[I have already asked this question on CrossValidated but until now received no answer]
I have read some explanations about the properties of linear vs nonlinear models, but still I am sometimes not sure if a model on hand is a linear or a nonlinear one. For example, is the following model linear or nonlinear?
$$y_t=\beta_0 + \beta_1B(L;\theta)X_t+\epsilon_t$$
With:
$$B(L;\theta)=\sum_{k=1}^{K}b(k,;\theta)L^k$$
$$L^kX_t=X_{t-k}$$
Where $b(k;\theta)$ represents (a decaying) Exponential Almon Polynomial function of the form:
$$b(k;\theta)=\frac{exp(\theta_1*k+\theta_2*k^2)}{\sum_{k=1}^{K}exp(\theta_1*k+\theta_2k^2)}$$
In my view, my main equation (the first one) is linear with respect to $X_t$, because this term is just multiplied with a weight. But I would say the weighting function (the last equation) is nonlinear with respect to the parameters $\theta_1$ ans $\theta_2$.
Can someone explain to me if my main function is a linear or a nonlinear one and what does it mean for the estimation procedure - do I have to apply linear or nonlinear least s squares method?. Furthermore, what is the discernible feature by means of which I can definitely identify if a function is a nonlinear or linear one?
Thanks!