Distribution Of Residual Autocorrelations Research Articles

A Portmanteau Test for Smooth Transition Autoregressive Models

This article investigates a portmanteau test statistic for checking model adequacy of smooth transition autoregressive (STAR) models. The asymptotic distribution of residual autocorrelations and the least‐squares estimators are also derived. Hence, the correct asymptotic standard errors for residual autocorrelations are also obtained facilitating model diagnostic checking. Through the graphical display of the simulation results concerning the size and power, for commonly used nominal sizes (), the portmanteau test appears to be more advantageous than the Lagrange multiplier tests in checking serial independence for the errors of STAR models.

RESIDUAL AUTOCOVARIANCES AND UNIT ROOT TESTS BASED ON INSTRUMENTAL VARIABLE ESTIMATORS FROM TIME SERIES REGRESSION MODELS

. Hall (Testing for a unit root in the presence of moving average errors. Biometrika 76 (1989), 49–56; Joint hypothesis tests for a random walk based on instrumental variable estimators. J. Time Ser. Anal. 13 (1992), 29–45), Pantula and Hall (Testing for unit roots in autoregressive moving average models:an instrumental variable approach. J. Econometrics 48 (1991), 325–53) and Lee and Schmidt (Unit root tests based on instrumental variable estimation. Int. Econ. Rev. 39 (1994), 449–62) proposed instrumental variable (IV) based tests for a unit root in an ARMA(p+ 1, q) time series. To perform the tests it is essentially necessary to know (p, q) but in many cases this information is unknown. In practice a natural solution to this problem is to estimate (p, q) from the data using a strategy based on the residual autocovariances from the IV regression. In this paper we examine the properties of these residual autocovariances under various assumptions about the true nature of the time series. This analysis allows us to propose a model selection procedure which has desirable asymptotic and finite sample properties whether the time series is stationary or possesses a unit root. A sideproduct of our analysis is that we extend Box and Pierce's (Distribution of residual autocorrelations in autoregressive integrated moving average time series models. J. Am. Statist. Assoc. 65 (1970), 1509–26) analysis of the least squares residual autocorrelations to the residual autocovariances from IV regressions.

DIAGNOSTIC CHECKING OF PERIODIC AUTOREGRESSION MODELS WITH APPLICATION

Abstract. An overview of model building with periodic autoregression (PAR) models is given emphasizing the three stages of model development:identification, estimation and diagnostic checking. New results on the distribution of residual autocorrelations and suitable diagnostic checks are derived. The validity of these checks is demonstrated by simulation. The methodology discussed is illustrated with an application. It is pointed out that the PAR approach to model development offers some important advantages over the more general approach using periodic autoregressive moving‐average models.

Testing model adequacy for some Markov regression models for time series

SUMMARY The asymptotic distribution of residual autocorrelations and a score statistic are derived for checking model adequacy for some Markov regression models for time series. These models are natural extensions of the popular generalized linear models to time series data. The score statistic appears to be somewhat easier to use in practice. Some empirical results are also obtained for the score statistic in some simple cases. A real example is given.

Equivalent Forms of the Multivariate Portmanteau Statistic

Journal of the Royal Statistical Society: Series B (Methodological)Volume 51, Issue 2 p. 303-303 CorrigendumFree Access Equivalent Forms of the Multivariate Portmanteau Statistic This article corrects the following: Equivalent Forms of the Multivariate Portmanteau Statistic J. R. M. Hosking, Volume 43Issue 2Journal of the Royal Statistical Society: Series B (Methodological) pages: 261-262 First Published online: December 5, 2018 J. R. M. Hosking, J. R. M. HoskingSearch for more papers by this author J. R. M. Hosking, J. R. M. HoskingSearch for more papers by this author First published: 1989 https://doi.org/10.1111/j.2517-6161.1989.tb01768.xCitations: 1 Address for correspondence: IBM Research Division, Thomas J. Watson Research Center, PO Box 218, Yorktown Heights, NY 10598, USA. AboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. REFERENCES Chitturi, R. V. (1974) Distribution of residual autocorrelations in multiple autoregressive schemes. J. Amer. Statist. Ass., 69, 928– 934. Hosking, J. R. M. (1981) Lagrange-multiplier tests of multivariate time-series models. J. R. Statist. Soc. B, 43, 219– 230. Citing Literature Volume51, Issue21989Pages 303-303 ReferencesRelatedInformation

Distribution of residual autocorrelations in multivariate autoregressive index models

where at are independent N(0, A), and A = ((nij)). Denote by ?D(L) the polynomial Im -1L-...-pLP, where L is the lag operator, LYt = Yt-1, and Im is the mxm identity matrix. It is assumed that det {(D(z)} has all roots lying outside the unit circle. Consequently Yt = X 'at-,, where 10 = I and /' -+ 0 as s -+ oo. It may happen that an m-dimensional series can be predicted by a lower dimensional index series it. Reinsel (1983) discusses the modelling of (1) under the assumption that

Distribution of the Residual Autocorrelations in Multivariate Arma Time Series Models

SUMMARY The large-sample distribution of the multivariate residual autocorrelations in the vector arma model is derived. This result is somewhat less complicated for the vector autoregressive model. A new multivariate portmanteau test for checking the adequacy of fitted vector arma models is developed. A simulation study shows that a simple modification of the portmanteau test improves its accuracy in small samples.

Real Disturbances, Perfect Capital Mobility, and Exchange Rate Policy

Auerbach, Robert D. and Jack L. Rutner (1978) 'A causality test of Canadian money and income: a comment on Barth and Bennett.' This JOURNAL 11, 583-94 Barth, James R. and James T. Bennett (1974) 'The role of money in the Canadian economy: an empirical test.' This JOURNAL 7, 306-11 Box, G.E.P. and David A. Pierce (1970) 'Distribution of residual autocorrelations in autoregressive integrated moving average time series models.' Journal of the American Statistical Association 65, 1509-26 Dy Reyes, Felix (1974) 'A test of the direction of causation between money and income in Canada, Japan, and the us.' PH D dissertation, Department of Economics, Iowa State University Mundell, Robert A. (1968) International Economics (New York: Macmillan) Pierce, David A. and Larry D. Haugh (1977) 'Causality in temporal systems characterizations and a survey.' Journal of Econometrics 5, 265-93 Sharpe, Barry C. and Michael B. Miller (1975) 'The role of money in the Canadian economy.' This JOURNAL 8, 289-90 Sims, Christopher A. (1972) 'Money, income and causality.' American Economic Review 62, 540-52

On the finite sample distribution of residual autocorrelations in autoregressive-moving average models

SUMMARY We examine by simulation the finite sample properties of tests of model adequacy based on individual residual autocorrelations, and of portmanteau statistics based on several residual autocorrelations, for autoregressive-moving average models. Both nonseasonal and seasonal models are considered.

On the Definition of Money: Some Canadian Evidence

Anderson, T.W. (1971) The Statistical Analysis of Time Series (New York: John Wiley and Sons) Auerbach, Robert D. and Jack L. Rutner (forthcoming) 'The misspecification of a non-seasonal cycle as a seasonal by the X-1 1 seasonal adjustment program.' Review of Economics and Statistics Barth, James R. and James T. Bennett (1974) 'The role of money in the Canadian economy: an empirical test.' This JOURNAL 7, 306-11 Box, George E.P. and David Pierce (1971) 'Distribution of residual autocorrelations in autoregressive-integrated moving average time series models.' Journal of the American Statistical Association 65, 1509-26 Granger, C.W.J. (1969) 'Investigating causal relations by econometric models and cross-spectral methods.' Econometrica 37, 424-38 Nerlove, Marc ( 1965) 'A comparison of a modified 'Hannan' and the BLS seasonal adjustment filters.' Journal of the American Statistical Association 60, 442-91 Pierce, David A. and Larry D. Haugh (1975) 'The assessment and detection of causality in temporal systems.' (Mimeo. available from Pierce at the Federal Reserve Board). Rutner, Jack L. (1974) 'Time series analysis of income and several definitions of money.' Monthly Review, Federal Reserve Bank of Kansas City, 9-16 Sims, Christopher A. (1972) 'Money, income, and causality.' American Economic Review 62, 540-52

Distribution of Residual Autocorrelations in Multiple Autoregressive Schemes

Distribution of Residual Autocorrelations in Multiple Autoregressive Schemes

Distribution of Residual Autocorrelations in Multiple Autoregressive Schemes

Abstract Box and Pierce [3] showed that the residual autocorrelations computed from an autoregressive-moving average time series model (single variate) can be successfully utilized for testing the goodness of fit. Here we extend their results to multiple autoregressive time series models. It is shown that the residual autocorrelations can be approximately represented as a singular linear transform of the corresponding white noise autocorrelations and that they possess a multivariate singular normal distribution. Finally a simple, approximate chi-square statistic is proposed to test the fit.

Distribution of Residual Autocorrelations in the Regression Model with Autoregressive–Moving Average Errors

Summary In examining the adequacy of a statistical model an analysis of the residuals is often carried out; and for models involving a time series structure the serial correlations of the residuals are natural statistics to consider. In this paper it is shown that asymptotically the first s sample autocorrelations of the residuals, calculated from a least-squares fit of a regression model in which the errors follow a stationary autoregressive–moving average time series, possess a multivariate normal distribution. For moderately sized s this is nearly a singular distribution, with the “singularity” concentrated heavily on the autocorrelation coefficients of lowest order or lag. This distribution was first obtained by Box and Pierce (1970) for time series with no deterministic component; that it is independent of the regression structure of the model is shown to follow from general specification results of Durbin (1970), utilizing the large sample distribution of the parameter estimates recently obtained by the author (1971). Application of these results to testing model adequacy is also considered.

Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models

Many statistical models, and in particular autoregressive-moving average time series models, can be regarded as means of transforming the data to white noise, that is, to an uncorrelated sequence of errors. If the parameters are known exactly, this random sequence can be computed directly from the observations; when this calculation is made with estimates substituted for the true parameter values, the resulting sequence is referred to as the residuals, which can be regarded as estimates of the errors. If the appropriate model has been chosen, there will be zero autocorrelation in the errors. In checking adequacy of fit it is therefore logical to study the sample autocorrelation function of the residuals. For large samples the residuals from a correctly fitted model resemble very closely the true errors of the process; however, care is needed in interpreting the serial correlations of the residuals. It is shown here that the residual autocorrelations are to a close approximation representable as a singular linear transformation of the autocorrelations of the errors so that they possess a singular normal distribution. Failing to allow for this results in a tendency to overlook evidence of lack of fit. Tests of fit and diagnostic checks are devised which take these facts into account.

Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models

Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models