Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch–Singer Hypothesis

Abstract

In this paper we propose tests for hypotheses regarding the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data and they are robust to strong serial correlation. The data can contain a unit root and the tests still have the correct size asymptotically. The tests we analyze are standard heteroskedasticity autocorrelation (HAC) robust tests based on nonparametric kernel variance estimators. We analyze these tests using the …xed-b asymptotic framework recently proposed by Kiefer and Vogelsang (2002). This analysis allows us to analyze the power properties of the tests with regards to bandwidth and kernel choices. Our analysis shows that among popular kernels, there are speci…c kernel and bandwidth choices that deliver tests with maximal power within a speci…c class of tests. Based on the theoretical results, we propose a data dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test proposed by Vogelsang (1998). We apply the recommended test to the logarithm of a net barter terms of trade series and we …nd that this series has a statistically signi…cant negative slope. This …nding is consistent with the well known Prebisch-Singer hypothesis.

When Grilli and Yang meet Prebisch and Singer: Piecewise linear trends in primary commodity prices

“…15 They also became negative or more negative after around the mid-1970s. Our finding of negative trend for GYCPI agrees well with that in Bunzel and Vogelsang (2005) and Zhou and Shao (2013), whose sample period ended at 1995. 16 Overall, stronger evidence for the Prebisch-Singer hypothesis is found with the aggregate commodity price indexes.…”

Assessing the dynamics of terms of trade in a model of cumulative causation and structural change

“…His results rely on the alleged fact that prices of manufactures imported by developing countries from the g5 increased considerably higher than that the prices of manufactures exported by developing countries. Other authors such as grilli and yang (1988), Bunzel and Vogelsang (2005) and Zanias (2005) have also found a negative long-run trend in the relative price of primary commodities, confirming the importance of movements in the relative prices of exports of rich and poor nations.…”

Patterns and Pricing of Idiosyncratic Volatility in the French Stock Market

“…However, Vogelsang [34] points out that when errors in the trend regression are persistent, the student t-value often rejects the null hypothesis of no trend. As a consequence Bunzel and Vogelsang [25] developed the t-dan test which we employ in this study. 3 This test is valid whether or not a unit root exists in the error terms.…”

“…We can easily summarize our results. First, we test for the presence of trends in aggregate idiosyncratic and market volatility using Bunzel and Vogelsang's [25] t-dan test. We also follow Bekaert et al's [22] method to further test for regime shifts.…”