Causality tests in the Granger's sense are increasingly applied in empirical research. Since the unit root revolution in time-series analysis, several modifications of tests for causality have been introduced in the literature. One of the recent developments is the Toda-Yamamoto modified Wald (MWALD) test, which is attractive due to its simple application, its absence of pre-testing distortions, and its basis on a standard asymptotical distribution irrespective of the number of unit roots and the cointegrating properties of the data. This study investigates the size properties of the MWALD test and finds that in small sample sizes this test performs poorly on those properties when using its asymptotical distribution, the chi-square. It is suggested that use be made of a leveraged bootstrap distribution to lower the size distortions. Monte Carlo simulation results show that an MWALD test based on a bootstrap distribution has much smaller size distortions than corresponding cases when the asymptotic distribution is used. These results hold for different sample sizes, integration orders, and error term processes (homoscedastic or ARCH). This new method is applied to the testing of the efficient market hypothesis.

Granger causality tests have become among the most popular empirical applications with time series data. Several new tests have been developed in the literature that can deal with different data generating processes. In all existing theoretical papers it is assumed that the lag length is known a priori. However, in applied research the lag length has to be selected before testing for causality. This paper suggests that in investigating the effectiveness of various Granger causality testing methodologies, including those using bootstrapping, the lag length choice should be endogenized, by which we mean the data-driven preselection of lag length should be taken into account. We provide and accordingly evaluate a Granger-causality bootstrap test which may be used with data that may or may not be integrated, and compare the performance of this test to that for the analogous asymptotic test. The suggested bootstrap test performs well and appears to be also robust to ARCH effects that usually characterize the financial data. This test is applied to testing the causal impact of the US financial market on the market of the United Arab Emirates.

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Monthly and quarterly data for the spot exchange rate of the Swedish Krona against major currencies have been used in this paper to investigate the causality in a Granger sense at different time scales between the spot exchange rate and the nominal interest rate differential by using wavelet analysis. Impulse response functions are also utilized to examine the signs of how one of these variables affects the other over time. One key empirical finding from the causality tests is that there is only substantial evidence of a causal relationship in the long run between the two variables. When using monthly data, this is true in both directions. When considering impulse responses on how the interest rate differential affects the exchange rate, there appears to be some evidence of more negative relationships at the shorter time scales and more positive relationships at the longer time scales.

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The performance of different information criteria - namely Akaike, corrected Akaike (AICC), Schwarz-Bayesian (SBC), and Hannan-Quinn - is investigated so as to choose the optimal lag length in stable and unstable vector autoregressive (VAR) models both when autoregressive conditional heteroscedasticity (ARCH) is present and when it is not. The investigation covers both large and small sample sizes. The Monte Carlo simulation results show that SBC has relatively better performance in lag-choice accuracy in many situations. It is also generally the least sensitive to ARCH regardless of stability or instability of the VAR model, especially in large sample sizes. These appealing properties of SBC make it the optimal criterion for choosing lag length in many situations, especially in the case of financial data, which are usually characterized by occasional periods of high volatility. SBC also has the best forecasting abilities in the majority of situations in which we vary sample size, stability, variance structure (ARCH or not), and forecast horizon (one period or five). frequently, AICC also has good lag-choosing and forecasting properties. However, when ARCH is present, the five-period forecast performance of all criteria in all situations worsens.VAR, lag length, information criteria, Monte Carlo simulations, ARCH, stability,

Using generalized impulse response functions, this study tests for the trade J-curve for three transitional central European countries -the Czech Republic, Hungary, and Poland -in their bilateral trade with respect to Germany. Our findings suggest that for each country there are some characteristics associated with a J-curve effect: after a (real or nominal) depreciation the export-to-import ratio briefly drops to below its initial value within a few months and then rises to a long run equilibrium value higher than the initial one.JEL classifications: F10, C30.

This paper uses wavelet analysis to investigate the relationship between the spot exchange rate and interest rate differential for seven pairs of countries, with a small country, Sweden, included in each case. The key empirical results show that there tends to be a negative relationship between the spot exchange rate (domestic‐currency price of foreign currency) and nominal interest rate differential (approximately the domestic interest rate minus the foreign interest rate) at the shortest timescales, while a positive relationship is more frequently found at the longest timescales. This indicates that among models of exchange rate determination using the asset approach, the sticky‐price models are supported in the short run and flexible‐price models in the long run.