Recent Estimates of Time-Variation in the Conditional Variance and in the Exchange Risk Premium

The optimal-diversification model of investors' portfolio behavior can give a linear relationship between the exchange risk premium and the conditional exchange rate variance. This note surveys recent empirical work that allows for the conditional variance itself, and therefore the risk premium, to vary over time. In particular, it examines the implications of recent empirical estimates for earlier arguments, based on the assumption that the conditional variance was constant over time, that the exchange risk premium had to be small in magnitude and variability.

Forecasting electricity spot market prices with a k-factor GIGARCH process

In this article, we investigate conditional mean and variance forecasts using a dynamic model following a k-factor GIGARCH process. We are particularly interested in calculating the conditional variance of the prediction error. We apply this method to electricity prices and test spot prices forecasts until one month ahead forecast. We conclude that the k-factor GIGARCH process is a suitable tool to forecast spot prices, using the classical RMSE criteria.Conditional mean ; conditional variance ; forecast ; electricity prices ; GIGARCH process

Conditional variance forecasts for long-term stock returns

In this paper, we apply machine learning to forecast the conditional variance of long-term stock returns measured in excess of different benchmarks, considering the short- and long-term interest rate, the earnings-by-price ratio, and the inflation rate. In particular, we apply in a two-step procedure a fully nonparametric local-linear smoother and choose the set of covariates as well as the smoothing parameters via cross-validation. We find that volatility forecastability is much less important at longer horizons regardless of the chosen model and that the homoscedastic historical average of the squared return prediction errors gives an adequate approximation of the unobserved realised conditional variance for both the one-year and five-year horizon

Forecasting electricity spot market prices with a k-factor GIGARCH process

In this article, we investigate conditional mean and variance forecasts using a dynamic model following a k-factor GIGARCH process. We are particularly interested in calculating the conditional variance of the prediction error. We apply this method to electricity prices and test spot prices forecasts until one month ahead forecast. We conclude that the k-factor GIGARCH process is a suitable tool to forecast spot prices, using the classical RMSE criteria.Conditional mean - conditional variance - forecast - electricity prices - GIGARCH process

Decomposition of variance in terms of conditional means

We test against two different sets of data an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative characters. We suggest that this approach be used to complement other existing techniques to study the interdependence of the variables involved. According to our method the variance is expressed as a sum of orthogonal components, obtained as differences of conditional means, with respect to the qualitative characters. The resulting expression for the variance depends on the ordering in which the characters are considered. We suggest an algorithm which leads to an ordering which is deemed natural. The first set of data concerns the score achieved by a population of students, on an entrance examination, based on a multiple choice test with 30 questions. In this case the qualitative characters are dyadic and correspond to correct or incorrect answer to each question. The second set of data concerns the delay in obtaining the degree for a population of graduates of Italian universities. The variance in this case is analyzed with respect to a set of seven specific qualitative characters of the population studied (gender, previous education, working condition, parent's educational level, field of study, etc.)Comment: 3 figure

Modelling the Density of Inflation Using Autoregressive Conditional Heteroscedasticity, Skewness, and Kurtosis Models

The paper aimed at modelling the density of inflation based on time-varying conditional variance, skewness and kurtosis model developed by Leon, Rubio, and Serna (2005) who model higher-order moments as GARCH-type processes by applying a Gram-Charlier series expansion of the normal density function. Additionally, it extended their work by allowing both conditional skewness and kurtosis to have an asymmetry term. The results revealed the significant persistence in conditional variance, skewness and kurtosis which indicate high asymmetry of inflation. Additionally, diagnostic tests reveal that models with nonconstant volatility, skewness and kurtosis are superior to models that keep them invariant.inflation targeting, conditional volatility, skewness and kurtosis, modelling uncertainty of inflation

Modeling Conditional Skewness in Stock Returns

In this paper we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling moderate skewness and kurtosis typically encountered in stock return series. The need to allow for skewness can also be readily tested. Our empirical results indicate the presence of conditional skewness in the postwar U.S. stock returns. Small positive news is also found to have a smaller impact on conditional variance than no news at all. Moreover, the symmetric GARCH-M model not allowing for conditional skewness is found to systematically overpredict conditional variance and average excess returns.Conditional skewness, GARCH-in-Mean, Risk-return tradeoff

There is a Risk-Return Tradeoff After All

This paper studies the ICAPM intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns - the Mixed Data Sampling (or MIDAS) approach. Using MIDAS, we find that there is a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process, and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the ICAPM based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance. Dans ce papier, nous estimons le modèle ICAPM intertemporal avec une nouvelle classe d'estimateurs, intitulée MIDAS. Cette procédure d'estimation combine des données échantillonnées à différentes fréquences. Utilisant le nouvel estimateur, nous constatons une relation positive et significative entre le rendement et la volatilité.ICAPM, GARCH, volatility risk, ICAPM, GARCH, risque de volatilité