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# Questions tagged [ergodic]

An ergodic dynamic system or stochastic process is one in which time averages agree with averages over the state space of the process.

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### How do you check ergodicity of a stochastic processes from its sample path(s)?

How do you check ergodicity of a wide-sense stationary stochastic processes from its sample path(s)? Can we check ergodicity from a single sample path? Or do we need multiple sample paths? One ...
813 views

### When is a ARMA(p,q) process ergodic?

We know that a ARMA(p,q) process is weakly stationary, iff there is no root of the characteristic polynomial of its AR part lying on the unit circle. But what is the necessary and sufficient ...
869 views

### Derivation of sample autocovariance

The autocovariance is defined as $$\gamma(t,s) = Cov(X_{t}, X_{s})=E[(X_{t}-\mu_{t})(X_{s}-\mu_{s})]$$ When we have a stationary process the only thing that matters is the lag between the variables: ...
918 views

### How to detect if Ergodicity, Stationarity and Martingale. dif. sequence?

I'm not sure, but I think I've read somewhere that because the Classical Linear Regression model assumes to have a random sample, when researchers they might not be in presence of a sample with that ...
24 views

### Is the Metropolis-Hastings kernel always aperiodic, irreducible and geometrically ergodic?

Let $(E,\mathcal E,\lambda)$ be a measure space, $Q$ be a Markov kernel on $(E,\mathcal E)$ with $$Q(x,B)=\int_B\lambda({\rm d}y)q(x,y)\;\;\;\text{for all }(x,B)\in E\times\mathcal E$$ for some ...