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. The article introduces and evaluates by Monte Carlo simulation experiments bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test. It finds that the performance of the bootstrap test is very good. The more sophisticated FDB produces a further improvement in cases where the performance of the asymptotic test is very unsatisfactory and the ordinary bootstrap does not work as well as it might. Furthermore, the Monte Carlo simulations provide a number of guidelines on when the bootstrap and FDB tests can be expected to work well. Finally, the tests are applied to US interest rates and international stock prices series. It is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series

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 correspond- ing asymptotic tests. The e¤ect 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 asymp- totic 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.

Tests for Cointegration Rank and the Initial Condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence.

Inference on Cointegration in Vector Autoregressive Models (summary section only)

In the thesis we consider inference for cointegration in vector autoregressive (VAR) models. The thesis consists of an introduction and four papers. The first paper proposes a new test for cointegration in VAR models that is directly based on the eigenvalues of the least squares (LS) estimate of the autoregressive matrix. In the second paper we compare a small sample correction for the likelihood ratio (LR) test of cointegrating rank and the bootstrap. The simulation experiments show that the bootstrap works very well in practice and dominates the correction factor. The tests are applied to international stock prices data, and the .nite sample performance of the tests are investigated by simulating the data. The third paper studies the demand for money in Sweden 1970—2000 using the I(2) model. In the fourth paper we re-examine the evidence of cointegration between international stock prices. 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. In all papers we work with two data sets. The first data set is a Swedish money demand data set with observations on the money stock, the consumer price index, gross domestic product (GDP), the short-term interest rate and the long-term interest rate. The data are quarterly and the sample period is 1970(1)—2000(1). The second data set consists of month-end stock market index observations for Finland, France, Germany, Sweden, the United Kingdom and the United States from 1980(1) to 1997(2). Both data sets are typical of the sample sizes encountered in economic data, and the applications illustrate the usefulness of the models and tests discussed in the thesis.

Markers of systemic inflammation in diagnostics and in prediction of outcome of community-acquired infection

Sepsis is associated with a systemic inflammatory response. It is characterised by an early proinflammatory response and followed by a state of immunosuppression. In order to improve the outcome of patients with infection and sepsis, novel therapies that influence the systemic inflammatory response are being developed and utilised. Thus, an accurate and early diagnosis of infection and evaluation of immune state are crucial. In this thesis, various markers of systemic inflammation were studied with respect to enhancing the diagnostics of infection and of predicting outcome in patients with suspected community-acquired infection. A total of 1092 acutely ill patients admitted to a university hospital medical emergency department were evaluated, and 531 patients with a suspicion of community-acquired infection were included for the analysis. Markers of systemic inflammation were determined from a blood sample obtained simultaneously with a blood culture sample on admission to hospital. Levels of phagocyte CD11b/CD18 and CD14 expression were measured by whole blood flow cytometry. Concentrations of soluble CD14, interleukin (IL)-8, and soluble IL-2 receptor α (sIL-2Rα) were determined by ELISA, those of sIL-2R, IL-6, and IL-8 by a chemiluminescent immunoassay, that of procalcitonin by immunoluminometric assay, and that of C-reactive protein by immunoturbidimetric assay. Clinical data were collected retrospectively from the medical records. No marker of systemic inflammation, neither CRP, PCT, IL-6, IL-8, nor sIL-2R predicted bacteraemia better than did the clinical signs of infection, i.e., the presence of infectious focus or fever or both. IL-6 and PCT had the highest positive likelihood ratios to identify patients with hidden community-acquired infection. However, the use of a single marker failed to detect all patients with infection. A combination of markers including a fast-responding reactant (CD11b expression), a later-peaking reactant (CRP), and a reactant originating from inflamed tissues (IL-8) detected all patients with infection. The majority of patients (86.5%) with possible but not verified infection showed levels exceeding at least one cut-off limit of combination, supporting the view that infection was the cause of their acute illness. The 28-day mortality of patients with community-acquired infection was low (3.4%). On admission to hospital, the low expression of cell-associated lipopolysaccharide receptor CD14 (mCD14) was predictive for 28-day mortality. In the patients with severe forms of community-acquired infection, namely pneumonia and sepsis, high levels of soluble CD14 alone did not predict mortality, but a high sCD14 level measured simultaneously with a low mCD14 raised the possibility of poor prognosis. In conclusion, to further enhance the diagnostics of hidden community-acquired infection, a combination of inflammatory markers is useful; 28-day mortality is associated with low levels of mCD14 expression at an early phase of the disease.

Informational efficiency of the European Union emission allowance market

This thesis studies the informational efficiency of the European Union emission allowance (EUA) market. In an efficient market, the market price is unpredictable and profits above average are impossible in the long run. The main research problem is does the EUA price follow a random walk. The method is an econometric analysis of the price series, which includes an autocorrelation coefficient test and a variance ratio test. The results reveal that the price series is autocorrelated and therefore a nonrandom walk. In order to find out the extent of predictability, the price series is modelled with an autoregressive model. The conclusion is that the EUA price is autocorrelated only to a small degree and that the predictability cannot be used to make extra profits. The EUA market is therefore considered informationally efficient, although the price series does not fulfill the requirements of a random walk. A market review supports the conclusion, but it is clear that the maturing of the market is still in process.

Using a botanic garden collection to test a bioclimatic vegetation scheme

Vegetation maps and bioclimatic zone classifications communicate the vegetation of an area and are used to explain how the environment regulates the occurrence of plants on large scales. Many practises and methods for dividing the world’s vegetation into smaller entities have been presented. Climatic parameters, floristic characteristics, or edaphic features have been relied upon as decisive factors, and plant species have been used as indicators for vegetation types or zones. Systems depicting vegetation patterns that mainly reflect climatic variation are termed ‘bioclimatic’ vegetation maps. Based on these it has been judged logical to deduce that plants moved between corresponding bioclimatic areas should thrive in the target location, whereas plants moved from a different zone should languish. This principle is routinely applied in forestry and horticulture but actual tests of the validity of bioclimatic maps in this sense seem scanty. In this study I tested the Finnish bioclimatic vegetation zone system (BZS). Relying on the plant collection of Helsinki University Botanic Garden’s Kumpula collection, which according to the BZS is situated at the northern limit of the hemiboreal zone, I aimed to test how the plants’ survival depends on their provenance. My expectation was that plants from the hemiboreal or southern boreal zones should do best in Kumpula, whereas plants from more southern and more northern zones should show progressively lower survival probabilities. I estimated probability of survival using collection database information of plant accessions of known wild origin grown in Kumpula since the mid 1990s, and logistic regression models. The total number of accessions I included in the analyses was 494. Because of problems with some accessions I chose to separately analyse a subset of the complete data, which included 379 accessions. I also analysed different growth forms separately in order to identify differences in probability of survival due to different life strategies. In most analyses accessions of temperate and hemiarctic origin showed lower survival probability than those originating from any of the boreal subzones, which among them exhibited rather evenly high probabilities. Exceptionally mild and wet winters during the study period may have killed off hemiarctic plants. Some winters may have been too harsh for temperate accessions. Trees behaved differently: they showed an almost steadily increasing survival probability from temperate to northern boreal origins. Various factors that could not be controlled for may have affected the results, some of which were difficult to interpret. This was the case in particular with herbs, for which the reliability of the analysis suffered because of difficulties in managing their curatorial data. In all, the results gave some support to the BZS, and especially its hierarchical zonation. However, I question the validity of the formulation of the hypothesis I tested since it may not be entirely justified by the BZS, which was designed for intercontinental comparison of vegetation zones, but not specifically for transcontinental provenance trials. I conclude that botanic gardens should pay due attention to information management and curational practices to ensure the widest possible applicability of their plant collections.