lag selection - Lag length Phillips-Perron example UNIT...

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Lag length & Phillips-Perron example UNIT ROOT TESTS 1
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Choosing the Lag Length for the ADF Test An important practical issue for the implementation of the ADF test is the specification of the lag length p . If p is too small, then the remaining serial correlation in the errors will bias the test. If p is too large, then the power of the test will suffer. 2
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Choosing the Lag Length for the ADF Test Ng and Perron (1995) suggest the following data dependent lag length selection procedure that results in stable size of the test and minimal power loss: First, set an upper bound p ma x for p . Next, estimate the ADF test regression with p = p max . If the absolute value of the t-statistic for testing the significance of the last lagged difference is greater than 1.6, then set p = p max and perform the unit root test. Otherwise, reduce the lag length by one and repeat the process. 3
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Choosing the Lag Length for the ADF Test A useful rule of thumb for determining p max , suggested by Schwert (1989), is where [ x ] denotes the integer part of x . This choice allows p max to grow with the sample so that the ADF test regressions are valid if the errors follow an ARMA process with unknown order. 4 4 / 1 max 100 12 n p
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ADF TEST EXAMPLE: n =54 Let’s assume that p =3. Fit the model with t = 4, 5,…, 54. 5 t t t t t a Y Y Y Y 2 2 1 1 1 0 2 1369 . 0 1 1353 . 0 1 08699 . 0 97 . 87 326 . 0 141 . 0 856 . 0 139 t t t t Y Y Y Y : equation OLS
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PHILLIPS-PERRON (PP) UNIT ROOT TEST Phillips and Perron (1988) have developed a more comprehensive theory of unit root nonstationarity. The tests are similar to ADF tests. The Phillips-Perron (PP) unit root tests differ from the ADF tests mainly in how they deal with serial correlation and heteroskedasticity in the errors. In particular, where the ADF tests use a parametric autoregression to approximate the ARMA
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