Table of Contents
Does stationary imply IID?
For an arbitrary distribution, the stationary distribution is not necessarily IID. For example, consider a simple 2-state Markov chain, where the probability of staying in the same state is .
Is stochastic process stationary?
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.
Does stationary imply independence?
Stationarity is a type of independence, but if you have some other type of independence in mind, you will need to specify what that is.
Does stationarity imply Ergodicity?
Yes, ergodicity implies stationarity. Consider an ensemble of realizations generated by a random process. Ergodicity states that the time-average is equal to the ensemble average.
What stationary random process?
4 Stationary Processes. Intuitively, a random process {X(t),t∈J} is stationary if its statistical properties do not change by time. For example, for a stationary process, X(t) and X(t+Δ) have the same probability distributions.
Is a random walk with drift stationary?
Examples of non-stationary processes are random walk with or without a drift (a slow steady change) and deterministic trends (trends that are constant, positive, or negative, independent of time for the whole life of the series). It also does not revert to a long-run mean and has variance dependent on time.
What is a stationary random process?
Intuitively, a random process {X(t),t∈J} is stationary if its statistical properties do not change by time. For example, for a stationary process, X(t) and X(t+Δ) have the same probability distributions. In particular, we have FX(t)(x)=FX(t+Δ)(x), for all t,t+Δ∈J.
What’s the difference between ergodic and stationary?
That is, if we shift all time instants by τ, the statistical description of the process does not change at all: the process is stationary. Ergodicity, on the other hand, doesn’t look at statistical properties of the random variables but at the sample paths, i.e. what you observe physically.
What is a stationary variable?
Statistical stationarity: A stationary time series is one whose statistical properties such as mean, variance, autocorrelation, etc. are all constant over time. Such statistics are useful as descriptors of future behavior only if the series is stationary.
When a random process is said to be strict sense or strictly stationary?
A random process X(t) is said to be stationary or strict-sense stationary if the pdf of any set of samples does not vary with time.
Can a weakly stationary stochastic process be obtained from a random walk?
An important example of weakly non-stationary stochastic processes is the following. Let {yt;t = 0,1,2.} u). Thus a random walk is not weakly stationary process.
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