Can white noise be non-stationary?
For example, a white noise is stationary but may not be strict stationary, but a Gaussian white noise is strict stationary. Loosely speaking, if a series does not seem to have a constant mean or variance, then very likely, it is not stationary.
Are all white noise process stationary?
White Noise Process: A white noise process is a serially uncorrelated stochastic process with a mean of zero and a constant and finite variance. Note that this implies that every white noise process is a weak stationary process.
Is white Gaussian noise wide sense stationary?
Now, if the common distribution function of random variables does not have a variance, e.g. Cauchy random variables, then white noise is not a wide-sense-stationary process (even though it is a strictly stationary process).
Is Random Walk A white noise?
The change in price of a random walk is just White Noise. Incidentally, if prices are in logs, then the difference in log prices is one way to measure returns. The bottom line is that if stock prices follow a random walk, then stock returns are White Noise.
What is a strictly stationary model?
In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.
Which is the best definition of weak stationarity?
3.1 Definition: Weak stationarity and strict stationarity A time series model which is both mean stationary and covariance stationary is called weakly stationary. A time series model for which all joint distributions are invariant to shifts in time is called strictly stationary.
What kind of time series is weakly stationary?
A time series model which is both mean stationary and covariance stationary is called weakly stationary. A time series model for which all joint distributions are invariant to shifts in time is called strictly stationary.
What causes non stationary data to become stationary?
Since stationarity is an assumption underlying many statistical procedures used in time series analysis, non-stationary data is often transformed to become stationary. The most common cause of violation of stationarity is a trend in the mean, which can be due either to the presence of a unit root or of a deterministic trend.