Table of Contents
Does strict stationarity imply weak stationarity?
First note that finite second moments are not assumed in the definition of strong stationarity, therefore, strong stationarity does not necessarily imply weak stationarity.
What is strict sense stationary process?
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.
Are all identically distributed variables independent?
Thus, the formal definition of the independent and identically distributed random variable is as follows: A collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent.
Is random walk weakly stationary?
A random-walk series is, therefore, not weakly stationary, and we call it a unit-root nonstationary time series.
Is Random Walk mean stationary?
In fact, all random walk processes are non-stationary. Note that not all non-stationary time series are random walks. Additionally, a non-stationary time series does not have a consistent mean and/or variance over time.
How would you identify the strict-sense 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. R X 0 = E X 2 t gives the average power (second moment) or the mean-square value of the random process.
Is Gaussian process strict-sense stationary?
A Gaussian stochastic process is strict-sense stationary if, and only if, it is wide-sense stationary.
Is random walk stationary?
What does it mean for a random variable to be identically distributed?
In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent.