Granger Representation Theorem Research Articles

On the Granger Representation Theorem: a counter example?

This note provides an example in which a cointegrated time series does not have an error correction representation. In this example, the Granger Representation Theorem fails to hold because one of the conditions for the theorem is violated. Economists need to be careful about this possibility because a simple model of the uncovered interest parity and purchasing power parity conditions leads to this case in which the theorem fails.

Cointegration in interest rate futures trading on the Sydney future exchange

The term structure of interest rates defined by the yields on interest rate futures contracts on 90 day bank bills, ranging in delivery periods from the near quarter month up to five quarters ahead, is examined using unit roots and cointegration tests. Since cointegration indicates a causal relationship, its existence implies an opportunity for profitable forecasting technique. A cointegrated yield series is also inconsistent with the notion of a weakly efficient bill futures market. Although the spreads between the futures yields are shown to be stationary, they do not belong to the cointegrating space. Granger's representation theorem is then applied to identify the error-correction models for these bill futures yield data. The performance of the error-correction model in forecasting out-of-sample futures yield is compared with that of a naive (no change) model. In terms of root mean squared error (RMSE) the error-correction models show modest improvement relative to the naive forecast. It is further sh...

PRACTITIONERS' CORNER:Triangular Representation and Error Correction Mechanism in Cointegrated Systems

ABSTRACTIn this paper we provide a proof of the ‘Granger representation theorem’ starting from Phillips' triangular representation of a cointegrated system. Proofs of the theorem have already been provided but starting either from the MA representation or from the AR representation. Conversely, we derive and characterize analytically the MA and the AR representations in terms of the parameters of the triangular system.

Companion form representation of cointegrating VARs

In this paper the issues deriving from the companion form representation of a cointegrating Vector Autoregressive system are analysed. Spectral decomposition of the companion matrix makes it possible to derive several results (including the Granger representation theorem) in a unified framework; notably, the coefficient matrices of the VMA representation are represented in such a way that long- and short-run features of the model are clearly divided. Moreover, the method proposed lends itself quite naturally to software implementations that could improve cointegrated VAR-related algorithms by avoiding recursive formulae.

The implications of cointegration in financial markets

The associations between cointegration and the measurement of volatility and risk in traditional financial analysis literature are investigated and conferred empirical meanings under various market circumstances via the Granger representation theorem.

A vector of quarters representation for bivariate time series

In this paper it is shown that several models for a bivariate nonstationary quarterly time series are nested in a vector autoregression with cointegration restrictions for the eight annual series of quarterly observations. Or, the Granger Representation Theorem is extended to incorporate, e.g., seasonal and periodic cointegration.

Multivariate Time Series: A Polynomial Error Correction Representation Theorem

We consider a class of multivariate processes which, when differenced enough, yield covariance stationary processes whose determinants of the Wold representation have I as their only root on the unit circle. A representation theorem is proved for this class of processes that generalizes the Granger representation theorem.

FORECASTING METROPOLITAN EMPLOYMENT USING AN EXPORT‐BASE ERROR‐CORBECTION MODEL

ABSTRACTThis paper shows that a time‐series version of export‐based location quotients, which decompose area employment into export and local components are co‐integrated. Given the statistically established co‐integrating relation between the time series for export and local employment, the Granger Representation Theorem tells us that an error‐correction mechanism model is the appropriate time‐series model specification. A set of forecasting experiments is carried out, in order to test whether the error‐correction model produces better long‐run forecasts that hold together in economically meaningful ways. Given the computer hardware and software that currently exist, the model developed here represents a simple, low‐cost method for accurately forecasting local‐area employment in the tradition of past work on export‐base models.