ML-Estimation in the Location-Scale-Shape Model of the Generalized Logistic Distribution

A three parameter (location, scale, shape) generalization of the logistic distribution is fitted to data. Local maximum likelihood estimators of the parameters are derived. Although the likelihood function is unbounded, the likelihood equations have a consistent root. ML-estimation combined with the ECM algorithm allows the distribution to be easily fitted to data.ECM algorithm, generalized logistic distribution, location-scale-shape model, maximum likelihood estimation

ML-Estimation in the Location-Scale-Shape Model of the Generalized Logistic Distribution

A three parameter (location, scale, shape) generalization of the logistic distribution is fitted to data. Local maximum likelihood estimators of the parameters are derived. Although the likelihood function is unbounded, the likelihood equations have a consistent root. ML-estimation combined with the ECM algorithm allows the distribution to be easily fitted to data.ECM algorithm, generalized logistic distribution, location-scale-shape model, maximum likelihood estimation

Qualitative Business Surveys in Manufacturing and Industrial Production - What can be Learned from Industry Branch Results?

Business tendency surveys are a popular tool for the timely assessment of the business cycle, used by economists and by the public. This article considers survey results in the manufacturing sector in more detail and looks into the question of, whether the analysis of branch results leads to an information gain. The business cycle turning points are identified in the filtered series and average leads to the turning point of industrial production are calculated. In addition to these leads the ratios of the signal variances to the noise variances are calculated to assess the clarity of the signal contained in the indicator series. Apart from assessing the general business cycle course the survey results in manufacturing are often used to forecast moment-to-moment changes of industrial production. Analyses based on wavelets show that the survey balances are useful to forecast the larger scale movements only. Nevertheless, the comparison of out-of-sample forecast errors show that the inclusion of survey results as independent variables in an autoregressive model improves the forecasts.Business tendency surveys, business cycle analysis, turning points, Grnager causality, wavelet cross-correlations.

Forecasting Quarter-on-Quarter Changes of German GDP with Monthly Business Tendency Survey Results

Results from business tendency surveys are often used to construct leading indicators. The indicators are then, for example, employed to forecast GDP growth. In this article more detailed results of business tendency surveys are used to forecast quarter-onquarter GDP growth. The target series is very challenging because this type of growth rate leads to quite volatile time series. The present study focuses on German GDP data and survey results provided by the Ifo Institute. Since numerous time series of possible indicators result from the surveys, methods that can handle this setting are applied. One candidate method is principal component analysis, which is used to reduce dimensionality. On the other hand, subset selection procedures are applied. For the present setting the latter method seems more successful than principal components. But this is not a statement about the two types of procedures in general. Which method should be favoured depends very much on the aims of the specific study.Business tendency surveys, business cycle analysis, principal component regression, subset selection.

The Use of Qualitative Business TendencySurveys for Forecasting Business Investmentin Germany

Investment in equipment and machinery is a very important component of GDP. In this paper we examine whether data from business tendency surveys are useful for a timely assessment of current investment behavior. In addition we investigate whether the survey results are helpful for forecastinginvestment growth in the short run. The first question is addressed with thehelp of spectral analysis. To study the forecast ability we estimate linearautoregressive and additive autoregressive models. The forecasting performance is assessed through filtered residuals. The analyses show that the business survey is indeed a useful tool for assessing investment in equipment and machinery.Business tendency surveys, forecasting, investment, linear autoregression, additive autoregression

Nonparametric Regression and the Detection of Turning Points in the Ifo Business Climate

Business climate indicators are used to receive early signals for turning points in the general business cycle. Therefore methods for the detection of turning points in time series are required. Estimations of slopes of a smooth component in the data can be calculated with local polynomial regression. A change in the sign of the slope can be interpreted as a turning point. A plug-in method is used for data-based bandwidth choice. Since in practice the identification of turning points at the actual boundary of the time series is of special interest, this situation is discussed in more detail. The nonparametric approach is applied to the Ifo Business Climate to demonstrate the application of the nonparametric approach and to analyze the time lead of the indicator.Nonparametric regression, slope estimation, turning points, business climate indicators

Exploring local dependence

This paper discusses two graphical methods for the investigation of local association of two continuous random variables. Often, scalar dependence measures, such as correlation, cannot reflect the complex dependence structure of two variables. However, dependence graphs have the potential to assess a far richer class of bivariate dependence structures. The two graphical methods discussed in this article are the chi-plot and the local dependence map. After the introduction of these methods they are applied to different data sets. These data sets contain simulated data and daily stock return series. With these examples the application possibilities of the two local dependence graphs are shown.Association, bivariate distribution, chi-plot, copula, correlation, kernel smoothing, local dependence, permutation test

A simple graphical method to explore tail-dependence in stock-return pairs

For a bivariate data set the dependence structure can not only be measured globally, for example with the Bravais-Pearson correlation coefficient, but the dependence structure can also be analyzed locally. In this article the exploration of dependencies in the tails of the bivariate distribution is discussed. For this a graphical method which is called chi-plot and which was introduced by Fisher and Switzer (1985, 2001) is used. Examples with simulated data sets illustrate that the chi-plot is suitable for the exploration of dependencies. This graphical method is then used to examine stock-return pairs. The kind of tail-dependence between returns has consequences, for example, for the calculation of the Value at Risk and should be modelled carefully. The application of the chi-plot to various daily stock-return pairs shows that different dependence structures can be found. This graph can therefore be an interesting aid for the modelling of returns.Association, bivariate distribution, chi-plot, copula, correlation, local dependence, tail-dependence

How to Define a Recession?

Konjunktur, Definition, Business cycle

Markov-Switching and the Ifo Business Climate: The Ifo Business Cycle Traffic Lights

Business cycle indicators are used to assess the economic situation of countries or regions. They are closely watched by the public, but are not easy to interpret. Does a current movement of the indicator signal a turning point or not? With the help of Markov Switching Models movements of indicators can be transformed in probability statements. In this article, the most important leading indicator of the German business cycle, the Ifo Business Climate, is described by a Markov Switching Model. Real-time probabilities for the current business-cycle regime are derived and presented in an innovative way: as the Ifo traffic lights.Ifo business climate, growth cycle, turning points, Markov-switching