Gauss Markov Process

1. Is Gaussian process Markov?
2. What defines a Markov process?
3. What is Gauss Markov theorem in econometrics?
4. What result is proved by the Gauss Markov theorem?

Is Gaussian process Markov?

Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. A stationary Gauss–Markov process is unique up to rescaling; such a process is also known as an Ornstein–Uhlenbeck process.

What defines a Markov process?

A Markov process is a random process in which the future is independent of the past, given the present. Thus, Markov processes are the natural stochastic analogs of the deterministic processes described by differential and difference equations. They form one of the most important classes of random processes.

What is Gauss Markov theorem in econometrics?

The Gauss–Markov theorem asserts that the ordinary least-squares estimator. ˆ β = (X X) −1X y of the parameter β in the classical linear regression model (y;Xβ,σ2I) is the unbiased linear estimator of least dispersion.

What result is proved by the Gauss Markov theorem?

The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.