AR Modeling Why residual is white noise?

1. Why should residuals be white noise?
2. What is white noise in AR model?
3. What is white noise in time series analysis?
4. What does white noise mean in statistics?

Why should residuals be white noise?

The residuals are the differences between the fitted model and the data. In a signal-plus-white noise model, if you have a good fit for the signal, the residuals should be white noise. Create a noisy data set consisting of a 1st-order polynomial (straight line) in additive white Gaussian noise.

What is white noise in AR model?

In time series analysis, a sequence of independent identically distributed (IID) Normal random variables with mean zero and variance σ2 is known as Gaussian white noise. We write this model as ϵ1:N∼IID N[0,σ2].

What is white noise in time series analysis?

A time series is white noise if the variables are independent and identically distributed with a mean of zero. This means that all variables have the same variance (sigma^2) and each value has a zero correlation with all other values in the series.

What does white noise mean in statistics?

The white noise is a stationary time series or a stationary random process with zero autocorrelation. In other words, in white noise any pair of values and taken at different moments and of time are not correlated - i.e. the correlation coefficient. is equal to null.