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An Introduction to Time Series

Some Basic Examples of Time Series

Explore the fundamental examples of time series: white noise and random walk. Understand their statistical properties, differences, and significance in time series analysis and modeling, including how white noise serves as a diagnostic tool for model residuals and why random walks are important in fields like finance and statistics.

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White noise

Simply put, white noise is a time series with 0 mean, some variance, σ2\sigma^2, and 0 autocovariance. More formally, we would say that a series yty_t is white noise if E(yt)=0E(y_t) = 0 and σ2≠0\sigma^2 \neq0 ...