To my knowledge, all white noise tests are to test whether a process is a white noise or not. Is there any test in time or frequency domain, that test for a white noise, whether its variance is equal to a certain value $\sigma^2$ or not? Given a white noise process $X_1,\cdots, X_N$, I want to test $H_0$: $$H_0: \sigma_X^2 =\sigma^2 \hspace{0.3cm}\text{vs}\hspace{0.3cm} H_1: \sigma_X^2 \neq \sigma^2$$
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2Have you looked up "variance test"? – rolando2 Feb 19 '18 at 13:20
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1The results at https://stats.stackexchange.com/questions/121662 lead naturally to a simple, effective test. – whuber Feb 19 '18 at 15:25