This paper considers a seasonal adjustment procedure that is capable of preparing data to the use in applied general equilibrium models. It is shown that standard seasonal adjustment procedures do not satisfy the property of invariance to deflating, that hinders their use in applied general equilibrium models. A system of axioms that describes the desired properties of a seasonal adjustment procedure is suggested. The impossibility of simultaneous fulfillment of additivity and invariance to deflation properties is shown. Therefore, one needs to choose the desired property depending on the type of the task that is solved. The proposed procedure models the seasonality as a set of seasonal multiplicative dummy variables, so it can not only remove the seasonality, but also return it to the data in order to obtain forecasts. The procedure also has a built-in outlier detector, which enables it to handle noise and outliers in data of different types. It is compared to the popular X12 seasonal adjustment procedure using Monte-Carlo method. It is shown that the preciseness of the proposed procedure is comparable to X12 in terms of resistance to outliers and preservation of statistical properties of the series in the specific set of problems connected to the estimation of general equilibrium models. Several examples of its application to real data are shown. The obtained results allow us to make a conclusion about applicability of the suggested procedure to the removal of seasonality from the data that is used in the estimation of macroeconomic models.
The paper offers a new method of decomposition of GDP and its elements. It is based on the idea that every сomponent can be represented as a combination of a smaller number of aggregates. The proposed method has a range of important theoretical properties that insure its correctness and reproduces the statistics with very high quality. The theoretical reasoning of the procedure is presented, 3-product decomposition is analysed. Decomposition of indicators in both current and fixed prices is presented. The proposed decomposition has a range of advantages compared to earlier procedures. First, it does not link any model products to aggregates, observed in statistics. Second, it decomposes the statistics into a higher number of unobserved products, and these products and their prices can be reasonably interpreted. Finally, the important distinction from earlier procedures in non-linearity in real prices. Apart from that, the paper proposes a method of harmonization of GDP and its elements statistics that is needed to work with these indicators after two recent methodology changes.
Models for time series are very important for the stock market. Fuzzy Takagi – Sugeno models (functional fuzzy systems) are a promising and already common approach, in which different regression dependencies are used for different areas of variation of certain parameters, and soft switching is performed using the fuzzy logic rules. This is the advantage of this approach over conventional stochastic models. Each Takagi-Sugeno model is based on its set of fuzzy rules. These models can be viewed as a generalization of classical econometric models, if one such model corresponds to one fuzzy rule. This paper studies the possibility of using the wavelet transform and fuzzy Takagi – Sugeno model to analyze the dynamics of stock prices for the following Russian companies: Gazprom, Sberbank, Magnit, Yandex and Aeroflot; this approach was previously used to study some foreign stock markets. Wavelet analysis quite often acts as a tool for signal processing, including time series, as it allows for a multi-level approximation. In this paper, the Takagi – Sugeno model is based on untransformed data as well as data transformed using Haar wavelets. Fuzzy clustering is used to construct membership functions. Calculations show that the use of wavelets often improves the predictive characteristics of the model.
This paper examines two Markov chain Monte Carlo methods that have been widely used in econometrics. An introductory exposition of the Metropolis algorithm and the Gibbs sampler is provided. These methods are used to simulate multivariate distributions. Many problems in Bayesian statistics can be solved by simulating the posterior distribution. Invariance condition is of importance, the proofs are given for both methods. We use finite Markov chains to explore and substantiate the methods. Several examples are provided to illustrate the applicability and efficiency of the Markov chain Monte Carlo methods. They include bivariate normal distribution with high correlation, bivariate exponential distribution, mixture of bivariate normals.
There is no accurate answer for the question, which method of modeling of uncertainty is preferable: random or fuzzy. Today both of these approaches are highly popular. Fuzzy and probabilistic approaches are commonly used for modeling of uncertainty. Fuzzy numbers can be used for modeling vagueness of parameters, such as risk-free rate or volatility in option pricing. Under these assumptions, option value depends on believe degree and turns to fuzzy number. In this paper the Black – Scholes formula and it’s modification for American option arbitrage-free value are used. Fuzzy representations of underlying asset price, volatility of asset price and risk-free rate are used as parameters. There is set of papers regarding fuzzy approach for European option pricing. In this paper fuzzy approach is used for arbitrage-free American option pricing for the first time. The fuzzy American call value is compared with fuzzy European option value.