How to tell if a set of data points are independent random variables, normally distributed with expectation zero and has a variance of x?

I need to confirm if the process I have simulated is indeed a Brownian Motion. One of the properties of a Brownian Motion are: 1. independent increments (which means that the difference between succeeding points on the Brownian Motion are independent random variables. I tried to use a correlation function, however, I have only one path and I do not know how to correlate the data) 2. the increments B(t + h) - B(t) must be normally distributed and has a variance of h.