# Questions tagged [white-noise]

White noise is a random process whose "components each have a probability distribution with zero mean and finite variance, and are statistically independent".

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### Calculating covariance and correlation of a moving average time series

I'm learning about MA(1) time series models and I have an example with the answers but not the worked through solutions. Let {$ϵ_t$} be a zero mean white noise with variance $σ^2$ and $X_t=ϵ_t+ϵ_{t−1}$...
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### Yule-Walker equations (ARMA(1,1))

My professor assigned me this task: Let $\{X_T\}$ be causal $ARMA(1,1)$ process, i.e. $X_t - \varphi X_{t-1} = Z_t + \theta Z_{t-1}, \ \ Z_t \sim WN(0,\sigma^2)$. i) Using Yule-Walker equations, ...
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### How is adding noise to training data equivalent to regularization?

I've noticed that some people argue that adding noise to training data equivalent to regularizing our predictor parameters. How is this the case? Some of the examples listed on SE discussing this ...