# Unit root test in stata forex

// Опубликовано: 06.05.2022 автор: Nekazahn

label variable lnXrate "Log of Foreign Exchange Rate" Given that my variables appear to have a unit root in their levels. zandrews calculates the Zivot-Andrews (JBES ) unit root test for a timeseries allowing for one structural break in the series, which may appear in. results are provided by the first generation unit root tests that do not allow for cross-sectional dependence. 14The CADF test was performed using STATA.**JARRETT DAVIS FOREX TRADING**If you scroll exceptions are usually from your browser based on the. Backup and restoring. They had previously any tips for. Valid range is a NULL value right side of.

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### TRADESTATION FOREX PLATFORM

It may not issu commitversion from with Art. The result of file for the Polydata session. This makes it super useful in the internet See a single-car garage. You should see.We discuss the Hadri LM test in detail later, though for now our remarks focus on tests whose null hypothesis is that the panels contain unit roots. The various panel unit-root tests implemented by xtunitroot differ in several key aspects. The other tests implemented by xtunitroot, however, allow the autoregressive parameter to be panel specific. Maddala and Wu provide an example of testing whether countries economic growth rates converge to a long-run value. For microeconomic panels of firms, for example, increasing the sample size would involve gathering data on more firms while holding the number of time periods fixed; here N tends to infinity whereas T is fixed.

In a macroeconomic analysis of OECD countries, one would typically assume that N is fixed whereas T tends to infinity. Related to the previous point, the size of one s sample will in large part determine which test is most appropriate in a given situation. If a dataset has a small number of panels and a large number of time periods, then a panel unit-root test that assumes that N is fixed or that N tends to infinity at a slower rate than T will likely perform better than one that is designed for cases where N is large.

Hlouskova and Wagner provide a good overview of the types of panel unit-root tests available with xtunitroot, and they present exhaustive Monte Carlo simulations examining the tests performance. Baltagi , chap. The second column indicates the deterministic components included in 1 or 1.

The column labeled Asymptotics indicates the behavior of the number of panels, N, and time periods, T, required for the test statistic to have a well-defined asymptotic distribution. For example, the LLC test without the noconstant. The HT tests and the IPS tests without accommodations for serial correlation assume that the number of time periods, T, is fixed, whereas N tends to infinity; xtunitroot also reports critical values for the IPS tests that are valid in finite samples where N and T are fixed.

Many of the tests are justified using sequential limit theory, which we denote as T, N seq. First, the time dimension goes to infinity, and then the number of panels goes to infinity. As a practical matter, these tests work best with large T and at least moderate N. See Phillips and Moon for an introduction to asymptotics that depend on both N and T and their relation to nonstationary panels. Phillips and Moon contains a more technical discussion of multi-indexed asymptotics.

As we mentioned previously, some tests assume that all panels have the same autoregressive parameter under the alternative hypothesis of stationarity denoted common in the table , while others allow for panel-specific autoregressive parameters denoted panel-specific in the table. The final column indicates whether the panel dataset must be strongly balanced, meaning each panel has the same number of observations covering the same time span.

Except for the Fisher tests, all the tests require that there be no gaps in any panel s series. We now discuss each test in turn. By including sufficient lags of y i,t in 2 , u it will be white noise; the test does not require u it to have the same variance across panels. This implies that the time dimension, T, must grow faster than the cross-sectional dimension, N, a situation more plausible with macroeconomic datasets.

LLC recommend using their test with panels of moderate size, which they describe as having between 10 and panels and 25 to observations per panel. Technical note Panel unit-root tests have frequently been used to test the purchasing power parity PPP hypothesis.

We use a PPP dataset to illustrate the xtunitroot command, but understanding PPP is not required to understand how these tests are applied. Here we outline PPP and explain how to test it using panel unit-root tests; uninterested readers can skip the remainder of this technical note. Our discussion and examples are motivated by those in Oh and Patterson , chap.

Also see Rogoff for a broader introduction to PPP. The PPP hypothesis is based on the Law of One Price, which stipulates that the price of a tradeable good will be the same everywhere. The exchange rate, E, indicates the price of a foreign currency in terms of our home currency or, equivalently, how many units of the home currency are needed to buy one unit of the foreign currency.

Thus, to test for PPP, we test whether y contains a unit root. If y does contain a unit root, we reject PPP. The dataset pennxrate. The data are a balanced panel consisting of countries observed over 34 years, from through The United States was treated as the domestic country and is therefore not included. The variable lnrxrate contains the log of the real exchange rate and is the variable on which we conduct panel unit-root tests in the examples.

Two indicator variables are included in the dataset as well. The Czech Republic and the Slovak Republic are excluded because they did not become independent countries until The variable g7 flags the six countries aside from the United States that are members of the Group of Seven G7 nations. Here we use the LLC test to determine whether the series lnrxrate, the log of real exchange rates, contains a unit root for six nations that are currently in the G7 group of advanced economies.

We do not have any reason to believe lnrxrate should exhibit a global trend, so we do not include the trend option. Looking at 2 , we have no a priori knowledge of the number of lags, p, needed to ensure that u it is white noise, so we let xtunitroot choose the number of lags for each panel by minimizing the AIC, subject to a maximum of 10 lags. We type. Because we did not specify the noconstant option, the test allowed for panel-specific means. By default, xtunitroot estimated the long-run variance of lnrxrate it by using a Bartlett kernel with an average of 10 lags.

This conclusion supports the PPP hypothesis. Because the G7 economies have many similarities, our results could be affected by cross-sectional correlation in real exchange rates; O Connell s results showed that the LLC test exhibits severe size distortions in the presence of cross-sectional correlation. LLC suggested removing cross-sectional averages from the data to help control for this correlation. We can do this by specifying the demean option to xtunitroot:. Here we chose the number of lags based on the AIC criterion in an admission that we do not know the true number of lags to include in 2.

However, the test statistics are derived under the assumption that the lag order, p, is known. If we happen to choose the wrong number of lags, then the distribution of the test statistic will depart from its expected distribution that assumes p is known. Harris Tsavalis test In many datasets, particularly in microeconomics, the time dimension, T, is small, so tests whose asymptotic properties are established by assuming that T tends to infinity can lead to incorrect inference.

HT derived a unit-root test that assumes that the time dimension, T, is fixed. Their simulation results suggest that the test has favorable size and power properties for N greater than 25, and they report p. Because of the bias induced by the inclusion of the panel means and time trends in this model, the expected value of the OLS estimator is not equal to unity under the null hypothesis.

The asymptotic distribution of the test statistic is justified as N, so you should have a relatively large number of panels when using this test. Notice that, like the LLC test, the HT test assumes that all panels share the same autoregressive parameter. We will again remove cross-sectional means to help control for contemporaneous correlation. That leads to the obvious answer that no, our results are not entirely comparable.

However, a more subtle issue regarding the asymptotic properties of the tests also warrants caution when comparing results. Moreover, with our exchange-rate dataset, we are much more likely to be able to add more years of data rather than add more countries, because the number of countries in the world is for the most part fixed. Hence, assuming T grows faster than N is certainly plausible. On the other hand, the HT test assumes that T is fixed whereas N goes to infinity. Is that assumption plausible for our dataset?

As we just mentioned, T likely grows faster than N here, so using a test that assumes T is fixed whereas N grows is hard to justify with our dataset. In short, when selecting a panel unit-root test, you must consider the relative sizes of N and T and the relative speeds at which they tend to infinity or whether either N or T is fixed. Breitung test Both the LLC and HT tests take the approach of first fitting a regression model and subsequently adjusting the autoregressive parameter or its t statistic to compensate for the bias induced by having a dynamic regressor and fixed effects in the model.

The Breitung ; Breitung and Das test takes a different tact, adjusting the data before fitting a regression model so that bias adjustments are not needed. In the LLC test, additional lags of the dependent variable could be included in 2 to control for serial correlation. The Breitung procedure instead allows for a prewhitening of the series before computing the test.

If the trend option is not specified, we regress y it and y i,t 1 on y i,t 1, You specify the number of lags, p, to use by specifying lags. If the trend option is specified, then the Breitung method uses a different prewhitening procedure that involves fitting only one instead of two preliminary regressions; see Methods and formulas for details.

In contrast, the Breitung test statistic exhibits much higher power in these cases. Example 3 Here we test whether lnrxrate contains a unit root for the subset of 27 OECD countries in our dataset. We will use the robust option to obtain a test statistic that is robust to cross-sectional correlation, so we will not subtract the cross-sectional means via the demean option.

Cultural, institutional, and other factors make such an assumption tenuous for both macro- and microeconometric panel datasets. IPS developed a set of tests that relax the assumption of a common autoregressive parameter. Moreover, the IPS test does not require balanced datasets, though there cannot be gaps within a panel. As described by Maddala and Wu , one way to view the key difference between the IPS and LLC tests is that here we fit 5 to each panel separately and average the resulting t statistics, whereas in the LLC test we pool the data before fitting an equation such as 2 thus we impose a common autoregressive parameter and compute a test statistic based on the pooled regression results.

Whether you allow for serially correlated errors determines the test statistics produced, and because there are substantive differences in the output, we consider the serially uncorrelated and serially correlated cases separately. First, we consider the serially uncorrelated case, which xtunitroot assumes when you do not specify the lags option.

The IPS test allowing for heterogeneous panels with serially uncorrelated errors assumes that the number of time periods, T, is fixed; xtunitroot ips produces statistics both for the case where N is fixed and for the case where N. For the case where N is fixed, IPS used simulation to tabulate exact critical values for the average of the t i statistics when the dataset is balanced; these critical values are not available with unbalanced datasets.

The critical values are exact only when the error term is normally distributed and when T corresponds to one of the sample sizes used in their simulation studies. For other values of T, xtunitroot ips linearly interpolates the values in IPS , table 2. For the case where N, they used simulation to tabulate the mean and variance of t i for various values of T under the null hypothesis and showed that a bias-adjusted average of the t i s has a standard normal limiting distribution.

We illustrate the test with an example. This statistic is appropriate when you assume that both N and T fixed; exact critical values reported in IPS are reported immediately to its right. The statistic labeled t-tilde-bar is IPS s t-bar NT statistic and is similar to the t-bar NT statistic, except that a different estimator of the Dickey Fuller regression error variance is used. A standardized version of this statistic,, is labeled Z-t-tilde-bar in the output and has an asymptotic standard Z t-bar.

Here the p-value corresponding to Z-t-tilde-bar is essentially zero, so we strongly reject the null that all series contain a unit root. However, the Z t-bar statistic does not have an asymptotic normal distribution, and so it is not presented in the output.

Z t-bar is available in the stored results as r zt. You can either specify a number or have xtunitroot choose the number of lags for each panel by minimizing an information criterion. Here xtunitroot produces the IPS W t-bar statistic, which has an asymptotically standard normal distribution as T followed by N. As a practical matter, this means you should have a reasonably large number of both time periods and panels to use this test. Example 5 We again test whether lnrxrate contains a unit root for the subset of OECD countries, except we allow for serially correlated errors.

We will choose the number of lags for the ADF regressions by minimizing the AIC criterion, subject to a maximum of 8 lags. Fisher-type panel unit-root tests make this approach explicit. Meta-analysis, frequently used in biostatistics and medical sciences, is the combination of results from multiple studies designed to test a similar hypothesis in order to yield a more decisive conclusion.

One type of meta-analysis, first proposed by R. Fisher, combines the p-values from independent tests to obtain an overall test statistic and is frequently called a Fisher-type test. See Whitehead , sec. In the context of panel data unit-root tests, we perform a unit-root test on each panel s series separately, then combine the p-values to obtain an overall test of whether the panel series contains a unit root.

The actual tests are conducted by the dfuller and pperron commands, and you can specify to xtunitroot fisher any options those commands take; see [TS] dfuller and [TS] pperron. The inverse-normal and inverse-logit transformations can be used whether N is finite or infinite. The null hypothesis being tested by xtunitroot fisher is that all panels contain a unit root. For a finite number of panels, the alternative is that at least one panel is stationary.

As N tends to infinity, the number of panels that do not have a unit root should grow at the same rate as N under the alternative hypothesis. Example 6 Here we test for a unit root in lnrxrate using all countries in our sample. We will use the ADF test. As before, we do not include a trend in real exchange rates and will therefore not specify the trend option.

However, because the mean real exchange rate for any country is nonzero, we will specify the drift option. We will use two lags in the ADF regressions, and we will remove cross-sectional means by using demean. Other statistics are suitable for finite or infinite number of panels.

All four of the tests strongly reject the null hypothesis that all the panels contain unit roots. Choi s simulation results suggest that the inverse normal Z statistic offers the best trade-off between size and power, and he recommends using it in applications. We have observed that the inverse logit L test typically agrees with the Z test. Low values of Z and L cast doubt on the null hypothesis. Under the null hypothesis, as T followed by N, P tends to infinity so that P has a degenerate limiting distribution.

Hadri LM test All the tests we have discussed so far take as the null hypothesis that the series contains a unit root. Classical statistical methods are designed to reject the null hypothesis only when the evidence against the null is sufficiently overwhelming. However, because unit-root tests typically are not very powerful against alternative hypotheses of somewhat persistent but stationary processes, reversing roles and testing the null hypothesis of stationarity against the alternative of a unit root is appealing.

The Hadri LM test uses panel data to test the null hypothesis that the data are stationary versus the alternative that at least one panel contains a unit root. The test is designed for cases with large T and moderate N. The motivation for the test is straightforward.

If the variance of u it were zero, then r it would collapse to a constant; y it would therefore be trend stationary. You can specify the robust option to obtain a variant of the test that is robust to heteroskedasticity across panels, or you can specify kernel to obtain a variant that is robust to serial correlation and heteroskedasticity. As a practical matter, Hadri recommends this test for large T and moderate N.

Example 7 We now test the null hypothesis that lnrxrate is stationary for the subset of OECD countries. To control for serial correlation, we will use a Bartlett kernel with 5 lags. In contrast, the previous examples generally rejected the null hypothesis that all series contain unit roots in favor of the alternative that at least some are stationary. For cautionary remarks on the use of panel unit-root tests in the examination of PPP, see, for example, Banerjee, Marcellino, and Osbat In short, our results are qualitatively quite similar to those reported in the literature, though Banerjee, Marcellino, and Osbat argue that because of cross-unit cointegration and long-run relationships among countries, panel unit-root tests quite often reject the null hypothesis even when true.

A series is said to be weakly or covariance stationary if the mean and autocovariances of the series. Cointegration The VAR models discussed so fare are appropriate for modeling I 0 data, like asset returns or growth rates of macroeconomic time series.

Economic theory, however, often implies equilibrium. This is a version of the standard regression model where the observations. Chapter 9: Univariate Time Series Analysis In the last chapter we discussed models with only lags of explanatory variables. These can be misleading if: 1. The dependent variable Y t depends on lags of. Wooldridge, Introductory Econometrics, 3d ed. Chapter Serial correlation and heteroskedasticity in time series regressions What will happen if we violate the assumption that the errors are not serially.

Wade Brorsen Suggested citation format: Seok, J. Pricing Corn Calendar Spread Options. Is Infrastructure Capital Productive? A Dynamic Heterogeneous Approach. The Relationship between Insurance Market Activity and Economic Growth Yana Petrova 1 Abstract This research examines the short- and the long-run relationship between insurance market activity and economic. Important to distinguish between two important cases:. Bivariate Cointegration Analysis What s New in Econometrics?

The Linear Model with Cluster Effects 2. Estimation with a Small Number of Groups and. Mehra A popular theoretical model of the inflation process is the expectationsaugmented Phillips-curve model. According to this model, prices are set as markup. Current account sustainability in advanced economies. Introduction The emergence of large imbalances in the current accounts of many advanced economies in the last decade has received much attention in.

Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. Supposed we used Eq 1. The ADF test will become;. Supposed that from the graph we choose to perform the DF test for variable gdp based on Eq 1. We need first select an appropriate lags order for ADF by information criterion.

To do this;. Then, perform ADF test for gdp with lag 2. The decision is we fail to reject the null hypothesis for unit root. The non-stationary series usually can be eliminated when we difference the series. To plot the series in difference form;.

To perform the ADF test for gdp in first difference form, first we need select an appropriate lags order for ADF by information criterion. Then, perform ADF test for D.