I want to make a function that does GARCH and ARCH in python for calculating variance. But I only have a general understanding of the model. Are there any good papers that can be recommend to give me a step by step calculation. I am not a statistician or have a econometrics background so it is difficult for me to get a detailed understanding.
Right now my understanding is:
Input: Error terms, alpha values, beta values, orders p and q
Error terms are from the difference between the best fit Autoregressive model and the actual data. (not sure if this is correct). The error at time t is made up of 2 terms a standard deviation at time t and a stochastic variable.
q is the ARCH term used for squared of errors. p is the used for variance.
Alpha is a 1 x q length matrix and beta 1 x p length matrix. Both are coefficients larger than 0 and less than 1. (not sure how they are calculated) Alpha represents internal volatility (not sure if this is correct) Beta represents external volatility(not sure if this is correct)
Output: variance at time t
Statistics Test:
Jarque-Bera test: Checks if the error terms are normal distributed
White test: checks for heteroskedasticity in error terms
Wald test: used to check how alpha and beta influence the time series (not sure if this is correct)
Lagrange multiplier test: determines the order of the model (not sure if this is correct)
