An Introduction To Applied Econometrics

by Kerry Patterson

• ISBN13: 9780312235123
• ISBN10: 0312235127
• Format: Trade Book
• Copyright: 2000-10-13
• Publisher: Palgrave Macmillan

Summary

Covering the essential elements of the subject of econometrics, the author also introduces and explains techniques that are now widely used in applied work, although rarely introduced in detail in non-specialist texts, such as integrated time series, cointegration, simulation analysis, Johansen's Approach to multivariate co-integration and ARCH. The author explains the central distinction between stationary and nonstationary time series, which is of crucial importance in many areas of analysis, especially in macroeconomics and financial economics.

Author Biography

Kerry Patterson is Professor of Econometrics at the University of Reading.

Table of Contents

List of Figures	xviii
Preface	xxiii
Acknowledgements	xxvii
PART I Foundations	1	(84)
Economics and quantitative economics	3	(21)
Introduction	3	(1)
Defining economics	3	(1)
Description, construction and models in economics	4	(1)
The scope of model building in quantitative economics	5	(9)
A historical debate	5	(3)
Present-day concerns	8	(2)
Stylisations of methodology	10	(4)
The structure and aims of this book	14	(7)
General aims	14	(3)
Parts and chapters	17	(2)
General comments about the structure of this book	19	(1)
Further reading	20	(1)
Concluding remarks	21	(3)
Review	21	(2)
Review questions	23	(1)
Some preliminaries	24	(27)
Introduction	24	(1)
Distinguishing characteristics of the data	24	(8)
Series and cross-section data	24	(1)
Time series graphs	25	(1)
Frequency	26	(1)
Dimension of a variable	26	(1)
Some examples of time series data	27	(3)
Nonexperimental data	30	(1)
Experimental data	31	(1)
Lagging and leading time series data	32	(2)
Lagging time series data	32	(1)
Leading time series data	33	(1)
The lag operator	34	(2)
Definition of the lag operator	34	(1)
The lag polynomial	34	(1)
Obtaining the sum of the lag coefficients	34	(1)
A univariate dynamic model	35	(1)
Bivariate relationships	36	(6)
A deterministic bivariate model	36	(1)
A stochastic bivariate model	36	(1)
Visual representation of two variables	37	(1)
Dynamic bivariate models	38	(1)
Autoregressive distributed lag (ADL) models	39	(1)
The distributed lag function	40	(1)
More than one conditioning variable	41	(1)
Notation in more complex models	42	(1)
Several equations together	42	(3)
Concluding remarks	45	(6)
Review	46	(3)
Review questions	49	(2)
An introduction to stationary and nonstationary random variables	51	(34)
Introduction	51	(1)
Time series with a varying mean	52	(4)
Some examples	52	(4)
Random variables	56	(6)
The expected value of a random variable	56	(3)
The variance of a random variable	59	(2)
Continuous random variables	61	(1)
Joint events, covariance, autocovariance and autocorrelation	62	(12)
Joint events	62	(2)
Covariance and autocovariance	64	(2)
Conditional expectation	66	(1)
Autocovariances and second order stationarity	67	(1)
Linear combinations of random variables	68	(1)
An example of a nonstationary time series	69	(1)
Correlation and the autocorrelation function	70	(2)
The variance decomposition	72	(1)
Iterating expectations	73	(1)
A random walk	74	(2)
The coin-tossing game	74	(2)
Estimation	76	(3)
Nonstationary processes	76	(1)
Stationary processes	77	(2)
Centred moving variance	79	(1)
Concluding remarks	79	(6)
Review	80	(2)
Review questions	82	(3)
PART II Estimation and simulation	85	(328)
Estimation and hypothesis testing in simple regression models	87	(61)
Introduction	87	(1)
Statistical background	88	(7)
Factorisation of the joint density	88	(2)
The conditional expectation function, CEF, as the regression function	90	(4)
Some important distributions	94	(1)
Estimation, estimators and estimates	95	(4)
The least squares principle	95	(3)
Instrumental variables estimation	98	(1)
Properties of estimators	99	(4)
Bias	99	(1)
Consistency	100	(1)
Examples	100	(1)
Speed of convergence	100	(2)
Asymptotic bias	102	(1)
Efficiency	103	(1)
Linearity	103	(1)
Properties of the OLS estimators β1 and β2	103	(6)
Conditionally and unconditionally unbiased	103	(1)
Minimum variance in the class of linear unbiased estimators	104	(1)
The variance of β2	105	(1)
The variance of β1	106	(1)
The unconditional variances of β1 and β2	106	(1)
The Gauss--Markov theorem	107	(2)
A nonlinear CEF	109	(1)
Goodness of fit	109	(6)
Goodness of fit in the population, η2	110	(1)
Goodness of fit in the sample, R2	111	(3)
% σ as a measure of goodness of fit	114	(1)
Estimation of dynamic models	115	(1)
Structure and regression	116	(5)
Weak exogeneity and the parameters of interest	117	(1)
Instrumental variables estimation	118	(3)
Tests and associated concepts	121	(5)
Significance tests	121	(2)
The alternative hypothesis	123	(2)
Power	125	(1)
Summary of OLS estimators and an empirical example	126	(4)
Tabular summary	127	(1)
Typical computer output	127	(3)
Concluding remarks	130	(6)
Review	130	(4)
Review questions	134	(2)
Appendices	136	(1)
Maximum likelihood estimation	136	(8)
The likelihood function	137	(1)
The binomial distribution of probabilities	137	(2)
Maximum likelihood estimation: the regression model	139	(1)
Estimation in simultaneous models	140	(3)
Hypothesis testing	143	(1)
Computer output	144	(4)
MICROFIT	144	(1)
TSP	145	(1)
RATS	146	(1)
PCGIVE	146	(2)
Extending estimation and model building to several regressors	148	(60)
Introduction	148	(1)
Extending the bivariate model: more than two regressors	148	(4)
Multiple regressors: the basic set-up	149	(2)
Deriving the OLS estimator	151	(1)
The variance--covariance matrix of β	151	(1)
Generalised least squares, GLS	152	(3)
The GLS estimator	153	(1)
The variance--covariance matrix of the GLS estimator, Var(β0)	154	(1)
OLS or GLS?	154	(1)
Testing hypotheses	155	(6)
Testing principles: Lagrange-Multiplier, Wald, likelihood ratio	155	(1)
Extension of multiple hypotheses	156	(5)
Heteroscedasticity: implications for OLS estimation and tests	161	(8)
Implications of heteroscedasticity	161	(1)
Tests for heteroscedasticity	161	(1)
White's (1980) test	161	(4)
The Goldfeld--Quandt test	165	(1)
The Breusch--Pagan/Godfrey test	165	(2)
Interpretation of significant test statistics for heteroscedasticity	167	(2)
Misspecification: diagnosis and effects	169	(11)
Serial correlation of &epsis;t	170	(1)
The Durbin--Watson, DW, statistic	171	(2)
The Lagrange-Multiplier (LM) test for serial correlation	173	(1)
The Box--Pearce and Ljung--Box tests	174	(1)
An illustration of the DW and LM tests	174	(1)
Interpretation of significant test statistics for serial correlation	175	(3)
The Newey--West estimator of the variance(--covariance) matrix of β	178	(2)
Normality and the Jarque--Bera test	180	(3)
Normality of &epsis;t	181	(1)
The Jarque--Bera test	181	(2)
Functional form and the RESET test	183	(2)
Developing a test for nonlinearity	183	(1)
Ramsay's RESET test	184	(1)
Stability of the regression coefficients	185	(4)
Chow's (first) test	185	(1)
Predictive/forecast failure tests	186	(1)
Chow's (second) test: a test for predictive failure	186	(2)
A forecast (deterioration) test	188	(1)
Unknown breakpoint(s)	188	(1)
Model building and evaluation	189	(1)
An estimation regression model	190	(11)
The basic model	190	(2)
Estimation of the basic model	192	(1)
Diagnostic and misspecification tests	192	(1)
Serial correlation	192	(1)
Heteroscedasticity	193	(3)
Normality	196	(1)
Functional form: the RESET test	196	(1)
Chow tests	196	(1)
Chow's first test	196	(2)
Chow's second test: predictive failure	198	(1)
An extended model	198	(3)
Concluding remarks	201	(7)
Review	202	(2)
Review questions	204	(4)
An introduction to nonstationary univariate time series models	208	(45)
Introduction	208	(1)
Nondeterministic time series	209	(18)
A pure random walk	209	(5)
A near random walk	214	(2)
A random walk with drift	216	(4)
Unit roots	220	(2)
A near random walk with drift	222	(1)
The persistence of shocks	223	(1)
The mean, variance and autocorrelation of an AR(1) process	223	(2)
Difference stationary and trend stationary series	225	(2)
Testing for a unit root	227	(14)
τ test	227	(2)
Φ1 and τ test statistics	229	(4)
Φ3 and τβ test statistics	233	(3)
The empirical power of some Dickey--Fuller test statistics	236	(1)
Distribution of the test statistics on the intercept and trend	237	(1)
The augmented Dickey--Fuller, ADF, test	238	(3)
A framework for testing	241	(6)
Is the data series trended?	242	(2)
The data is not obviously trended and the mean under the alternative is nonzero	244	(1)
The data is not obviously trended and the mean under the alternative is zero	245	(1)
Cumulation of type 1 error	246	(1)
Concluding remarks	247	(6)
Review	248	(2)
Review questions	250	(3)
Development of nonstationary univariate time series models	253	(63)
Introduction	253	(1)
ARIMA models	254	(3)
Pre-testing, power and model selection strategies using ADF test statistics	257	(3)
Other tests	260	(5)
Dickey and Fuller's ρ, ρpμ and ρβ	260	(2)
The weighted symmetric (WS) estimator, Pantula et al. (1994)	262	(2)
Phillips and Perron versions of the DF tests	264	(1)
Structural and reduced form univariate time series models	265	(5)
Structural univariate time series models	265	(3)
Stationarity as the null hypothesis	268	(2)
Testing for 2 unit roots	270	(2)
Seasonality and seasonal integration	272	(5)
Integration in seasonal processes	272	(1)
Testing for a unit root in a seasonal process	273	(4)
Structural breaks	277	(8)
The Perron (1989) approach to a single structural break	278	(5)
Additive outliers, Franses and Haldrup (1994)	283	(1)
Summary	284	(1)
Applications to some economic time series	285	(16)
UK consumers' expenditure on nondurables	285	(7)
UK employment rate	292	(3)
US unemployment rate	295	(4)
Testing for seasonal nonstationarity: UK employees	299	(2)
`Nearly' integrated and `nearly' stationary time series	301	(4)
Concluding remarks	305	(11)
Review	308	(4)
Review questions	312	(3)
Appendix	315	(1)
Stationarity and nonstationarity in single-equation regression analysis	316	(57)
Introduction	316	(1)
Examining the properties of estimators by simulation	317	(11)
Xt is fixed in repeated samples	317	(3)
Xt is a stationary, stochastic variable	320	(1)
Xt stationary: white noise	320	(1)
Xt stationary: an AR(1) process	321	(1)
Xt is a nonstationary, stochastic variable	322	(2)
A spurious regression	324	(2)
The distribution of R2	326	(2)
Cointegration	328	(2)
Cointegration: basic concepts	328	(2)
Cointegrating versus spurious regressions	330	(1)
Testing for noncointegration: the Engle--Granger (1987) approach	330	(10)
The Engle--Granger (1987) approach (the bivariate case)	330	(2)
Critical values for the test statistic τγ: simulation	332	(1)
MacKinnon's response surface for critical values	333	(1)
More than two variables	334	(1)
An illustration of the testing procedure	335	(3)
An illustration of a spurious regression	338	(2)
Links between cointegration and error correction models	340	(9)
Engle and Granger's two-stage estimation method	341	(2)
Cointegration and error correction: an alternative test statistic for cointegration	343	(1)
Known cointegration coefficients	344	(2)
Unknown cointegration coefficients	346	(3)
Alternative representations of the long-run relationship	349	(6)
The ADL model and the ECM (the two variable case)	349	(2)
The Bewley transformation	351	(1)
A numerical example	352	(1)
The more general ADL model: alternative representations	352	(3)
Estimation, inference and simulation	355	(11)
A comparison of alternative ways of estimating the cointegrating coefficients	356	(1)
Simulation set-up	356	(2)
Simulation results	358	(1)
Estimating the coefficients	359	(5)
Distribution of the `t' statistics	364	(2)
Concluding remarks	366	(7)
Review	368	(1)
Review questions	369	(3)
Appendix	372	(1)
Endogeneity and the fully modified OLS estimator	373	(40)
Introduction	373	(1)
Distinguishing variance matrices	374	(8)
Conditional, unconditional and long-run variance matrices	375	(1)
Autoregressive processes	375	(2)
First order moving average process	377	(1)
Decomposition of the long-run variance matrix	378	(1)
A general result	379	(1)
MA(1) example	380	(1)
AR(1) example	380	(2)
Endogeneity	382	(4)
Preliminaries	383	(1)
Contemporaneity	383	(1)
Weak exogeneity	384	(1)
The regression (or conditional expectation) function and weak exogeneity	384	(2)
The fully modified (Phillips--Hansen) OLS estimator	386	(10)
Corrections for bias and endogeneity	386	(1)
A bias correction	386	(1)
An endogeneity correction	387	(1)
A semi-parametric approach to estimating the corrections	388	(1)
Variations on a theme: when OLS on the ADL model is optimal	389	(3)
Examples of FMOLS estimation	392	(1)
The consumption--income example	392	(1)
Long and short interest rates	393	(1)
Simulation findings	394	(1)
Simulation results: Phillips and Hansen (1990)	394	(1)
Simulation results: Hansen and Phillips (1990)	395	(1)
Simulation results: Inder (1993)	396	(1)
Complications: nearly integrated processes and endogeneity	396	(10)
Xt integrated/nearly integrated, no endogeneity	397	(2)
Xt integrated/nearly integrated and endogenous	399	(1)
Contemporaneity	399	(3)
Failure of weak exogeneity	402	(2)
Summary	404	(1)
Sensitivity to changes in the design parameters: slow adjustment	405	(1)
Concluding remarks	406	(7)
Review	408	(3)
Review questions	411	(2)
PART III Applications	413	(184)
The demand for money	415	(52)
Introduction	415	(1)
The demand for money	415	(10)
A definition of money	415	(1)
The transactions motive	416	(3)
The precautionary motive	419	(2)
The speculative motive	421	(2)
Bringing the motives together	423	(1)
Some variations on a theme: the velocity of circulation	424	(1)
The demand for money during the German hyperinflation	425	(15)
Historical background	426	(1)
Cagan's specification of the demand for money function: background	426	(1)
Cagan's demand for money function: basic specification	427	(2)
A graphical analysis of the data	429	(1)
Testing for nonstationarity	430	(4)
Cointegration	434	(4)
Dynamic models	438	(2)
The demand for M1: a study using recent US data	440	(16)
Model specification	441	(1)
Data definitions	441	(2)
A graphical analysis of the data	443	(1)
Testing for nonstationarity	444	(2)
Cointegration	446	(4)
Dynamic models	450	(4)
Out of sample performance	454	(1)
A brief comparison with Hoffman and Rasche (1991) and Baba, Hendry and Starr (1992)	455	(1)
Concluding remarks	456	(11)
Review	458	(5)
Review questions	463	(4)
The term structure of interest rates	467	(41)
Introduction	467	(1)
Term structure of interest rates	468	(4)
Term to maturity	468	(1)
The discount rate, the interest rate and continuous compounding	469	(2)
The yield curve	471	(1)
The expectations model of the term structure	472	(5)
The yield to maturity and the forward rate	472	(3)
The spread	475	(1)
Implications for economic policy	476	(1)
Assessing the expectations model	477	(17)
Three implications of the expectations model	477	(2)
The data	479	(1)
A graphical analysis of the data: yields	480	(1)
Unit root tests on the yields	481	(2)
A graphical analysis of the data: spreads	483	(1)
Unit root tests on the spreads	484	(1)
Estimation of the spread equations	485	(6)
Bivariate regressions: the perfect foresight spread	491	(3)
Other studies and other methods of testing the expectations model	494	(8)
Methods and results	494	(5)
Why do tests of EH + REH tend to indicate rejection?	499	(3)
Concluding remarks	502	(6)
Review	503	(3)
Review questions	506	(2)
The Phillips curve	508	(45)
Introduction	508	(1)
The Phillips curve	509	(9)
Basic ideas	509	(1)
Phillips' original estimates and interpretation	510	(1)
The Phillips curve: a menu of choice?	511	(1)
The Phillips curve in the United States: an early view	512	(1)
A graphical analysis of Phillips' data for 1861--1913	513	(1)
Testing for nonstationarity	514	(3)
Re-estimation of the Phillips curve, 1861--1913	517	(1)
Is the Phillips curve misspecified?	518	(7)
Fisher (1926) and Phillips (1958)	519	(1)
Friedman's model	520	(2)
Imperfect competition	522	(1)
The Phillips, `Fisher' and `Friedman' curves	523	(1)
Expectations and the reformulation of the Phillips curve	523	(2)
A supply side interpretation of the importance of inflation expectations	525	(1)
Estimation of the expectations augmented Phillips curve (EAPC)	525	(11)
Timing of expectations	525	(1)
The adaptive expectations hypothesis: formulation	526	(1)
The AEH: estimation	527	(2)
The Lucas/Sargent critique of the identifying assumption	529	(2)
Estimation results: adaptive expectations augmented Phillips curve	531	(2)
Rational expectations (RE): general principles	533	(1)
Implementing rational expectations	533	(2)
Estimation results with (weakly) rational expectations	535	(1)
The Phillips correlation	536	(9)
Granger-causation tests	537	(2)
Estimation and hypothesis tests	539	(1)
Practical problems	540	(1)
Granger-causation tests: wage/price inflation and unemployment, United Kingdom	541	(2)
Granger-causation tests: wage/price inflation and unemployment, United States	543	(2)
Concluding remarks	545	(8)
Review	548	(3)
Review questions	551	(2)
The exchange rate and purchasing power parity	553	(44)
Introduction	553	(1)
Purchasing power parity	554	(5)
Complications for PPP	555	(1)
Short-run and long-run considerations	556	(1)
The nominal exchange rate, Et, and the real exchange rate, REt	557	(1)
A strategy for testing RPPP	558	(1)
Assessing the evidence for PPP	559	(13)
The nature of the evidence	559	(1)
Measuring the real exchange rate	560	(1)
Visual impression of the data	561	(5)
Dickey--Fuller unit root tests	566	(6)
The real exchange rate: some more considerations and tests	572	(7)
An example of the persistence of shocks	573	(1)
Pooling observations: a panel unit root test	573	(3)
Estimating the speed of response to a shock to the real exchange rate	576	(3)
Simple tests for noncointegration	579	(4)
Relaxing the (1, --1) cointegrating vector	579	(1)
OLSEG estimation of the cointegrating regressions	580	(2)
An illustration of the modified ADF test statistic	582	(1)
(Very) `weak' form PPP	582	(1)
Other models of the exchange rate	583	(5)
The flexible price monetary model	583	(2)
An illustration of the FPMM with US: UK quarterly data	585	(3)
Concluding remarks	588	(9)
Review	590	(3)
Review questions	593	(4)
PART IV Extensions	597	(155)
Multivariate models and cointegration	599	(54)
Introduction	599	(1)
Some basic concepts	600	(8)
The VAR	600	(1)
Stability and stationarity in the VAR	601	(3)
Stability and roots in the univariate model	604	(1)
Eigenvalues and roots: the multivariate model	604	(3)
What to do if there is a unit root	607	(1)
Simple multivariate (vector) error correction models	608	(7)
A bivariate model	608	(2)
The eigenvalues of II and the existence of cointegrating vectors	610	(1)
More than one cointegrating vector	611	(1)
Longer Lags	612	(1)
The multivariate model: the existence of a unit root and reduced rank of II	613	(2)
Testing for cointegration	615	(16)
Establishing a firm base for inference on the cointegrating rank	615	(1)
Estimation of the UVAR and test statistics for testing the cointegrating rank (optional)	616	(3)
Hypothesis tests on the cointegrating rank	619	(4)
An alternative method of selecting the cointegrating rank	623	(1)
Intercepts and trends in the VAR for the trace and λmax statistics	624	(6)
Separating I(1) and I(0) variables	630	(1)
Identification	631	(13)
Structural and reduced form error correction models	632	(3)
Identification of the cointegrating vectors	635	(6)
Testing overidentifying restrictions on the cointegrating vectors	641	(2)
Identification of the short-run structure	643	(1)
Concluding remarks	644	(9)
Review	646	(4)
Review questions	650	(3)
Applications of multivariate models involving cointegration	653	(55)
Introduction	653	(1)
Purchasing power parity and uncovered interest parity, Johansen and Juselius (1992)	654	(5)
An outline of PPP and UIP	654	(1)
Generic identification of the cointegrating relationships	655	(1)
Estimating the cointegrating rank	656	(2)
Interpreting the unrestricted cointegrating vectors	658	(1)
Wage differentials in the United States, Dickey and Rossana (1994)	659	(5)
Estimating the cointegrating rank	659	(2)
Cointegration of real wages	661	(1)
Identification of the cointegrating vectors	661	(3)
The IS/LM model, Johansen and Juselius (1994)	664	(3)
Identifying the short-run structure	665	(1)
The simultaneous structure	666	(1)
The demand for money in the United Kingdom, Hendry and Mizon (1993)	667	(4)
Estimating the cointegrating rank	667	(1)
Unrestricted estimates of the cointegrating vectors and adjustment coefficients	668	(1)
Identification of the cointegrating vectors	668	(1)
Estimating an SECM	669	(1)
Identification of the short-run structure	670	(1)
Weak exogeneity: when is it valid to model the partial system?	671	(7)
Containing the number of variables in the VAR	673	(1)
Closed or open systems?	674	(2)
Joint, conditional and marginal models	676	(1)
Hypothesis testing and weak exogeneity	677	(1)
Examples of testing for weak exogeneity	677	(1)
An extended illustration: Urban's (1995) study of the demand for imports in Belgium	678	(6)
Estimating the cointegrating rank	678	(2)
Identification of the cointegrating vectors	680	(1)
Testing restrictions	681	(1)
The parsimonious VAR, PVAR, and SECM	682	(2)
Revisiting the demand for money in the United States	684	(14)
A multivariate approach: choosing the lag length	685	(1)
A multivariate approach: estimating the cointegrating rank by the Johansen method	686	(4)
A multivariate approach: estimating the cointegrating rank by the Schwarz Information Criterion (SIC)	690	(1)
Robustness of specification	691	(2)
A comparison with OLS results	693	(1)
A structural error correction model and parsimonious encompassing	693	(2)
An estimated SECM for money, income and the interest rate	695	(3)
Concluding remarks	698	(10)
Review	700	(3)
Review questions	703	(5)
Autoregressive conditional heteroscedasticity: modelling volatility	708	(44)
Introduction	708	(1)
Basic concepts	709	(6)
Conditional and unconditional variances: a crucial distinction	710	(1)
ARCH(q)	711	(2)
GARCH(p, q)	713	(1)
What does data with an ARCH effect look like?	714	(1)
Stationarity and persistence in some standard models	715	(4)
ARCH(q)	716	(1)
GARCH(p, q)	716	(1)
IGARCH(1, 1)	717	(1)
Nonnegativity constraints in GARCH models	718	(1)
Estimation	719	(2)
Specification	719	(1)
A nonlinear estimator `beats' the linear OLS estimator	720	(1)
Testing for ARCH/GARCH effects	721	(1)
LM test for ARCH effects	721	(1)
GARCH(p, q)	722	(1)
Variations on an ARCH/GARCH theme	722	(2)
ABSGARCH, EGARCH	722	(1)
ABSGARCH	723	(1)
EGARCH	723	(1)
ARCH-M, GARCH-M, ABSGARCH-M, EGARCH-M	724	(1)
The importance of asymmetry in ARCH models	724	(6)
The news impact curve	725	(1)
Examples of the news impact curve	726	(1)
Asymmetry in more detail	727	(1)
The AGARCH and GJR asymmetric models	727	(2)
Tests for asymmetry	729	(1)
Examples	730	(9)
The US inflation rate	730	(1)
The UK savings ratio	731	(3)
ARCH-M applied to excess returns	734	(2)
Testing for asymmetry in the returns for Standard and Poor's 500 index for the United States	736	(3)
Concluding remarks	739	(5)
Review	740	(3)
Review questions	743	(1)
Appendix	744	(1)
The likelihood function for the ARCH model	744	(1)
Nonnormality	745	(1)
Properties of the maximum likelihood estimators in GARCH models	745	(1)
Practical ARCH/GARCH	746	(6)
Appendix -- Statistical tables	752	(8)
A1 The normal distribution	753	(1)
A2 The `t' distribution	754	(1)
A3 The X2 distribution	755	(1)
A4 The F Distribution	756	(2)
A5 Critical values of the Durbin--Watson test	758	(2)
References	760	(15)
Index	775