A note on forecasting demand using the multivariate exponential smoothing framework

Simple exponential smoothing is widely used in forecasting economic time series. This is because it is quick to compute and it generally delivers accurate forecasts. On the other hand, its multivariate version has received little attention due to the complications arising with the estimation. Indeed, standard multivariate maximum likelihood methods are affected by numerical convergence issues and bad complexity, growing with the dimensionality of the model. In this paper, we introduce a new estimation strategy for multivariate exponential smoothing, based on aggregating its observations into scalar models and estimating them. The original high-dimensional maximum likelihood problem is broken down into several univariate ones, which are easier to solve. Contrary to the multivariate maximum likelihood approach, the suggested algorithm does not suffer heavily from the dimensionality of the model. The method can be used for time series forecasting. In addition, simulation results show that our approach performs at least as well as a maximum likelihood estimator on the underlying VMA(1) representation, at least in our test problems

Aggregation of exponential smoothing processes with an application to portfolio risk evaluation

In this paper we propose a unified framework to analyse contemporaneous and temporal aggregation of exponential smoothing (EWMA) models. Focusing on a vector IMA(1,1) model, we obtain a closed form representation for the parameters of the contemporaneously and temporally aggregated process as a function of the parameters of the original one. In the framework of EWMA estimates of volatility, we present an application dealing with Value-at-Risk (VaR) prediction at different sampling frequencies for an equally weighted portfolio composed of multiple indices. We apply the aggregation results by inferring the decay factor in the portfolio volatility equation from the estimated vector IMA(1,1) model of squared returns. Empirical results show that VaR predictions delivered using this suggested approach are at least as accurate as those obtained by applying the standard univariate RiskMetrics TM methodology.contemporaneous and temporal aggregation, EWMA, volatility, Value-at-Risk

What do we know about comparing aggregate and disaggregate forecasts?

This paper compares the performance of "aggregate" and "disaggregate" predictors in forecasting contemporaneously aggregated vector ARMA processes. An aggregate predictor is built by forecasting directly the aggregate process, as it results from contemporaneous aggregation of the data generating vector process. A disaggregate predictor is obtained by aggregating univariate forecasts for the individual components of the data generating vector process. The necessary and sufficient condition for the equality of mean squared errors associated with the two competing methods is provided in the bivariate VMA(1) case. Furthermore, it is argued that the condition of equality of predictors as stated in Lütkepohl (1984b, 1987, 2004) is only sufficient (not necessary) for the equality of mean squared errors. Finally, it is shown that the equality of forecasting accuracy for the two predictors can be achieved using specific assumptions on the parameters of the VMA(1) structure. Monte Carlo simulations are in line with the analytical results. An empirical application that involves the problem of forecasting the Italian monetary aggregate M1 in the pre-EMU period is presented to illustrate the main findings.contemporaneous aggregation, forecasting

Determinants and dynamics of schooling and child labor in Bolivia

This paper investigates the determinants of primary school enrollment, attendance and child labor in Bolivia from 1999 to 2007. The analysis also aims at identifying the substitution and complementary relationships between schooling and working. Although enrollment rates show a significant improvement, lack of attendance remains an issue. The empirical results reveal that the increase in enrollment is led by indigenous children and those living in urban areas. Moreover, contrary to common belief, being extremely poor and indigenous are the main determinants of school attendance. Although extremely poor children increased their school attendance, they were not able to reduce child labor. However, for indigenous children school attendance and child labor were substitutes, increasing schooling and reducing child labor.Street Children,Primary Education,Education For All,Youth and Governance,Children and Youth

A closed-form estimator for the multivariate GARCH(1,1) model

We provide a closed-form estimator based on the VARMA representation for the unrestricted multivariate GARCH(1,1). We show that all parameters can be derived using basic linear algebra tools. We show that the estimator is consistent and asymptotically normal distributed. Our results allow also to derive a closed form for the parameters in the context of temporal aggregation of multivariate GARCH(1,1) by solving the equations as in Hafner [2008]

MULTIVARIATE TREND–CYCLE EXTRACTION WITH THE HODRICK–PRESCOTT FILTER

The Hodrick–Prescott filter represents one of the most popular methods for trend–cycle extraction in macroeconomic time series. In this paper we provide a multivariate generalization of the Hodrick–Prescott filter, based on the seemingly unrelated time series approach. We first derive closed-form expressions linking the signal–noise matrix ratio to the parameters of the VARMA representation of the model. We then show that the parameters can be estimated using a recently introduced method, called “Moment Estimation Through Aggregation (META).” This method replaces traditional multivariate likelihood estimation with a procedure that requires estimating univariate processes only. This makes the estimation simpler, faster, and better behaved numerically. We prove that our estimation method is consistent and asymptotically normal distributed for the proposed framework. Finally, we present an empirical application focusing on the industrial production of several European countries

Feasible generalized least squares estimation of multivariate GARCH(1, 1) models

We provide a feasible generalized least squares estimator for (unrestricted) multivariate GARCH(1, 1) models. We show that the estimator is consistent and asymptotically normally distributed under mild assumptions. Unlike the (quasi) maximum likelihood method, the feasible GLS is considerably fast to implement and does not require any complex optimization routine. We present numerical experiments on simulated data showing the performance of the GLS estimator, and discuss the limitations of our approach. © 2014 Elsevier Inc

Trayectoria a largo plazo de algunas especies de Elasmobranquios en los mares de Toscana (Mediterráneo noroccidental) a través de 50 años de datos de captura

The time series of elasmobranch catch rates off the Tuscany coasts (NW Mediterranean) were investigated by means of min/max auto-correlation factor analysis in order to estimate variations in population abundance and evaluate the influence of environmental and anthropogenic factors. The analyses highlighted a general decreasing trend in the catch rates of sharks and skates from 1961 to the mid-1990s, mainly influenced by the increase in fishing effort. Since the 1990s, the EU Common Fishery Policy for the Mediterranean has promoted the reduction of fishing fleets through incentives to vessel demolition. The Porto S. Stefano trawl fleet has decreased by about 50%, leading to a decrease in fishing effort which seemed to be the most relevant factor affecting the increasing trend shown by the catch rates of Galeus melastomus, Scyliorhinus canicula and skates from 1991 to 2009. The elasmobranch assemblage did not undergo major shifts but the weighted frequency of occurrence shows that elasmobranchs were more frequent in the past. Particular caution should be paid in interpreting the recent rebound of some species as an early sign of recovery: trawl survey data and landing data show that over the last 50 years elasmobranch fauna have undergone a drastic decline and that recent rebounds are still far from a recovery to historical levels.Se investigaron las series históricas de datos de captura de algunas especies de Elasmobranquios en los mares de Toscana (Mediterráneo noroccidental), por medio del análisis de auto-correlación factorial MAFA, con el fin de evaluar las variaciones en la abundancia de poblaciones y la influencia de factores ambientales y antropogénicos. Los análisis permitieron poner en relieve una tendencia a la disminución, a partir de 1961 hasta la mitad de los años 1990, de las tasas de captura de las especies de tiburones y rayas demersales. Esta disminución parece ser debida principalmente al aumento del esfuerzo pesquero. Sin embargo, desde 1990 capacidad y actividad pesquera mostraron una tendencia a la disminución, como resultado de la Política Pesquera Común de la UE para el Mediterráneo. La flota de arrastre de Porto Santo Stefano disminuyó en un 50%; esta reducción parece ser el factor más importante que produjo un aumento en los indices de abundancia relativa de Galeus melastomus, Scyliorhinus canicula y de las rayas, desde 1991 a 2009. Sin embargo la composición en especies de los Elasmobranquios no ha mostrado evidentes cambios en el tiempo, a pesar de muchas especies que han sufrido una disminución en la frecuencia de occurrencia. Por lo tanto, la interpretación de estos resultados como señal de recuperación de las poblaciones de elasmobranquios, necesita de una precaución especial. De hecho durante los últimos 50 años la fauna de elasmobranquios en el Mediterráneo ha sufrido una drástica reducción y todavía no se está observando ninguna considerable señal de recuperación

“Once upon a Time in the Mediterranean”. Long Term Trends of Mediterranean Fisheries Resources Based on Fishers’ Traditional Ecological Knowledge

We investigate long-term changes in the Mediterranean marine resources driving the trawl fisheries by analysing fishers’ perceptions (Traditional Ecological Knowledge, TEK) throughout the Mediterranean Sea for the last 80 years. To this end, we conducted an extended set of interviews with old experienced fishers that enabled us to classify species (or taxa) as 'decreasing' or 'increasing' both in terms of abundance, as well as average size in the catch. The aspect that most clearly emerged in all the investigated areas over time was the notable increase of fishing capacity indicators, such as engine power and fishing depth range. Atlantic mackerel, poor cod, scorpionfishes, striped seabream, and John Dory demonstrated a decreasing trend in the fishers' perceived abundance, while Mediterranean parrotfish, common pandora, cuttlefish, blue and red shrimp, and mullets gave indications of an increasing temporal trend. Although, as a rule, trawler captains did not report any cataclysmic changes (e.g. extinctions), when they were invited to estimate total overall catches, a clear decreasing pattern emerged; this being a notable finding taking into account the steep escalation of fishing efficiency during the past century. The overall deteriorating status of stocks in most Mediterranean regions calls for responsible management and design of rebuilding plans. This should include historical information accounting for past exploitation patterns that could help defining a baseline of fish abundance prior to heavy industrial fisheries exploitation.JRC.G.3-Maritime affair