Niklas Ahlgren

Testing for cointegration between international stock prices

This paper re-examines the evidence for cointegration between international stock prices. It applies Johansens maximum likelihood (ML) cointegration method and likelihood ratio (LR) tests for cointegration to stock prices. In monthly data it finds at most one cointegrating vector and in quarterly data finds no cointegrating vectors. Using the small-sample corrections or the small-sample critical values it finds no evidence of cointegration. Johansens LR tests for cointegration are sensitive to the lag length specification in the VAR model. In general it finds more evidence of cointegration in higher order VAR models. The paper shows that some of the previous empirical results can be explained by the small-sample bias and size distortion of Johansens LR tests for cointegration. It finds that international stock prices are not cointegrated.

Bootstrap and fast double bootstrap tests of cointegration rank with financial time series

The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. Bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test are introduced and evaluated by Monte Carlo simulation experiments. It is found that the performance of the ordinary (single) bootstrap test is in most cases good in terms of the size of the test. The FDB produces a further improvement in cases where the performance of the asymptotic test is unsatisfactory and the single bootstrap test overrejects noticeably. The FDB is shown to be a useful supplement to the single bootstrap as a tool for determining the cointegration rank. The tests are applied to US interest rates and international stock prices series. By simulating the data assuming that the cointegration rank is known, it is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

Panel cointegration of Chinese A and B shares

We study information flows in Chinas stock markets. By using panel data methods we test for a unit root in the price premium of domestic investors’ A shares over foreign investors’ B shares, as well as cointegration between the A- and B-share prices on the Shanghai and Shenzhen stock exchanges. We find that the A-share premia are nonstationary, and that the A- and B-share prices are not cointegrated up till January 2001. After February 2001, when domestic investors were allowed to trade B shares, the A-share premia become stationary and the A- and B-share prices cointegrated. One interesting result from the panel data analysis is that most firms’ A and B shares are cointegrated, but not all firms. Cointegration is more likely for firms with a small A-share premium, low ratio of nontradeable shares, high growth rate and large B-share market capitalization relative to the A-share market capitalization. Our findings suggest that the relaxation of the investment restrictions decreased the segmentation between the A- and B-share markets in China.

Practical Proposals for Specifying k-Nearest Neighbours Weights Matrices

Abstract In this article, we introduce and evaluate testing procedures for specifying the number k of nearest neighbours in the weights matrix of a spatial econometric model. An increasing and a decreasing neighbours testing procedure are suggested. Kelejians J-test for non-nested spatial models is used in the testing procedures. The testing procedures give formal justification for the choice of k, something which has been lacking in the classical spatial econometric literature. Simulations show that the testing procedures can be used in large samples to determine k. An empirical example involving house price data is provided.

Practical Problems with Tests of Cointegration Rank with Strong Persistence and Heavy-Tailed Errors

Financial time series have several distinguishing features which are of concern in tests of cointegration. An example considered in this paper is testing the approximate non-arbitrage relation between the credit default swap (CDS) price and bond spread. We show that strong persistence and very high persistence in volatility are stylised features of cointegrated systems of CDS prices and bond spreads. There is empirical support that the distribution of the errors is heavy-tailed with infinite fourth moment. Tests for cointegration have low power under such conditions. The asymptotic and bootstrap tests are unreliable if the errors are heavy-tailed with infinite fourth moment. Monte Carlo simulations indicate that the wild bootstrap (WB) test may be justified with heavy-tailed errors which do not have finite fourth moment. The tests are applied to CDS prices and bond spreads of US and European investment-grade firms.