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Stochastic processes and their moments
White noise, and weak- and wide-sense stationarity
Random walks
Martingale processes
Markov processes
Survival functions
Wiener processes and Brownian motion
Stochastic differential equations
Orders of integration
Auto-Regressive processes, Moving-Average processes and Wold's theorem
Markov chain Monte Carlo sampling
Sampling from processes
Forecasting stochastic processes
Quantisation and sample rates
Discrete Fourier Transform
Down sampling
Fast Fourier Transform
Noisy networks
Imputing missing data for time series
Estimating Markov chains
Estimating Hidden Markov Models (HMMs)
Univariate forecasting
Inference with time series
Survival analysis
For a process with the Martingale property, the expected value of all future variables is the current state.
This only restricts expectations.
\(E(X_{n+1}|X_0,...,X_n)=X_n\)