 - Because linear time series models are only designed to model linear trends in time series data.
Q2 - You may also have exponential trends (read COVID-19) and s-curve trends.
Q3 - You may have seasonality (additive or multiplicative) and cyclicity, none of which a linear model can address.
Q4 - Your eyes, decomposition and residuals.