Contents
Which is the best description of a stationary process?
In mathematics and statistics, a stationary process ( a.k.a. 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. Consequently, parameters such as mean and variance also do not change over time.
Which is an example of a discrete time stationary process?
An example of a discrete-time stationary process where the sample space is also discrete (so that the random variable may take one of N possible values) is a Bernoulli scheme.
Can a trend be transformed into a stationary process?
A trend stationary process is not strictly stationary, but can easily be transformed into a stationary process by removing the underlying trend, which is solely a function of time.
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.
What does stationarity mean in a stochastic process?
Having a basic definition of stochastic processes to build on, we can now introduce the concept of stationarity. Intuitively, stationarity means that the statistical properties of the process do not change over time. However, several different notions of stationarity have been suggested in econometric literature over the years.
What does stationarity mean in a time series?
In t he most intuitive sense, stationarity means that the statistical properties of a process generating a time series do not change over time. It does not mean that the series does not change over time, just that the way it changes does not itself change over time.
Are there any processes that are strict sense stationary?
However, it turns out that many real-life processes are not strict-sense stationary. Even if a process is strict-sense stationary, it might be difficult to prove it.
When is a stochastic process a wide-sense stationary process?
If a stochastic process is wide-sense stationary, it is not necessarily second order stationary. If a stochastic process is strict-sense stationary and has finite second moments, it is wide-sense stationary. If two stochastic processes are jointly (M+N)-th order stationary,…