FINANCIAL MARKETS AND TIME SERIES

The research project reports ongoing joint research of Niklas Ahlgren and Jan Antell about the statistical and econometric analysis of financial time series. The co-operation started in the late 1990s, and some of the output were included in our theses (Ahlgren, 2002, and Antell, 2004). (1) Ahlgren, N. and Antell, J. (2002), Testing for Cointegration between International Stock Prices, Applied Financial Economics, 12, 851-861. Abstract This paper re-examines the evidence for cointegration between international stock prices. It applies Johansen’s 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. Johansen’s 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 Johansen’s LR tests for cointegration. It finds that international stock prices are not cointegrated. (2) Ahlgren, N. and Antell, J. (2008), Bootstrap and Fast Double Bootstrap Tests of Cointegration Rank with Financial Time Series, Computational Statistics and Data Analysis, 52, 4754-4767. Abstract 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. (3) Ahlgren, N. and Antell, J. (2010), Stock Market Linkages and Financial Contagion: A Cobreaking Analysis, Quarterly Review of Economics and Finance, 50, 157-166. Abstract Financial crises have shown that dramatic movements in one financial market can have a powerful impact on other markets. This paper proposes to use cobreaking to model comovements between stock markets during crises and to test for contagion. We find evidence of cobreaking between developed stock markets. In emerging stock markets, the evidence of cobreaking is mainly due to the non-financial event of the World Trade Center terrorist attacks in 2001. We find evidence of short-term linkages during times of crisis but not contagion. These short-term linkages have important implications for investors, risk managers and regulators. (4) Ahlgren, N. and Antell, J. (2008), The Power of Boostrap Tests of Cointegration Rank with Financial Time Series, submitted to Computational Statistics. Abstract Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of the corresponding asymptotic tests. The effect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymptotic test. The bootstrap test estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.