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Autoregressive model

About: Autoregressive model is a(n) research topic. Over the lifetime, 20169 publication(s) have been published within this topic receiving 658019 citation(s). The topic is also known as: AR model. more


Open accessJournal ArticleDOI: 10.2307/1913236
Robert F. Engle1, Clive W. J. Granger1Institutions (1)
01 Mar 1987-Econometrica
Abstract: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x first achieves stationarity after differencing, but a linear combination a'x is already stationary, the time series x are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a becomes a matrix. Interpreting a'x,= 0 as a long run equilibrium, co-integration implies that deviations from equilibrium are stationary, with finite variance, even though the series themselves are nonstationary and have infinite variance. The paper presents a representation theorem based on Granger (1983), which connects the moving average, autoregressive, and error correction representations for co-integrated systems. A vector autoregression in differenced variables is incompatible with these representations. Estimation of these models is discussed and a simple but asymptotically efficient two-step estimator is proposed. Testing for co-integration combines the problems of unit root tests and tests with parameters unidentified under the null. Seven statistics are formulated and analyzed. The critical values of these statistics are calculated based on a Monte Carlo simulation. Using these critical values, the power properties of the tests are examined and one test procedure is recommended for application. In a series of examples it is found that consumption and income are co-integrated, wages and prices are not, short and long interest rates are, and nominal GNP is co-integrated with M2, but not M1, M3, or aggregate liquid assets. more

Topics: Autoregressive model (58%), Estimator (57%), Unit root (57%) more

25,329 Citations

Journal ArticleDOI: 10.2307/1912773
01 Jul 1982-Econometrica
Abstract: Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies. more

19,529 Citations

Open accessJournal ArticleDOI: 10.1016/0304-4076(86)90063-1
Tim Bollerslev1, Tim Bollerslev2Institutions (2)
Abstract: A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented. more

16,132 Citations

Open accessJournal ArticleDOI: 10.1111/J.1468-0084.1990.MP52002003.X
Søren Johansen1, Katarina Juselius1Institutions (1)
Abstract: The estimation and testing of long-run relations in economic modeling are addressed. Starting with a vector autoregressive (VAR) model, the hypothesis of cointegration is formulated as the hypothesis of reduced rank of the long-run impact matrix. This is given in a simple parametric form that allows the application of the method of maximum likelihood and likelihood ratio tests. In this way, one can derive estimates and test statistics for the hypothesis of a given number of cointegration vectors, as well as estimates and tests for linear hypotheses about the cointegration vectors and their weights. The asymptotic inferences concerning the number of cointegrating vectors involve nonstandard distributions. Inference concerning linear restrictions on the cointegration vectors and their weights can be performed using the usual chi squared methods. In the case of linear restrictions on beta, a Wald test procedure is suggested. The proposed methods are illustrated by money demand data from the Danish and Finnish economies. more

Topics: Wald test (56%), Statistical hypothesis testing (55%), Cointegration (54%) more

11,867 Citations

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Topic's top 5 most impactful authors

Pentti Saikkonen

77 papers, 4.3K citations

Helmut Lütkepohl

65 papers, 6.5K citations

Feng Ding

49 papers, 1.1K citations

Peter C.B. Phillips

48 papers, 3.2K citations

Piet M.T. Broersen

41 papers, 771 citations

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