Question

Is white noise predictable? Briefly explain.

Answer 1

First of all we try to find out what is white noise, then we will see if it is predictable or if not why?

White noise is random noise that has a flat spectral density — that is, the noise has the same amplitude, or intensity, throughout the audible frequency range (20 to 20,000 hertz). ... For example, some people use white noise machines as sleep aids to drown out annoying noises in the environment.

White noise is an important concept in time series forecasting.

If a time series is white noise, it is a sequence of random numbers and cannot be predicted. If the series of forecast errors are not white noise, it suggests improvements could be made to the predictive model.

In this tutorial, you will discover white noise time series with Python.

A time series may be white noise.

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.

If the variables in the series are drawn from a Gaussian distribution, the series is called Gaussian white noise.

White noise is an important concept in time series analysis and forecasting.

It is important for two main reasons:

Predictability: If your time series is white noise, then, by definition, it is random. You cannot reasonably model it and make predictions.
Model Diagnostics: The series of errors from a time series forecast model should ideally be white noise.
Model Diagnostics is an important area of time series forecasting.

Time series data are expected to contain some white noise component on top of the signal generated by the underlying process.