Lab4_flashcard_TimeSeries

A time series is weakly stationary if it has a constant mean, constant variance, and its autocovariance depends only on the lag, not on time. This ensures that the statistical properties do not change over time.

The key difference is that a random walk accumulates past values, leading to long-term dependence, while white noise consists of independent values with no memory, making it a purely random process.

In a White Noise process, future values are random and do not depend on past values, making them completely unpredictable. This rules out any patterns or trends that could aid in forecasting.

In random data (white noise), autocorrelations should be near zero for all lags, indicating no predictable pattern. This aligns with the correct choice, as significant positive or negative autocorrelations would suggest a structure that doesn't exist.

The autocorrelation function (ACF) reveals the dependence structure between current and past values in a time series, which is crucial for model selection and identifying patterns.

Ergodicity is crucial because it ensures that time averages converge to ensemble averages, enabling reliable estimates from a single time series realization. This consistency is essential for valid time series analysis.

The correlogram visually displays the autocorrelation coefficients at various lags, helping to identify patterns in the time series data. This makes it the correct choice, as it specifically represents the relationship of autocorrelations over time.

The second graph shows that while the mean value is increasing over time, the variance remains constant, indicating a steady spread of data points around the mean.

Stationarity ensures the mean and variance are constant over time, while ergodicity allows time averages to equal ensemble averages, avoiding excessive variability and strong dependence between distant events.