Autocorrelation, expectation, moment

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SUMMARY

The discussion centers on the relationship between expectations, moments, and autocorrelation in stochastic processes. Specifically, E(X(t)) represents the first moment, while E(X(t)n) denotes the nth moment. Additionally, E(X(t)X(s)) is identified as the autocorrelation function dependent on the time difference (t-s) when the process is stationary. These concepts are foundational in understanding the statistical properties of stochastic processes.

PREREQUISITES
  • Understanding of stochastic processes
  • Familiarity with statistical moments
  • Knowledge of autocorrelation functions
  • Basic concepts of stationarity in time series analysis
NEXT STEPS
  • Study the properties of stochastic processes in detail
  • Learn about higher-order moments and their significance
  • Explore the concept of stationarity in time series analysis
  • Investigate practical applications of autocorrelation in signal processing
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Statisticians, data scientists, and researchers in fields involving time series analysis and stochastic modeling will benefit from this discussion.

vptran84
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What is the relationship between Expectations, Moments, and Autocorrelation. Can someone please please give me some examples? thanks
 
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Let X(t) be a stochastic process and let E(Y) be the expectation of Y.

E(X(t)) is the first moment
E(X(t)n) is the nth moment
E(X(t)X(s)) is the autocorrelation as a function of t and s. If the process is stationary, it depends on (t-s).
 

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