Can a white noise process be correlated with its own values?

Can a white noise process be correlated with its own values?

A white noise process would not be correlated with its own values at any lag.Its mean is zero, variance is constant and autocovariance (using which the autocorrelation plots like acf and pacf are figured out) is also zero. Thus, your results are clearly indicative of the fact that its not a white noise process.

Which is the formula for white noise regression?

So, by the above mentioned formula, one can infer whether the series/data is white noise or not. A white noise process would not be correlated with its own values at any lag.Its mean is zero, variance is constant and autocovariance (using which the autocorrelation plots like acf and pacf are figured out) is also zero.

How to calculate the PSD of white noise?

associated with the white noise random process is obtained by taking the Fourier transformation on both sides: Pxx(Ω) = ¾2 x; Ω 2 R1: (2) This means that the PSD of white noise is flat across all frequencies, i.e., ”white”. The average power associated with the white-noise random process is therefore: Px ave = Rxx(0) = 1: (3)

What makes the ACF of a series make sense?

For an ACF to make sense, the series must be a weakly stationary series. This means that the autocorrelation for any particular lag is the same regardless of where we are in time. The mean E ( x t) is the same for all t.

When to use ACF and pacf in AR models?

The ACF and PACF should be considered together. It can sometimes be tricky going, but a few combined patterns do stand out. (These are listed in Table 3.1 of the book in Section 3.3). AR models have theoretical PACFs with non-zero values at the AR terms in the model and zero values elsewhere.

Why are ACFs and pacfs important in ARMA models?

ARMA models (including both AR and MA terms) have ACFs and PACFs that both tail off to 0. These are the trickiest because the order will not be particularly obvious. Basically you just have to guess that one or two terms of each type may be needed and then see what happens when you estimate the model.