Lab4_flashcard_TimeSeries

Front

Properties of weakly stationary time series:

Back

Constant mean, constant variance, and autocovariance depends on lag, not time.

Answer explanation

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.

Front

Key difference between random walk and white noise:

Back

A random walk accumulates past values and has a long memory; white noise has no memory.

Answer explanation

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.

Front

Predictability of a White Noise process:

Back

Future values are completely unpredictable from past values.

Answer explanation

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.

Front

ACF in random data (white noise)

Back

Near zero for all lags, within confidence intervals.

Answer explanation

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.

Front

Primary role of ACF in time series analysis

Back

Reveals dependence structure between current and past values, aiding model selection and pattern identification.

Answer explanation

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.

Front

Importance of ergodicity in time series analysis

Back

Ensures time averages reflect ensemble averages for consistent estimates from a single realization.

Answer explanation

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.

Front

ACF estimation correlogram represents:

Back

Graphical representation of autocorrelation coefficients for different lags.

Answer explanation

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.

Front

Primary characteristic in the second graph:

Back

Variance is constant; mean is increasing.

Answer explanation

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.

Front

Two restrictions for sample mean convergence:

Back

Stationarity and ergodicity; to avoid excessive variability and strong dependence between distant events.

Answer explanation

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.