"Cointegration is a statistical property of a collection (X1, X2, ..., Xk) of time series variables."
A property of two or more non-stationary time series that allows them to be expressed as a stationary linear combination.
Stationarity: A time series is said to be stationary when its statistical properties like mean, variance, etc., do not vary with time. This property is essential for cointegration analysis because non-stationary variables can lead to spurious regression results.
Unit Root: A unit root is a feature of a time series that indicates it is non-stationary. It means that the time series has a random walk property where the series tends to move in the same direction as the previous time period.
Differencing: Differencing is a technique used to transform a non-stationary time series into a stationary one. It involves taking the difference between consecutive observations.
Autocorrelation: Autocorrelation is a measure of the relationship between two observations in a time series. If the time series is not stationary, then there may be significant autocorrelation present.
Vector Autoregression (VAR): VAR is a statistical model used to analyze the relationship between two or more variables. It is especially useful in cointegration analysis because it can help identify the long-run equilibrium relationship between variables.
Error Correction Model (ECM): The ECM is a model used to analyze the relationship between non-stationary variables. It includes a term for the error correction process, which adjusts the variables back towards equilibrium.
Johansen Cointegration Test: This test is used to determine the number of cointegrating vectors between two or more non-stationary variables. It is a popular test used in cointegration analysis.
Granger Causality: Granger causality is a statistical concept that measures whether a time series can help predict the future values of another time series.
Co-integration Rank Test: This test is a refinement of the Johansen test and is used to identify the rank of the cointegrating space. It can help determine whether cointegration exists between two or more variables.
Vector Error Correction Model (VECM): The VECM is a model used to analyze the dynamics of cointegrated variables. It combines the VAR and ECM models to provide a more robust framework for analyzing these types of models.
The Johansen cointegration: This type of cointegration involves a multivariate time series that has more than one variable.
The dynamic cointegration: This cointegration examines how long-run equilibrium between two or more time series evolves over time.
The seasonal cointegration: This type of cointegration looks for cointegrating relationships between time series data that have a known seasonal pattern.
The partial cointegration: This type of cointegration describes situations where only a part of a time series exhibits a long-run relationship.
The cross-sectional cointegration: This type of cointegration identifies cointegrating relationships between a set of non-stationary time series observed cross-sectionally.
The dynamic partial adjustment cointegration: This cointegration looks at how long-run equilibrium changes over time and how the series adjusts to deviations from equilibrium.
The multivariate cointegration: This cointegration involves three or more non-stationary time series and seeks to identify the long-run equilibrium relationship between them.
The residual-based cointegration: This type of cointegration examines the residuals produced by models that have incorporated cointegration.
The instantaneous cointegration: This type of cointegration is concerned with testing for a relationship between two time series at a specific point in time.
The panel cointegration: This type of cointegration examines how cointegrating relationships change over time across a set of different groups or panels.
"First, all of the series must be integrated of order d."
"If a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated."
"If (X,Y,Z) are each integrated of order d, and there exist coefficients a,b,c such that aX + bY + cZ is integrated of order less than d, then X, Y, and Z are cointegrated."
"Cointegration has become an important property in contemporary time series analysis."
"Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends."
"Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends."
"First, all of the series must be integrated of order d (see Order of integration)."
"If a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated."
"(X,Y,Z) are each integrated of order d."
"Then there exist coefficients a,b,c such that aX + bY + cZ is integrated of order less than d."
"...provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends."
"many US macroeconomic time series (like GNP, wages, employment, etc.)"
"Cointegration has become an important property in contemporary time series analysis."
The paragraph does not mention non-macroeconomic time series.
The paragraph does not mention the specific proposer of the concept of cointegration.
"Charles Nelson and Charles Plosser (1982) provided statistical evidence..."
The paragraph does not explicitly state the limit or number of series in a cointegrated collection.
The paragraph does not discuss the specific applications of cointegration.
The paragraph does not provide information about the widespread adoption of cointegration in practical analysis.