A similar test involving more variables can be applied with vector autoregression.

This page shows the details for different matrix notations of a vector autoregression process with k variables.

Second, the authors investigate height and economic growth using the times series techniques of vector autoregression and cointegration tests.

Among other things, he was one of the main promoters of the use of vector autoregression in empirical macroeconomics.

Vector autoregression (VAR) is a statistical model used to capture the linear interdependencies among multiple time series.

A vector error correction model (VECM) adds error correction features to a multi-factor model such as a vector autoregression model.

Finally, the vector autoregression methods allow the authors to see if skyscraper height can predict changes in gross domestic product (GDP) (i.e., if height predict recessions).

In addition time series models are also used to understand inter-relationships among economic variables represented by systems of equations using VAR (vector autoregression) and structural VAR models.

Statistical techniques used for prediction include regression analysis and time series analysis, and their various sub-categories such as ordinary least squares, logistic regression, autoregressive moving average models, and vector autoregression models.

If both variables are time series, a particular type of causality known as Granger causality can be tested for, and vector autoregression can be performed to examine the intertemporal linkages between the variables.

Now assume that the only information available is and, and suppose that we write the vector autoregression (VAR): where and are random errors with zero means, and are uncorrelated with and.

In statistics, Bayesian vector autoregression (BVAR) uses Bayesian methods to estimate a vector autoregression (VAR).

In economics, and especially in contemporary macroeconomic modeling, impulse response functions describe how the economy reacts over time to exogenous impulses, which economists usually call 'shocks', and are often modeled in the context of a vector autoregression.

Extensions for the multivariate case are the Vector Autoregression (VAR) and Vector Autoregression Moving-Average (VARMA).

In econometrics and other applications of multivariate time series analysis, a variance decomposition or forecast error variance decomposition is used to aid in the interpretation of a vector autoregression (VAR) model once it has been fitted.

Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector autoregression.

This analysis is supported in a study conducted by Sarno, where it is concluded that while conventional bivariate procedure provides mixed results, the more powerful testing procedures, for example expanded vector autoregression test, suggest rejection of the expectation hypothesis throughout the maturity spectrum examined.

Leveraging vector autoregression analysis upon an established marine fossil record, Lu, Yogo and Marshall found that a "speed limit," which was previously thought to restrict the reemergence of biodiversity following a mass extinction, may be an artifact of the incompleteness of the fossil record.