Robust critical values for unit root tests for series with conditional heteroscedasticity errors: An application of the simple NoVaS transformation

In this paper, we introduce a set of critical values for unit root tests that are robust in the presence of conditional heteroscedasticity errors using the normalizing and variance-stabilizing transformation (NoVaS) in Politis (2007) and examine their properties using Monte Carlo methods. In terms of the size of the test, our analysis reveals that unit root tests with NoVaS-modified critical values have actual sizes close to the nominal size. For the power of the test, we find that unit root tests with NoVaS-modified critical values either have the same power as, or slightly better than, tests using conventional Dickey–Fuller critical values across the sample range considered.Critical values; normalizing and variance-stabilizing transformation; unit root tests

Bootstrapping the Breusch-Godfrey autocorrelation test for a single equation dynamic model: Bootstrapping the Restricted vs. Unrestricted model

We use Monte Carlo methods to study the properties of the bootstrap Breusch-Godfrey test for autocorrelated errors in two versions a) by bootstrapping under the null hypothesis, restricted and b) by bootstrapping under the alternative hypothesis, unrestricted. We use the residual bootstrap for the bootstrap-BG test. Our analysis regarding the size of the test reveals that both bootstrap tests have actual sizes that lie close to the nominal size, with the restricted being better. Regarding the power of the test we find that with bootstrapping under the alternative hypothesis, the unrestricted bootstrap test has the greater power in small samples

Two Sides Of The Same Coin: Bootstrapping The Restricted Vs. Unrestricted Model

The properties of the bootstrap test for restrictions are studied in two versions: 1) bootstrapping under the null hypothesis, restricted, and 2) bootstrapping under the alternative hypothesis, unrestricted. This article demonstrates the equivalence of these two methods, and illustrates the small sample properties of the Wald test for testing Granger-Causality in a stable stationary VAR system by Monte Carlo methods. The analysis regarding the size of the test reveals that, as expected, both bootstrap tests have actual sizes that lie close to the nominal size. Regarding the power of the test, the Wald and bootstrap tests share the same power as the use of the Size-Power Curves on a correct size-adjusted basis

Size and Power of the RESET Test as Applied to Systems of Equations: A Bootstrap Approach

The size and power of various generalization of the RESET test for functional misspecification are investigated, using the “Bootsrap critical values”, in systems ranging from one to ten equations. The properties of 8 versions of the test are studied using Monte Carlo methods. The results are then compared with another study of Shukur and Edgerton (2002), in which they used the asymptotic critical values instead and found that in general only one version of the tests works well regarding size properties. In our study, when applying the bootstrap critical values, we find that all the tests exhibits correct size even in large systems. The power of the test is low, however, when the number of equations grows and the correlation between the omitted variables and the RESET proxies is small

The Effect Of GARCH (1,1) On The Granger Causality Test In Stable VAR Models

Using Monte Carlo methods, the properties of Granger causality test in stable VAR models are studied under the presence of different magnitudes of GARCH effects in the error terms. Analysis reveals that substantial GARCH effects influence the size properties of the Granger causality test, especially in small samples. The power functions of the test are usually slightly lower when GARCH effects are imposed among the residuals compared with the case of white noise residuals

Testing for Cointegrating Relations - A Bootstrap Approach.’ Working paper

considering the size and power properties, we could not find any noticeable differences between the two test methods

Testing for cointegrating relations - A bootstrap approach

Using Monte Carlo methods together with the Bootstrap critical values, we have studied the properties of two tests (Trace and L-max), derived by Johansen (1988) for testing for cointegration in V AR systems. Regarding the size of the tests, the results show that both of the test methods perform satisfactorily when there are mixed stationary and nonstationary components in the model. The analyses of the power functions indicate that both of the test methods can effectively detect the present of cointegration vector(s). Finally, when considering the size and power properties, we could not find any noticeable differences between the two test methods

Robust critical values for unit root tests for series with conditional heteroscedasticity errors: An application of the simple NoVaS transformation

In this paper, we introduce a set of critical values for unit root tests that are robust in the presence of conditional heteroscedasticity errors using the normalizing and variance-stabilizing transformation (NoVaS) and examine their properties using Monte Carlo methods. In terms of the size of the test, our analysis reveals that unit root tests with NoVaS-modified critical values have actual sizes close to the nominal size. For the power of the test, we find that unit root tests with NoVaS-modified critical values either have the same power as, or slightly better than, tests using conventional Dickey–Fuller critical values across the sample range considered

Monte Carlo Results for Bootstrap Tests in Systems with Integrated-Cointegrated Variables.

When we study the properties of a test procedure, two aspects are of prime importance. Firstly, we wish to know if the actual size of the test (i.e., the probability of rejecting the null when true) is close to the nominal size (used for calculating the critical values). Given that the actual size is a reasonable approximation to the nominal size, we then wish to investigate the actual power of the test (i.e., the probability of rejecting the null when false) for a number of different alternative hypotheses. When comparing different tests, we will therefore prefer those in which (a) actual size lies closest to the nominal size and, given that (a) holds, (b) have the greatest power. In most cases, however, the distributions of the test statistics we use are known only asymptotically and, unfortunately, unless the sample size is very large indeed, it is difficult to know whether asymptotic theory is sufficiently accurate to allow us to interpret our results with confidence. As a result, the tests may not have the correct size and inferential comparisons and judgements based on them might be misleading. In recent years, an approach is beginning to become popular to deal with this situation, namely to employ some variant of the Bootstrap. The basic idea of Bootstrapping test statistics is to draw a large number of “ Bootstrap samples,” which obey the null hypothesis and, as far as possible, resemble the real sample, and then compare the observed test statistic to the ones calculated from the Bootstrap samples. By using Bootstrap tests we are able to improve the critical values so that the true size of the test approaches its nominal value. It is possible to use Bootstrapping either to calculate a critical value, or to calculate the significance level, or P-value, associated with it. In this thesis, by using Monte Carlo experiments, we show a number of useful results about the small sample properties of what we shall call “ Bootstrap tests,” in systems with Integrated-Cointegrated variables. We show the ability of the Bootstrap technique to produce critical values which are much more accurate than the asymptotic ones: a) In the case of the Error Correction Model Cointegration test for a simple, single-lag, bivariate process. b) For testing Cointegration in a Vector Error Correction Model system. c) For testing Granger-causality in a Vector Autoregressive (VAR ) system. d) And for testing Granger-causality in a (VAR) system by using only the Dolado and Lütkepohl corrected test. Finally, an application of the four previous tests concludes this thesis by studying the comovement and Granger-cause effects between the French and German stock markets

Greek Debt Crisis : “An Introduction to the Economic Effects of Austerity”

We trace the reasons for the negative development of Greek government debt from 1980 to 2014 by studying the deficits of the Greek state under the same period. We also see the Greek debt under the different political regimes. We briefly describe the two bailout programs for Greece and finally we name the amount and Euro states that own the Greek loans. The negative effects of austerity are about 22% less GDP and total household and government consumption and monthly wages; finally, the unemployment rate grew 21%.Working paper</p