stationarity

Time Series Data: A time series data is a set of observations collected at different points in time.

Trend: Trend refers to the long-term patterns in a time series data. A time series is said to have a trend if there is a consistent increase or decrease in its values over time.

Seasonality: Seasonality is the repetitive and predictable fluctuations that occur in a time series data at regular intervals. It is usually associated with recurring events such as the changing of seasons or holidays.

Stationarity: Stationarity refers to the property of a time series data that its statistical properties such as mean, variance, and autocorrelation do not change over time. A stationary time series is easier to model and analyze.

Autocorrelation: Autocorrelation is the correlation between a time series data and its lagged values. A positive autocorrelation indicates that the values in the time series tend to follow a similar pattern at successive time points.

White Noise: White noise is a type of time series data that has no correlation between its values at different time points.

Unit Root: A unit root is a statistical property of a time series data that indicates that it has a trend and is non-stationary.

Detrending: Detrending is the process of removing the trend component from a time series data to make it stationary.

Differencing: Differencing is the process of subtracting the time series data from its lagged values to remove the trend and make it stationary.

ARIMA Models: An ARIMA (Autoregressive Integrated Moving Average) model is a statistical model used for time series data that takes into account the autoregressive, differencing, and moving average components.

Exponential Smoothing: Exponential smoothing is a technique used for time series forecasting that gives greater weight to more recent observations.

Box-Jenkins Methodology: The Box-Jenkins methodology is a standard approach to time series modeling that involves model identification, estimation, and diagnostics.

Strict Stationarity: A time series process is considered to be strictly stationary if its statistical properties, such as the mean, variance, and autocovariance, do not depend on the time index.

Second-order Stationarity: A weaker form of stationarity compared to strict stationarity. A time series process is said to be second-order stationary if the mean and the autocovariance structure are constant over time, but its variance may still change over time.

Trend Stationarity: It refers to the type of stationarity where there is a trend (upward or downward movement) present over time, but the statistical properties of the series remain constant.

Seasonal Stationarity: When the statistical properties of a time series remain constant over time, but a seasonal pattern is observed in the series, it is called seasonal stationarity.

Cyclical Stationarity: It describes the type of stationarity where time series cycles occur over an extended period, and these cycles are not related to any seasonal or trend patterns.

Difference Stationarity: Also known as weak stationarity or covariance stationarity. A time series process is considered difference stationary if it becomes stationary after taking the first or second difference of the series.

Conditional Heteroscedasticity: It refers to the type of time series that exhibit a varying level of volatility or variance over time, and the variance of the series is conditionally dependent on its past values.