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.

Sexual reproduction in chydorid cladocerans (Anomopoda, Chydoridae) in southern Finland - implications for paleolimnology

The relationship between sexual reproduction of littoral chydorid cladocerans (Anomopoda, Chydoridae) and environmental factors in aquatic ecosystems has been rarely studied, although the sexual behavior of some planktonic cladocerans is well documented. Ecological monitoring was used to study the relationship between climate-related and non-climatic environmental factors and chydorid sexual reproduction patterns in nine environmentally different lakes that were closely situated to each other in southern Finland. Furthermore, paleolimnological ephippium analysis was used to clarify how current sexual reproduction is reflected in surface sediments of the same nine lakes. Additionally, short sediment cores from two of the lakes were studied with ephippium analysis to examine how recent climate-related and non-climatic environmental changes were reflected in chydorid sexual reproduction. Ephippium analysis uses the subfossil shells of asexual individuals to represent asexual reproduction and the shells of sexual females, i.e. ephippia, to represent sexual reproduction. The relative proportion of ephippia of all chydorid species, i.e. total chydorid ephippia (TCE) indicates the relative proportion of sexual reproduction during the open-water season. This thesis is part of the EPHIPPIUM-project which aims to develop ephippium analysis towards a quantitative climate reconstruction tool. To be able to develop a valid climate model, the influence of the environmental stressors other than climate on contemporary sexual reproduction and its reflection in sediment assemblages must be clarified so they can be eliminated from the model. During contemporary monitoring a few sexual individuals were observed during summer, apparently forced to sexual reproduction by non-climatic local environmental factors, such as crowding or invertebrate predation. Monitoring also revealed that the autumnal chydorid sexual reproduction period was consistent between the different lakes and climate-related factors appeared to act as the main inducers and regulators of autumnal sexual reproduction. However, during autumn, chydorid species and populations among the lakes exhibited a wide variation in the intensity, induction time, and length of autumnal sexual reproduction. These variations apparently act as mechanisms for local adaptations due to the genetic variability provided by sexual reproduction that enhance the ecological flexibility of chydorid species, allowing them to inhabit a wide range of environments. A large variation was also detected in the abundance of parthenogenetic and gamogenetic individuals during the open-water season among the lakes. On the basis of surface sediment samples, the general level of the TCE is ca. 3-4% in southern Finland, reflecting an average proportion of sexual reproduction in this specific climate. The variation in the TCE was much lower than could be expected on the basis of the monitoring results. This suggests that some of the variation detected by monitoring may derive from differences between sampling sites and years smoothed out in the sediment samples, providing an average of the entire lake area and several years. The TCE is always connected to various ecological interactions in lake ecosystems and therefore is always lake-specific. Hypothetically, deterioration of climate conditions can be detected in the TCE as an increase in ephippia of all chydorid species, since a shortening open-water season is reflected in the relative proportions of the two reproduction modes. Such an increase was clearly detected for the time period of the Little Ice Age in a sediment core. The paleolimnological results also indicated that TCE can suddenly increase due to ephippia of one or two species, which suggests that at least some chydorids can somehow increase the production of resting eggs under local environmental stress. Thus, some environmental factors may act as species-specific environmental stressors. The actual mechanism of the increased sexual reproduction seen in sediments has been unknown but the present study suggests that the mechanism is probably the increased intensity of gamogenesis, i.e. that a larger proportion of individuals in autumnal populations reproduce sexually, which results in a larger proportion of ephippia in sediments and a higher TCE. The results of this thesis demonstrate the utility of ephippium analysis as a paleoclimatological method which may also detect paleolimnological changes by identifying species-specific environmental stressors. For a quantitative TCE-based climate reconstruction model, the natural variation in the TCE of surface sediments in different climates must be clarified with more extensive studies. In addition, it is important to recognize the lakes where the TCE is not only a reflection of the length of the open-water season, but is also non-climatically forced. The results of ephippium analysis should always be interpreted in a lake-specific manner and in the context of other paleoecological proxies.

Studies on Binary Time Series Models with Applications to Empirical Macroeconomics and Finance

This thesis studies binary time series models and their applications in empirical macroeconomics and finance. In addition to previously suggested models, new dynamic extensions are proposed to the static probit model commonly used in the previous literature. In particular, we are interested in probit models with an autoregressive model structure. In Chapter 2, the main objective is to compare the predictive performance of the static and dynamic probit models in forecasting the U.S. and German business cycle recession periods. Financial variables, such as interest rates and stock market returns, are used as predictive variables. The empirical results suggest that the recession periods are predictable and dynamic probit models, especially models with the autoregressive structure, outperform the static model. Chapter 3 proposes a Lagrange Multiplier (LM) test for the usefulness of the autoregressive structure of the probit model. The finite sample properties of the LM test are considered with simulation experiments. Results indicate that the two alternative LM test statistics have reasonable size and power in large samples. In small samples, a parametric bootstrap method is suggested to obtain approximately correct size. In Chapter 4, the predictive power of dynamic probit models in predicting the direction of stock market returns are examined. The novel idea is to use recession forecast (see Chapter 2) as a predictor of the stock return sign. The evidence suggests that the signs of the U.S. excess stock returns over the risk-free return are predictable both in and out of sample. The new "error correction" probit model yields the best forecasts and it also outperforms other predictive models, such as ARMAX models, in terms of statistical and economic goodness-of-fit measures. Chapter 5 generalizes the analysis of univariate models considered in Chapters 2 4 to the case of a bivariate model. A new bivariate autoregressive probit model is applied to predict the current state of the U.S. business cycle and growth rate cycle periods. Evidence of predictability of both cycle indicators is obtained and the bivariate model is found to outperform the univariate models in terms of predictive power.

Residual noise covariance for Planck low-resolution data analysis

Aims: Develop and validate tools to estimate residual noise covariance in Planck frequency maps. Quantify signal error effects and compare different techniques to produce low-resolution maps. Methods: We derive analytical estimates of covariance of the residual noise contained in low-resolution maps produced using a number of map-making approaches. We test these analytical predictions using Monte Carlo simulations and their impact on angular power spectrum estimation. We use simulations to quantify the level of signal errors incurred in different resolution downgrading schemes considered in this work. Results: We find an excellent agreement between the optimal residual noise covariance matrices and Monte Carlo noise maps. For destriping map-makers, the extent of agreement is dictated by the knee frequency of the correlated noise component and the chosen baseline offset length. The significance of signal striping is shown to be insignificant when properly dealt with. In map resolution downgrading, we find that a carefully selected window function is required to reduce aliasing to the sub-percent level at multipoles, ell > 2Nside, where Nside is the HEALPix resolution parameter. We show that sufficient characterization of the residual noise is unavoidable if one is to draw reliable contraints on large scale anisotropy. Conclusions: We have described how to compute the low-resolution maps, with a controlled sky signal level, and a reliable estimate of covariance of the residual noise. We have also presented a method to smooth the residual noise covariance matrices to describe the noise correlations in smoothed, bandwidth limited maps.

Topics in Spatial Econometrics - With Applications to House Prices

Topics in Spatial Econometrics — With Applications to House Prices Spatial effects in data occur when geographical closeness of observations influences the relation between the observations. When two points on a map are close to each other, the observed values on a variable at those points tend to be similar. The further away the two points are from each other, the less similar the observed values tend to be. Recent technical developments, geographical information systems (GIS) and global positioning systems (GPS) have brought about a renewed interest in spatial matters. For instance, it is possible to observe the exact location of an observation and combine it with other characteristics. Spatial econometrics integrates spatial aspects into econometric models and analysis. The thesis concentrates mainly on methodological issues, but the findings are illustrated by empirical studies on house price data. The thesis consists of an introductory chapter and four essays. The introductory chapter presents an overview of topics and problems in spatial econometrics. It discusses spatial effects, spatial weights matrices, especially k-nearest neighbours weights matrices, and various spatial econometric models, as well as estimation methods and inference. Further, the problem of omitted variables, a few computational and empirical aspects, the bootstrap procedure and the spatial J-test are presented. In addition, a discussion on hedonic house price models is included. In the first essay a comparison is made between spatial econometrics and time series analysis. By restricting the attention to unilateral spatial autoregressive processes, it is shown that a unilateral spatial autoregression, which enjoys similar properties as an autoregression with time series, can be defined. By an empirical study on house price data the second essay shows that it is possible to form coordinate-based, spatially autoregressive variables, which are at least to some extent able to replace the spatial structure in a spatial econometric model. In the third essay a strategy for specifying a k-nearest neighbours weights matrix by applying the spatial J-test is suggested, studied and demonstrated. In the final fourth essay the properties of the asymptotic spatial J-test are further examined. A simulation study shows that the spatial J-test can be used for distinguishing between general spatial models with different k-nearest neighbours weights matrices. A bootstrap spatial J-test is suggested to correct the size of the asymptotic test in small samples.

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.

Bootstrapping the Error Correction Model Cointegration Test

This paper is concerned with using the bootstrap to obtain improved critical values for the error correction model (ECM) cointegration test in dynamic models. In the paper we investigate the effects of dynamic specification on the size and power of the ECM cointegration test with bootstrap critical values. The results from a Monte Carlo study show that the size of the bootstrap ECM cointegration test is close to the nominal significance level. We find that overspecification of the lag length results in a loss of power. Underspecification of the lag length results in size distortion. The performance of the bootstrap ECM cointegration test deteriorates if the correct lag length is not used in the ECM. The bootstrap ECM cointegration test is therefore not robust to model misspecification.

Applications of Treatment Effects Models and Semiparametric Estimation

This thesis is composed of an introductory chapter and four applications each of them constituting an own chapter. The common element underlying each of the chapters is the econometric methodology. The applications rely mostly on the leading econometric techniques related to estimation of causal effects. The first chapter introduces the econometric techniques that are employed in the remaining chapters. Chapter 2 studies the effects of shocking news on student performance. It exploits the fact that the school shooting in Kauhajoki in 2008 coincided with the matriculation examination period of that fall. It shows that the performance of men declined due to the news of the school shooting. For women the similar pattern remains unobserved. Chapter 3 studies the effects of minimum wage on employment by employing the original Card and Krueger (1994; CK) and Neumark and Wascher (2000; NW) data together with the changes-in-changes (CIC) estimator. As the main result it shows that the employment effect of an increase in the minimum wage is positive for small fast-food restaurants and negative for big fast-food restaurants. Therefore, it shows that the controversial positive employment effect reported by CK is overturned for big fast-food restaurants and that the NW data are shown, in contrast to their original results, to provide support for the positive employment effect. Chapter 4 employs the state-specific U.S. data (collected by Cohen and Einav [2003; CE]) on traffic fatalities to re-evaluate the effects of seat belt laws on the traffic fatalities by using the CIC estimator. It confirms the CE results that on the average an implementation of a mandatory seat belt law results in an increase in the seat belt usage rate and a decrease in the total fatality rate. In contrast to CE, it also finds evidence on compensating-behavior theory, which is observed especially in the states by the border of the U.S. Chapter 5 studies the life cycle consumption in Finland, with the special interest laid on the baby boomers and the older households. It shows that the baby boomers smooth their consumption over the life cycle more than other generations. It also shows that the old households smoothed their life cycle consumption more as a result of the recession in the 1990s, compared to young households.

Categorical Meteorological Products: Evaluation and Analysis

In meteorology, observations and forecasts of a wide range of phenomena for example, snow, clouds, hail, fog, and tornados can be categorical, that is, they can only have discrete values (e.g., "snow" and "no snow"). Concentrating on satellite-based snow and cloud analyses, this thesis explores methods that have been developed for evaluation of categorical products and analyses. Different algorithms for satellite products generate different results; sometimes the differences are subtle, sometimes all too visible. In addition to differences between algorithms, the satellite products are influenced by physical processes and conditions, such as diurnal and seasonal variation in solar radiation, topography, and land use. The analysis of satellite-based snow cover analyses from NOAA, NASA, and EUMETSAT, and snow analyses for numerical weather prediction models from FMI and ECMWF was complicated by the fact that we did not have the true knowledge of snow extent, and we were forced simply to measure the agreement between different products. The Sammon mapping, a multidimensional scaling method, was then used to visualize the differences between different products. The trustworthiness of the results for cloud analyses [EUMETSAT Meteorological Products Extraction Facility cloud mask (MPEF), together with the Nowcasting Satellite Application Facility (SAFNWC) cloud masks provided by Météo-France (SAFNWC/MSG) and the Swedish Meteorological and Hydrological Institute (SAFNWC/PPS)] compared with ceilometers of the Helsinki Testbed was estimated by constructing confidence intervals (CIs). Bootstrapping, a statistical resampling method, was used to construct CIs, especially in the presence of spatial and temporal correlation. The reference data for validation are constantly in short supply. In general, the needs of a particular project drive the requirements for evaluation, for example, for the accuracy and the timeliness of the particular data and methods. In this vein, we discuss tentatively how data provided by general public, e.g., photos shared on the Internet photo-sharing service Flickr, can be used as a new source for validation. Results show that they are of reasonable quality and their use for case studies can be warmly recommended. Last, the use of cluster analysis on meteorological in-situ measurements was explored. The Autoclass algorithm was used to construct compact representations of synoptic conditions of fog at Finnish airports.

Otoksen edustavuuden mittaus R-indikaattorin avulla Suomen uhritutkimuspilotissa

Tutkielmassa sovelletaan aineiston edustavuutta mittaavaa laatuindikaattoria Suomen uhritutkimuspilottiin tilanteessa, jossa ilmenee vastauskatoa. Vastauskato on kasvava ongelma tilastotutkimuksissa: jos tutkimukseen osallistuneet eivät edusta otosjoukkoa tutkittavan asian suhteen, voi vastauskadosta aiheutuva harha olla estimoiduissa tunnusluvuissa hyvinkin suuri. Tutkimuksissa näkee usein julkaistavan vastausasteen ikään kuin se kertoisi aukottomasti tutkimuksen laadusta. Pelkkä korkea vastausaste ei kuitenkaan välttämättä takaa estimaattien harhattomuutta, sillä se ei kerro mitään vastanneiden ja vastaamattomien eroista tutkittavan asian suhteen. Tarvitaan siis muita mittareita, joilla vastanneiden laatua voitaisiin paremmin arvioida, ja R-indikaattori tarjoaa yhden vaihtoehdon. R-indikaattori mittaa otosalkioiden vastausalttiuksien välistä vaihtelua. R-indikaattorin estimoiminen edellyttää siis vastausalttiuksien estimointia, mikä puolestaan edellyttää apumuuttujien olemassaoloa kaikille otosalkioille. Vastausalttiuksien estimoimiseen käytettiin linkkifunktiona sekä logistista mallia että ja Särndalin ja Lundströmin (2008) vastausvaikutusten mallia. Vastauskäyttäytymiseen vaikuttavan apumuuttujajoukon valinta tehtiin alan kirjallisuuteen perustuen (Groves & Couper 1998). Koska R-indikaattorin estimaattori on satunnaismuuttuja, täytyi sille estimoida varianssi ja mahdollinen harha (Shlomo ym. 2009). Estimoinnissa käytettiin Bootstrap-pseudotoistomenetelmää, jossa alkuperäisestä aineistosta poimitaan niin kutsuttuja pseudo-otoksia, joiden avulla R-indikaattorin estimaattorille voidaan laskea keskivirhe. Suomen uhritutkimuspilotti koostui kolmesta eri tiedonkeruumenetelmällä poimitusta otoksesta: CAPI-, CATI- CAVVIotoksesta. Vastausasteet vaihtelivat aineistoissa paljon, mutta R-indikaattorin estimaatit olivat kaikille aineistoille liki samat. Suurempi vastausaste ei siis merkinnyt parempaa edustavuutta. Lisäksi CAVVI-aineistossa muistutusviestein ja -kirjein suoritettu vastausasteen kasvattaminen huononsi edustavuutta R-indikaattorin näkökulmasta. Mielivaltainen vastausasteen kasvattaminen ei siis ole välttämättä perusteltua. R-indikaattorin estimaattorin ominaisuuksien osalta empiiriset tulokset vahvistivat RISQ-projektin aiempia tutkimustuloksia. Estimaattorin arvo oli sitä pienempi mitä enemmän vastausalttiuden mallissa oli selittäjiä, koska tällöin vastausalttiuksien varianssi kasvoi (Schouten ym. 2009). Otoskoko vaikutti merkittävästi varianssin suuruuteen: mitä pienempi otoskoko oli, sitä leveämmät olivat luottamusvälit ja sitä vaikeampi oli tehdä johtopäätöksiä edustavuudesta.

Microfinance, Efficiency and Agricultural Production in Bangladesh

The objectives of this study were to make a detailed and systematic empirical analysis of microfinance borrowers and non-borrowers in Bangladesh and also examine how efficiency measures are influenced by the access to agricultural microfinance. In the empirical analysis, this study used both parametric and non-parametric frontier approaches to investigate differences in efficiency estimates between microfinance borrowers and non-borrowers. This thesis, based on five articles, applied data obtained from a survey of 360 farm households from north-central and north-western regions in Bangladesh. The methods used in this investigation involve stochastic frontier (SFA) and data envelopment analysis (DEA) in addition to sample selectivity and limited dependent variable models. In article I, technical efficiency (TE) estimation and identification of its determinants were performed by applying an extended Cobb-Douglas stochastic frontier production function. The results show that farm households had a mean TE of 83% with lower TE scores for the non-borrowers of agricultural microfinance. Addressing institutional policies regarding the consolidation of individual plots into farm units, ensuring access to microfinance, extension education for the farmers with longer farming experience are suggested to improve the TE of the farmers. In article II, the objective was to assess the effects of access to microfinance on household production and cost efficiency (CE) and to determine the efficiency differences between the microfinance participating and non-participating farms. In addition, a non-discretionary DEA model was applied to capture directly the influence of microfinance on farm households production and CE. The results suggested that under both pooled DEA models and non-discretionary DEA models, farmers with access to microfinance were significantly more efficient than their non-borrowing counterparts. Results also revealed that land fragmentation, family size, household wealth, on farm-training and off farm income share are the main determinants of inefficiency after effectively correcting for sample selection bias. In article III, the TE of traditional variety (TV) and high-yielding-variety (HYV) rice producers were estimated in addition to investigating the determinants of adoption rate of HYV rice. Furthermore, the role of TE as a potential determinant to explain the differences of adoption rate of HYV rice among the farmers was assessed. The results indicated that in spite of its much higher yield potential, HYV rice production was associated with lower TE and had a greater variability in yield. It was also found that TE had a significant positive influence on the adoption rates of HYV rice. In article IV, we estimated profit efficiency (PE) and profit-loss between microfinance borrowers and non-borrowers by a sample selection framework, which provided a general framework for testing and taking into account the sample selection in the stochastic (profit) frontier function analysis. After effectively correcting for selectivity bias, the mean PE of the microfinance borrowers and non-borrowers were estimated at 68% and 52% respectively. This suggested that a considerable share of profits were lost due to profit inefficiencies in rice production. The results also demonstrated that access to microfinance contributes significantly to increasing PE and reducing profit-loss per hectare land. In article V, the effects of credit constraints on TE, allocative efficiency (AE) and CE were assessed while adequately controlling for sample selection bias. The confidence intervals were determined by the bootstrap method for both samples. The results indicated that differences in average efficiency scores of credit constrained and unconstrained farms were not statistically significant although the average efficiencies tended to be higher in the group of unconstrained farms. After effectively correcting for selectivity bias, household experience, number of dependents, off-farm income, farm size, access to on farm training and yearly savings were found to be the main determinants of inefficiencies. In general, the results of the study revealed the existence substantial technical, allocative, economic inefficiencies and also considerable profit inefficiencies. The results of the study suggested the need to streamline agricultural microfinance by the microfinance institutions (MFIs), donor agencies and government at all tiers. Moreover, formulating policies that ensure greater access to agricultural microfinance to the smallholder farmers on a sustainable basis in the study areas to enhance productivity and efficiency has been recommended. Key Words: Technical, allocative, economic efficiency, DEA, Non-discretionary DEA, selection bias, bootstrapping, microfinance, Bangladesh.