Luigi Grossi

Statistical detection of multiscale landscape patterns

Detection of discontinuities in landscape patterns is a crucial problem both in ecology and in environmental sciences since they may indicate substantial scale changes in generating and maintaining processes of landscape patches. This paper presents a statistical procedure for detecting distinct scales of pattern for irregular patch mosaics using fractal analysis. The method suggested is based on a piecewise regression model given by fitting different regression lines to different ranges of patches ordered according to patch size (area). Proper shift-points, where discontinuities occur, are then identified by means of an iterative procedure. Further statistical tests are applied in order to verify the statistical significance of the best models selected. Compared to the method proposed by Krummel et al. (1987), the procedure described here is not influenced by subjective choices of initial parameters. The procedure was applied to landscape pattern analysis of irregular patch mosaics (CORINE biotopes) of a watershed within the Map of the Italian Nature Project. Results for three different CORINE patch types are herein presented revealing different scaling properties with special pattern organizations linked to ecological traits of vegetation communities and human disturbance.

A robust forward weighted Lagrange multiplier test for conditional heteroscedasticity

Statistical tests routinely adopted for detecting nonlinear components in time series rely on the auxiliary regression of ARMA lagged residuals, and the Lagrange multiplier test to detect ARCH components is an example. The size distortion of such test suggests adopting a weighted test, where the weights are computed through a forward search algorithm. Simulations show that the forward weighted robust test is preferable to the classical Lagrange test and to existing robust tests, which are based on backward weighted regression or on estimated autocorrelation function. The forward weighted robust test is applied to daily financial and quarterly macroeconomic time series, showing its usefulness in detecting ARCH effects, even when outliers are present.

Revenues from Storage in a Competitive Electricity Market: Empirical Evidence from Great Britain

Despite the high upfront financial costs associated with the existing technologies for energy storage they have become more appealing in recent years in response to the increasing importance of non-dispatchable sources of generation in the energy systems of developed countries. One of the essential pieces of information required to value the monetary benefits which can be achieved when investing in energy storage is the price that energy will command when it is released, compared with the price paid when injected into the storage. In this paper we investigate this relationship using time series statistical techniques for various maturities of forward prices, using data on assessments of power prices for future delivery. We will examine the relationship for predictability and size of gap in order to answer questions about the likely financial benefits which can be obtained from optimal time management of storage facilities, using a technology neutral approach. Our initial results indicate that such arbitrage opportunities exist for storage facilities, especially when energy is stored over a short-term period of a day or a week.

Testing Gibrat's law in Italian macro-regions: Analysis on a panel of mechanical companies

The present paper deals with the question whether “Gibrats law” is applicable to Italian mechanical companies active between 1997 and 1999 or not. The analysis was carried out at a spatial level splitting companies in four macro-regions: North-West, North-East, Centre and South. On the basis of a set of descriptive and inferential tools, we find that firm size, measured by total assets, follows approximately a log-normal distribution in at least two of the four analyzed macro-regions. Nevertheless log-normality is only one necessary but not sufficient condition for the validity of the Gibrats law. Thus we analyzed the influence of firm size on growth rate finding a negative relation between the two variables in all macro-regions. This is a clear violation of Gibrats law. Another violation was found by the application of an econometric model which evidences the persistence of growth.

Analyzing Financial Time Series through Robust Estimators

In this paper we suggest an extension of the forward search methodology to GARCH models which are often used for forecasting stock market volatility. It is frequently found that estimated residuals from GARCH models have excess kurtosis, even when one allows for conditional t-distributed errors. Some papers have appeared on outlier detection in GARCH models but the proposed methods are iterative and may suffer from masking effects. The forward search is a method for determining the effect of outliers on fitted parameters and for detecting also masked outliers. In the case of GARCH models outliers are strictly related to extreme observations which are responsible for the well-known volatility clustering of financial returns. It is possible, through the forward search, to visualize the effect on estimated parameters of patches of extremal observations.

Robust Time Series Analysis through the Forward Search

The forward search (FS) is a powerful general method for detecting masked multiple outliers and for determining their effect on models fitted to the data (Atkinson and Riani, 2000). This method was originally introduced for models which assumed independent observations: linear and non linear regression, generalized linear models and multivariate analysis. In this paper we extend the forward search technique to the analysis of time series data. The basic ingredients of the FS are a robust start from an outlier-free subset of observations, a criterion for progressing in the search, which allows the subset to increase by one or more observations at each step, and a set of diagnostic tools that are monitored along the search. The robustness of the FS stems from the very definition of its algorithm, starting from “good” data points and including outliers at the end of the procedure. Computation of high-breakdown estimators is not required, except possibly at the starting stage. Indeed, the application of efficient likelihood or moment based methods at subsequent steps of the FS provides the analyst with more powerful tools than those obtained via traditional high-breakdown estimation.

Robust Estimation of Regime Switching Models

It is well known that generalized-M (GM) estimators for linear models are consistent and lead to a small loss of efficiency with respect to least squares (LS) estimator. When they are extended to threshold models the consistency of GM estimators is guaranteed only under certain objective functions. In this paper we explore, in a simulation experiment, the loss of consistency of GM-SETAR estimator under different objective functions, time-series length, parameter combinations and type of contaminations. Finally the best robust estimator is applied to study the dynamic of electricity prices where regime switching and high spikes are widely observed features.

Robust Self Exciting Threshold AutoRegressive models for electricity prices

In this paper we suggest the use of robust GM-SETAR (Self Exciting Threshold AutoRegressive) processes to model and forecast electricity prices observed on deregulated markets. The robustness of the model is achieved by extending to time series the generalized M-type (GM) estimator first introduced for independent multivariate data. As it has been shown in a very recent paper [1], the polynomial weighting function over-performs the classical ordinary least squares method when extreme observations are present. The main advantage of estimating robust SETAR models is the possibility to capture two very well-known stylized facts of electricity prices: nonlinearity produced by changes of regimes and the presence of sudden spikes due to inelasticity of demand. The forecasting performance of the model applied to the Italian electricity market (IPEX) is improved by the introduction of predicted demand as an exogenous regressor. The availability of this regressor is a particular feature of the Italian market. By means of prediction performance indexes and tests, it will be shown that this regressor plays a crucial role and that robust methods improve the overall forecasting performance of the model.

Robust estimation of efficient mean---variance frontiers

Standard methods for optimal allocation of shares in a financial portfolio are determined by second-order conditions which are very sensitive to outliers. The well-known Markowitz approach, which is based on the input of a mean vector and a covariance matrix, seems to provide questionable results in financial management, since small changes of inputs might lead to irrelevant portfolio allocations. However, existing robust estimators often suffer from masking of multiple influential observations, so we propose a new robust estimator which suitably weights data using a forward search approach. A Monte Carlo simulation study and an application to real data show some advantages of the proposed approach.

Volatility structures of the Italian electricity market: An analysis of leverage and volume effects

In this paper the volatility structure of electricity prices in the Italian zonal market is analyzed. Volatility should be a primary concern for investors and operators on energy markets because it is related to investment uncertainty and power plant management. Even if volatility of electricity prices received extensive attention in the past, the relationship with traded and demanded electricity volumes has not been explored. We try to fill this gap estimating the volatility-volume link within the framework of ARMA-GARCH models, using daily data on a five year period. Opposite to what usually argued about electricity prices, we found evidence of direct leverage effect in the Italian market. Furthermore our estimates highlight an inverse relation between price volatility and lagged volumes.