Adf test how many lags

One approach would be to run the test with both a constant and a linear trend since the other two cases are just special cases of this more general specification. However, including irrelevant regressors in the regression will reduce the power of the test to reject the null of a unit root. The standard recommendation is to choose a specification that is a plausible description of the data under both the null and alternative hypotheses. See Hamilton , p. The usual though not particularly useful advice is to include a number of lags sufficient to remove serial correlation in the residuals.

EViews provides both automatic and manual lag length selection options. As noted above, you may elect to include a constant, or a constant and a linear time trend, in your ADF test regression. ERS define a quasi-difference of that depends on the value representing the specific point alternative against which we wish to test the null:. Next, consider an OLS regression of the quasi-differenced data on the quasi-differenced :. All that we need now is a value for.

ERS recommend the use of , where:. We now define the GLS detrended data, using the estimates associated with the :. As with the ADF test, we consider the -ratio for from this test equation. While the DFGLS -ratio follows a Dickey-Fuller distribution in the constant only case, the asymptotic distribution differs when you include both a constant and trend. ERS , Table 1, p. Thus, the EViews lower tail critical values use the MacKinnon simulations for the no constant case, but are interpolated from the ERS simulated values for the constant and trend case.

The null hypothesis is rejected for values that fall below these critical values. Phillips and Perron propose an alternative nonparametric method of controlling for serial correlation when testing for a unit root. The PP method estimates the non-augmented DF test equation The PP test is based on the statistic:. In addition, is a consistent estimate of the error variance in The remaining term, , is an estimator of the residual spectrum at frequency zero.

There are two choices you will have make when performing the PP test. First, you must choose whether to include a constant, a constant and a linear time trend, or neither, in the test regression. Second, you will have to choose a method for estimating. EViews supports estimators for based on kernel-based sum-of-covariances, or on autoregressive spectral density estimation.

EViews reports MacKinnon lower-tail critical and p -values for this test. The KPSS test differs from the other unit root tests described here in that the series is assumed to be trend- stationary under the null. We point out that the estimator of used in this calculation differs from the estimator for used by GLS detrending since it is based on a regression involving the original data and not on the quasi-differenced data.

To specify the KPSS test, you must specify the set of exogenous regressors and a method for estimating. Define the residuals from The ERS feasible point optimal test statistic of the null that against the alternative that , is then defined as:.

Ng and Perron construct four test statistics that are based upon the GLS detrended data. First, define the term:. Many of the unit root tests described above require a consistent estimate of the residual spectrum at frequency zero. EViews supports two classes of estimators for : kernel-based sum-of-covariances estimators, and autoregressive spectral density estimators. The kernel-based estimator of the frequency zero spectrum is based on a weighted sum of the autocovariances, with the weights are defined by a kernel function.

The estimator takes the form,. Note that the residuals that EViews uses in estimating the autocovariance functions in Unit root test. Source of residuals for kernel estimator. The properties of these kernels are described in Andrews As with most kernel estimators, the choice of the bandwidth parameter is of considerable importance. EViews allows you to specify a fixed parameter or to have EViews select one using a data-dependent method. The autoregressive spectral density estimator at frequency zero is based upon the residual variance and estimated coefficients from the auxiliary regression:.

The following table summarizes the auxiliary equation estimated by the various AR spectral density estimators:. AR spectral method. Auxiliary AR regression specification. The AR spectral estimator of the frequency zero spectrum is defined as:. We note here that EViews uses the non-degree of freedom estimator of the residual variance.

As a result, spectral estimates computed in EViews may differ slightly from those obtained from other sources. Not surprisingly, the spectrum estimator is sensitive to the number of lagged difference terms in the auxiliary equation. You may either specify a fixed parameter or have EViews automatically select one based on an information criterion. By default, EViews will choose the estimator of used by the authors of a given test specification. You may, of course, override the default settings and choose from either family of estimation methods.

The default settings are listed below:. Frequency zero spectrum default method. There are three distinct situations in which EViews can automatically compute a bandwidth or a lag length parameter. The first situation occurs when you are selecting the bandwidth parameter for the kernel-based estimators of. For the kernel estimators, EViews provides you with the option of using the Newey-West or the Andrews data-based automatic bandwidth parameter methods.

See the original sources for details. For those familiar with the Newey-West procedure, we note that EViews uses the lag selection parameter formulae given in the corresponding first lines of Table II-C. The Andrews method is based on an AR 1 specification. The latter two situations occur when the unit root test requires estimation of a regression with a parametric correction for serial correlation as in the ADF and DFGLS test equation regressions, and in the AR spectral estimator for.

In all of these cases, lagged difference terms are added to a regression equation. The automatic selection methods choose less than the specified maximum to minimize one of the following criteria:. Information criterion. Ng and Perron propose and examine the modified criteria, concluding with a recommendation of the MAIC.

For the information criterion selection methods, you must also specify an upper bound to the lag length. By default, EViews chooses a maximum lag of:. See Hayashi , p. Quadratic Spectral. OLS detrended. GLS detrended.

Kernel Bartlett sum-of-covariances. ERS Point Optimal. AR spectral regression OLS. AR spectral regression GLS-detrended. Akaike AIC. In your specific situation, if you have quarterly data and you tested up to 4 lags, you are good. The ADF test has demonstrated that your variable is stationary. If you have monthly data, you may have to use more lags if the longest lag that has a statistically significant autocorrelation is longer than 4.

Very often the lag 12 mth has stat. In that case you should use lag 12 within your ADF test. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How many lags to use for ADF test if several values reject null hypothesis?

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Since you are dealing with annual data, from a seasonality and autocorrelation standpoint, only the first lag has true and independent meaning. The other lags greater than 1 are just a function of the strength of the first lag. So, use ADF with just 1 lag.

Your ADF test comes out with a high Tau stat and low p-value. So, you can reject the null hypothesis that this variable is non-stationary.