Mixtures of Distributions and Volatility

Using Monte Carlo methods we generate time series with the following features： a） series with distributions that are the mix of two normal distributions with different variances, b） series that satisfy volatility models, c） series that satisfy an AR（1） model but with contaminated errors that follow the same distribution as the mixes given in a） and d） series that follow the same distribution as the mixes given in a） but with conditional heterocedasticity. From the analysis we see that it is difficult to identify in practical situations the real generating process of the series. In fact, the processes that come from distribution mixes have many similar characteristics to the ones that satisfy the volatility scheme. We use the corresponding theoretical considerations and also the usual tools in the identifying process of any time series; that is, series graphs, histograms, the corresponding sampling distributions, correlograms and partial correlograms.

The Conditional Heterocedasticity on the Argentine Inflation. An Analysis for the Period from 1943 to 2013

Numerous economic time series do not have a constant mean and in practical situations, we often see that the variance of observational error is subject to a substantial variability over time. This phenomenon is known as volatility. To take into account the presence of volatility in an economic series, it is necessary to resort to models known as conditional heteroscedastic models. In these models, the variance of a series at a given time point depends on past information and other data available up to that time point, so that a conditional variance must be defined, which is not constant and does not coincides with the overall variance of the observed series. There is a very large variety of nonlinear models in the literature, which are useful for the analysis of any economic time series with volatility, but we will focus in analyzing our series of interest using ARCH type models introduced by Engle （1982） and their extensions. These models are non-linear in terms of variance. Our objective will be the study of the monthly inflation data of Argentina for the period from January 1943 to December 2013. The data is officially published by the National Institute of Statistics and Censuses （or INDEC as it is known in Argentina）. Although it is a very long period in which various changes and interventions took place, it can be seen that certain general patterns of behavior have persisted over time, which allows us to admit that the study can be appropriately based on available information.

The Multivariate Saddlepoint Approximation to the Distribution of Estimators： A General Approach

We develop the theory of multivariate saddlepoint approximations. Our treatment differs from the one in Barndorff-Nielsen and Cox （1979, equation （4.7）） in two aspects： 1） our results are satisfied for random vectors that are not necessarily sums of independent and identically distributed random vectors, and 2） we consider that the sample is taken from any distribution, not necessarily a member of the exponential family of densities. We also show the relationship with the corresponding multivariate Edgeworth approximations whose general treatment was developed by Durbin in 1980, emphasizing that the basic assumptions that support the validity of both approaches are essentially similar.