Andrews, D.W.K., and J.C. Monahan, 1992, An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica 60, pp.953-966.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(HAC) covariance matrices have largely focused on kernel based methods of estimating the spectral density matrix at frequency zero. Given that these methods tend to yield relatively poor inference properties in the presence of strong temporal dependence (cf. Andrews 1991) Andrews and Monahan (1992) proposed a class of kernel based HAC estimators that incorporate a fixed order of vector autoregressive (VAR) prewhitening. As originally suggested by Press and Tukey (1956) the approach of prewhitening is intended to flatten the relevant portion of the spectral density function, thereby ....

.... the relevant portion of the spectral density function, thereby reducing the bias of the kernel estimator and hence permitting the use of a smaller bandwidth parameter when the kernel is applied to the prewhitened residuals (cf. Priestley 1981, pp.556 7) In practice, the simulation experiments of Andrews and Monahan (1992) utilized first order VAR prewhitening, and this specification has generally been followed in subsequent research (e.g. Newey and West 1994) In this paper, we highlight the pitfalls of using a fixed order of VAR prewhitening, and then we analyze the benefits of using data dependent VAR ....

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Andrews, D.W.K., and J.C. Monahan, 1992, An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica 60, pp.953-966.

.... of 25 of the available observations (roughly corresponding to 300 observations) We also show the weights estimated from an OLS recursion on the entire past sample ( Recursive ) In each iteration, we reestimate all parameters, and select a new bandwidth following the data based procedure of Andrews and Monahan (1992), and imposing a Bartlett kernel smoother. The plots clearly confirm the presence of significant time variation in the baht basket weights. In the case of the German mark, the rolling regression procedure yields negative estimates of the weights in some instances. 4.2.d Cointegrating Regressions ....

Andrews, D.W.K., and Monahan, J.C. (1992), "Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, 60, 953-966.

.... existing results in the spectral density estimation literature (cf. Parzen 1957; Priestley 1982) have contributed to the rapid development of HAC covariance matrix estimation procedures (e.g. White 1984; Gallant 1987; Newey and West 1987, 1994; Gallant and White 1988; Andrews 1991; Robinson 1991; Andrews and Monahan 1992, Den Haan and Levin 1994; and Lee and Phillips 1994) 2 These HAC covariance matrix estimation procedures may be classified into two broad categories: non parametric kernel based procedures, and parametric procedures. Each kernel based procedure uses a weighted sum of the autocovariances to ....

....and for econometric problems that require estimates of the spectrum over a range of frequencies. 3 The remainder of this paper is organized as follows. Section 2 gives step by step descriptions of five HAC covariance matrix estimation procedures: the kernel based procedures proposed by Andrews and Monahan (1992) and Newey and West (1994) the parametric estimators proposed by Den Haan and Levin (1994) and Lee and Phillips (1994) and the non smoothed non parametric estimator proposed by Robinson (1995) Section 3 compares the asymptotic properties of kernel based and parametric estimation procedures. ....

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Andrews, D.W.K., and J.C. Monahan, 1992, An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica 60, pp. 953-966.

....T X t=s 1 u t u 0 t Gammas ; where h T is the bandwidth and K( Delta) is a kernel function. For instance, the quadratic kernel may be used: K(z) 25 12 2 z 2 sin(6z=5) 6z=5 Gamma cos(6z=5) # : Haug (1996) suggests to use a procedure of automatic bandwidth choice as proposed by Andrews Monahan (1992) and Andrews (1991) The nonparametric estimator of Phi is then Phi NP = T Gamma2 T X t=1 t 0 t Gamma1 Gamma T Gamma1 Omega u T Gamma2 T X t=1 t Gamma1 0 t Gamma1 Gamma1 : Denoting the real part of the eigenvalue with smallest modulus of this matrix by ....

Andrews, D. & Monahan, J. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica 60: 953--966.

....method suggested by Ng and Perron (1994) using a 5 per cent critical value. The initial number of ADF lags is set equal to the seasonal frequency plus 1 or 13. The PO test statistic is calculated using the prewhitened QS kernel estimator with automatic bandwidth parameter advocated by Andrews and Monahan (1992). For Tables 1 and 2, and indicate significance at the 1 and 5 per cent levels. a. We performed the tests under the assumption that the cointegrating vector annihilates any drift terms in the exchange rate or price of oil. Tests of this restriction are available from the authors. The critical ....

....a Trace Statistic Max. Statistic Equation Lags mark 5 19.81 3.84 15.98 3.84 yen 4 20.60 2.61 17.99 2.61 dollar 4 21.89 4.76 15.123 4.76 Z a Z a l r 1 r 0 r 1 r 0 26 of 37 a. Standard errors are in parentheses. The FMLS estimates are based on VAR(2) prewhitening procedure of Andrews and Monahan (1992) as this gave us serially uncorrelated residuals. The DLS estimates are based on sixth order leads and lags and Newey and West (1987) standard errors calculated using a truncation parameter equal to the seasonal frequency or 12. The CCR estimates are from the third stage of estimation as suggested ....

Andrews, Donald W. K. and J. Christopher Monahan. 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator." Econometrica 60: 953-66.

....authors. Furthermore, using the Andrews method may be problematic in the context of the KPS and Park tests since the regression residuals will have much more persistence than those in a Dickey Fuller or Phillips Perron test, and Andrews notes that his estimator does poorly in such cases. Andrews and Monahan (1990) suggest the use of a prewhitened version of the Andrews estimator may be helpful, but we find normally innocuous but necessary restrictions on the size of the prewhitening parameters are frequently binding for unit and near unit roots. 14. See Hakkio and Rush (1991) for a discussion. y t ry t ....

Andrews, Donald W.K. and J.C. Monahan (1990). `An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator', Cowles Foundation for Research in Economics at Yale University, Discussion Paper No. 942.

....that it is (1, 1) The null hypothesis in this case is 0 = b . Following Zivot (1995) and Hansen (1995) the test statistic for the ECM test depends on the asymptotic covariance matrix of the sample means of t h and . s 1 t D t q b a This matrix is calculated by the method suggested by Andrews and Monahan (1992), using a Bartlett kernel, with the selection rule for the order of the kernel weight function chosen as in Andrews (1991) 25 The critical values are presented in Hansen (1995) In each iteration of the Monte Carlo, then, we compute the long run covariance matrix and use it to compare the test ....

Andrews, Donald W.K., and J. Christopher Monahan, 1992, An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica 60, 953-966.

.... least squares under the assumption that the null hypothesis is correctly speci#ed, or they can be calculated from the residuals using a pre whitened autocorrelation and heteroskedasticity consistent covariance matrix estimator and an automatic lag truncation selection procedure as described in Andrews and Monohan (1992) or Newey and West (1994) 16 It is well known that a simple moment based estimator from equations (31) and (32) induces a dis cretization bias through the use of a #rst order approximation to the true discretely sampled moments. The magnitude of this bias should not be large when the estimator ....

....It is important to note that these results do not imply that the drift function is linear. However, they do demonstrate a lack of evidence of nonlinearity in the short rate drift, but this may be an artifact of the poor #nite sample performance of the robust covariance matrix estimator from Andrews and Monohan (1992) and Newey and West (1994) also, the speci#c functional form of equation (33 ) rules out certain forms of nonlinearity. The point estimates of the drift terms in the Eurodollar rate regression are larger in magnitude than the Treasury bill data, but they are also not signi#cantly different from ....

Andrews, Donald W. K., and J. Christopher Monohan, 1992, An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica 60, 953-966.

....of Andrews (1991) is used to calculate the test statistic denoted by CCR A. A quadratic spectral kernel with the associated automatic, data dependent, plug in bandwidth estimator is employed. Also, this kernel estimator is prewhitened with a first order vector autoregression, as suggested by Andrews and Monahan (1992). Furthermore, to provide a comparison for the performance of Andrews estimators, the Bartlett window with four lags is used instead to calculate the variances and covariances, denoted by CCR B. 2.3 Phillips and Loretan, Saikkonen, and Stock and Watson s dynamic ordinary least squares method: ....

Andrews, D. W. K., and Monahan, J. C., 1992, An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica 60, 953--966.

....j Omega 0 j ) 0 P m j=1 w(j; m) j 0 j ) where w( Delta) is a weight function (kernel) and m is a bandwidth parameter. The Bartlett kernel in Newey and West (1987) has the form, w(j; m) 1 Gamma j m 1 . A plug in bandwidth estimator for the Bartlett kernel recommended by Andrews and Monahan (1992) is m = 1:1147(ff(1)n) 1=3 where ff(1) p X a=1 4ae 2 a oe 2 a (1 Gamma ae a ) 6 (1 ae a ) 2 = p X a=1 oe 2 a (1 Gamma ae a ) 4 and (ae a ; oe 2 a ) denote the autoregressive and innovation variance estimates for the ath element of residual e t . The second ....

Andrews, D.W.K., and Monahan, J.C., 1992, "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, 60.

....Newey West (1987) estimator, B n ( n ) 1 n 8 : n X k=1 s k s 0 k L X h=1 n X k=h 1 1 Gamma h L 1 i s k s 0 k Gammah s k Gammah s 0 k j 9 = or another autocorrelation and heteroskedasticity consistent covariance matrix estimator. See Andrews (1991) Andrews and Monahan (1992), Gallant and White (1988; ch. 6) and Newey and West (1994) for further details. 5 Implementation of the QML IEKF technique Prior to computing the quasi log likelihood function (19) for a candidate value of the parameter vector , we must solve n non linear GLS problems as the prediction errors ....

Andrews, D.W.K. and J.C. Monahan (1992), "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, 60, 953--967.

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Andrews, D.W.K., and Monahan, J.C., (1992), "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator", Econometrica, 60, 953-966.

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