C32 - Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space ModelsReturn

The article focuses on various aspects of specification, estimation and identification of vector autoregression (VAR) models. Key VAR-specific topics of verification of an estimated model are also covered, as well as the differences between a standard (unrestricted) and structural VAR model. Subsequently, we address theoretical properties and practical aspects of impulse response functions (IRFs) as calculated upon estimated VAR models. Topics such as Cholesky decomposition (CHD), orthogonalised and generalised IRFs are discussed. Properties of VAR models are compared against alternative econometric modelling tools, such as simultaneous equation models and dynamic stochastic general equilibrium (DSGE) models. The article is supplemented with an illustrative example: on an aggregated EMU-wide level, we estimate a VAR (2) model for real GDP, CPI and PPI inflation. IRFs are calculated using two different CHD orderings and compared to generalised IRFs. We find the IRFs from our illustrative model to be very robust against the chosen IRF calculation method and against equation ordering changes.

An interesting approach to economic and financial time series forecasting consists of decomposing an input time series additively into several components, each component capturing the dynamics of a different frequency range. Consequently, each component is modelled and forecasted separately, the predictions being summed up to form an overall forecast of the input time series. The present paper considers one very important aspect of the forecasting procedure. More specifically, it provides a better understanding of how an additive decomposition of the input time series into several components can be obtained using the wavelet transform and how boundary conditions in the individual components should be properly treated. Even though these aspects are presented as a part of the wavelet theory in several books on wavelets, their implementation is prone to misinterpretations in the literature on applied time series forecasting, possibly due to the complexity of the wavelet transform. Since our exposition is focused predominantly on these aspects, it provides a concise explanation which may be helpful to practitioners. The maximal overlap discrete wavelet transform is employed, other types of wavelet transforms also being briefly discussed.

Enormous development of firm valuation from many aspects can be seen in the recent period. One of the main fields is scoring, which provides a probability verdict about the future development of a firm: its probability of default. This article focuses on introducing macroeconomic modelling using VEC models to predict the future level of default in the Czech economy. Our results have proven a general connection between corporate defaults and the macroeconomic condition of the economy, which is going through a convergence process. The specific findings are new and have not been observed yet. A connection between the GDP and defaults revealed a positive relationship, which is probably a consequence of the convergence process, a development of the economy in many new fields. We have also found a long-term equilibrium among unemployment, loans, price of oil and defaults. We have revealed a higher level of defaults can be expected in 2013, which is connected with the economic contraction in the prediction period.

By modifying and generalizing the wavelet-based approach of approximately simulating univariate long-memory processes that is available in the literature, we propose a methodology for simulating a bivariate stationary process, whose components exhibit different relationships at different scales. We derive the formulas for the autocovariance and cross-covariance sequences of the simulated bivariate process. We provide a setting for the parameters of the simulation which might generate a bivariate time series resembling that of stock log returns. Using this setting, we study the properties of our methodology via Monte Carlo simulation.

The article deal with the problems of weather derivatives which take the value in sequence nowadays. The aim of this work is the definition of weather derivatives and the way how to price them. We show as well that linear and nonlinear models of time series of temperatures measured in Prague and in Brno have not good results in the estimation of parameters μI and σI of the probability distribution function P(I) of the weather index which is essential in their pricing.

Based on cointegration analysis of daily data of the most liquid Czech stock from September 1, 1997 to February 28, 2007, a long run equilibrium relationship was revealed to exist between prices of stocks of Komerční banka (KB), České energetické závody (CEZ) and Unipetrol (UNPE). Prices time series of these stocks have a unit root and are cointegrated. There is a unique combination of these stocks which is mean reverting and can be used to achieve statistical arbitrage. However, in order to exploit this possibility, a number of challenges need to be dealt with. Investors should take into account the speed of the mean reversion rate, the size of the variation and the stability of the out of sample behaviour of this combination of these stocks.

The PSE noted incredible increase in both trading volumes and prices of traded stocks during last five years. The PX index (former PX-50) reached the level of 1600 points at the end of 2006, which is almost four times higher than in 2001. Cointegration analysis can show us if the growth has been driven by some hidden common factor(-s), either optimistic perception of the market or common fundamentals, or if the main forces have been in case of each stock individual and specific and the fact, that the increase was similar among many of stocks is only due to coincidence. We have found that the results differ substantially upon the choice of frequencies of the data. The interrelations are very small when using daily data, on the other hand weekly data lead to opposite result. Furthermore the analysis of daily data implies that the relations became closer in the long term and that they are almost negligible during the period of high growth (2005-2006), but again the weekly data showed the opposite. As far as results of the VECM and VAR estimates concern, they were surprisingly good: using weekly data we were able to explain up to 80% of variance in stock returns comparing to 20% with daily data. This difference can be explained partly as a consequence of high noise in daily data and excessive volatility on emerging markets.