Beginners issue in polynomial curve fitting [Part 1]

Question

I have just started understanding modeling techniques based on regression models and was going through MATLAB curve fitting toolbox and the SO. I have fundamental doubts and unable to proceed further. I have a single vector set with k=100 data points which I want to fit into an AR model,MA model,ARMA model successively to see which is better suited.Starting with an AR(p) model of the form y(k+1)=a*y(k)+ b*y(k-1)The command

coeff = polyfit(x,y,d) 

will fit a polynomial of degree say d=1 with p number of coefficients indicating the order of the model (AR(p)). But I just have 1 set of data which is the recording of the angular moment.So,what will go as the first parameter (x) of the function signature i.e what will be x,y?Then, what if the linear models are not good enough so I may have to select the nonlinear models.Can somebody please guide with code snippets what are the steps in fitting,checking for overfitting,residual calculation etc.

Answer 1

x is likely to be k (index of y). And the whole code:

c =polyfit(1:length(y), y, d).

Matlab has a curve fitting toolbox. You could use it to check different nonlinear fitting in GUI to get some intuition.

If you want steps there's a great Coursera Machine Learning course. The beginning of this course is related to linear regression and I recommend you to spend some hours at least on that beginning.