The partial correlation between a time series and a lagged version of itself, controlling for the contributions of all other lags.
Autocorrelation: Autocorrelation refers to the correlation between observations of a time series at different points in time. It is a measure of how similar an observation is to its previous observation.
Stationarity: Stationarity refers to the property of a time series where the statistical properties, such as mean, variance, and autocorrelation, remain constant over time. It is a prerequisite for studying autocorrelation.
PACF: The partial autocorrelation function or PACF measures the linear dependence between two time series observations at a given lag, controlling for the effect of all the previous lags. It is useful for identifying the direct and indirect relationship between two variables.
Lag: In time series analysis, a lag is the number of time intervals between two observations. It plays an important role in the calculation of the autocorrelation and partial autocorrelation.
Regression analysis: Regression analysis is used to estimate the relationship between an independent variable and a dependent variable. It is used in time series analysis to identify the relationship between the current observation and the previous observations.
ARIMA models: An ARIMA or Autoregressive Integrated Moving Average model is a statistical method used to model and forecast time series data. It is useful for predicting future values based on past observations.
Time series decomposition: Time series decomposition is a method used to break down a time series into its constituent components such as trend, seasonality, and error. It is useful for understanding the underlying patterns and structure of the data.
Residual analysis: Residual analysis is a method used to assess the goodness of fit of a model and the validity of its assumptions. It helps identify if there are any patterns or trends left in the data that the model has not accounted for.
Box-Jenkins methodology: The Box-Jenkins methodology is a statistical approach to time series analysis that involves identifying the appropriate ARIMA model for a given time series. It involves three main steps: model identification, estimation, and validation.
Spectral analysis: Spectral analysis is a method used to identify the periodic or cyclic patterns in a time series. It involves decomposing the time series into its frequency components using techniques such as Fourier transforms.