I always thought of null hypothesis as something you want to reject. For example, in checking the significance of co-efficient, we put the null hypothesis is equal to 0. Since we want the co-efficients to be significant and other than 0, we thereby reject the null hypothesis.
Why in checking heteroskedasticity, we put the null as : There is no heteroskedasticity (HS)
HS is bad for regression and we do not want it in the regression. So shouldn’t the null be - there is HS so that we can reject it.
One thing to consider is that the null hypothesis is often thought to be the assumed state of nature. In this case, recall that the method of ordinary least squares (linear regression) has assumptions pertaining to the random error term. One of these assumptions is that the variance on the error term is constant for all settings of the independent variables. More technically, this can be referred to as homoscedasticity; again, we are assuming this in regression and it must be tested.
Now-- the null hypothesis is what we are assuming is the true state of nature, and we try to find evidence of our alternative hypothesis. Based on our regression assumption, we can say that the null hypothesis is homoscedasticity of the error term (no heteroscedasticity). We search for evidence to conclude that heteroscedasticity is a problem (evidence in favor of our alternative hypothesis).
Please let me know if this is what you are looking for-- hope this helps!
Also, for general hypothesis tests it might help to consider the objective of the test. For example, if I claim that my average portfolio return is greater then 10% per year, then I should be trying to prove that the mean return is > 10% ---- then my alternative hypothesis is that R>10
the null hypothesis is then R=10
R is the mean return per year. I have made this claim that my average yearly return exceeds 10%, so logically, I must find evidence and prove this with a measure of statistical reliability. In other words, I need to find support of my alternative hypothesis (as I mentioned in my first post).