Nigel Meade

Heuristics for cardinality constrained portfolio optimisation

In this paper we consider the problem of finding the efficient frontier associated with the standard mean-variance portfolio optimisation model. We extend the standard model to include cardinality constraints that limit a portfolio to have a specified number of assets, and to impose limits on the proportion of the portfolio held in a given asset (if any of the asset is held). We illustrate the differences that arise in the shape of this efficient frontier when such constraints are present. We present three heuristic algorithms based upon genetic algorithms, tabu search and simulated annealing for finding the cardinality constrained efficient frontier. Computational results are presented for five data sets involving up to 225 assets.

An evolutionary heuristic for the index tracking problem

Abstract Index tracking is a popular form of passive fund management. The index tracking problem is the problem of reproducing the performance of a stock market index, but without purchasing all of the stocks that make up the index. Our formulation of the problem explicitly includes transaction costs (associated with buying or selling stocks) and a limit on the total transaction cost that can be incurred. Our formulation also includes a constraint limiting the number of stocks that can be purchased. An evolutionary heuristic (population heuristic) is presented for the solution of the index tracking problem. Reduction tests are also presented. Computational results are presented for five data sets drawn from major world markets. These data sets are made publicly available for use by other workers.

Renewable energy investments under different support schemes: A real options approach

This paper adopts a real options approach to analyze investment timing and capacity choice for renewable energy projects under different support schemes. The main purpose is to examine investment behavior under the most extensively employed support schemes, namely, feed-in tariffs and renewable energy certificate trading. We consider both multiple sources of uncertainty under each support scheme and uncertainty with respect to any change of support scheme, and we obtain both analytical (when possible) and numerical solutions. In a Nordic case study based on wind power, we find that the feed-in tariff encourages earlier investment. Nevertheless, as investment has been undertaken, renewable energy certificate trading creates incentives for larger projects. In our baseline scenario and taking the fixed feed-in tariff as a base, the revenue required to trigger investments is 61% higher with renewable certificates. At the same time, investment capacity is 61% higher.

The diffusion of successive generations of a technology: A more general model

Abstract In many cases of technological development, successive generations of a technology evolve, each more efficient than its predecessor. It has been assumed when modeling and forecasting the adoption of these technologies that the market reaction to each generation was similar. Using the terminology of the Bass model, this similarity is encapsulated in the assumption that the coefficients of innovation and imitation are constant. New data for two and three generations of mobile telephone technology from eleven countries are modeled. The modeling framework used—simultaneous estimation for successive generations using a full information maximum likelihood procedure—demonstrates that, in most cases, the hypothesis of constant coefficients can be rejected. Use of a model with changing coefficients is shown to considerably improve forecasting performance. These results were reinforced by analysis of data for four generations of IBM mainframes.

Forecasting with growth curves: An empirical comparison

Abstract The primary objective of this paper is to compare the forecasting performance of the increasingly wide range of growth curve models. Seventeen models are used to forecast the development of telecommunications markets, represented by 25 time series describing telephone penetration in 15 different countries. Forecasting performance is measured by root mean square error and mean absolute percentage error over the last 10 or 11 years of the series, the model parameters having been fitted over the previous 20 years. Note is taken of the convergence of the estimation process, the significance of parameters and the plausibility of the estimated saturation level. The local logistic, simple logistic and the Gompertz models are shown to significantly outperform more complex models such as the extended logistic and FLOG models.

Generalising about univariate forecasting methods: further empirical evidence

Abstract This paper extends the empirical evidence on the forecasting accuracy of extrapolative methods. The robustness of the major conclusions of the M-Competition data is examined in the context of the telecommunications data of Fildes (1992) . The performance of Robust Trend, found to be a successful method for forecasting the telecommunications data by Fildes, is compared with that of other successful methods using the M-Competition data. Although it is established that the structure of the telecommunications data is more homogeneous than that of the M-Competition data, the major conclusions of the M-Competition continue to hold for this new data set. In addition, while the Robust Trend method is confirmed to be the best performing method for the telecommunications data, for the 1001 M-Competition series, this method is outperformed by methods such as Single or Damped Smoothing. The performance of smoothing methods depended on how the smoothing parameters are estimated. Optimisation at each time origin was more accurate than optimisation at the first time origin, which in turn is shown to be superior to arbitrary (literature based) fixed values. In contrast to the last point, a data based choice of fixed smoothing constants from a cross-sectional study of the time series was found to perform well.

A comparison of the accuracy of short term foreign exchange forecasting methods

Abstract The hypothesis that foreign exchange rate behaviour is non-linear has been examined by several authors; others have proposed a linear framework. Here, evidence for a non-linear generating process is evaluated by an analysis of the comparative accuracy of short term forecasts of FX rates. Forecasts were generated by a linear AR-GARCH model and four non-linear methods, including three nearest neighbour methods and locally weighted regression. Five data frequencies were used: daily, four-hourly, two-hourly, hourly and half-hourly. Using root mean square error as a measure, significantly greater accuracy than a no-change forecast was achieved for two-hourly and higher frequency data sets. Using a test by Peseran and Timmerman, significant predictive directional accuracy was found for four-hourly and higher frequency data sets. These results were supported by simulated trading based on forecast direction. No evidence was found that the FX rate behaviour is better represented by a non-linear generating process than by a linear model.

Forecasting the Diffusion of Innovations: Implications for Time-Series Extrapolation

The selection of an S-shaped trend model is a common step in attempts to model and forecast the diffusion of innovations. From the innovation-diffusion literature on model selection, forecasting, and the uncertainties associated with forecasts, we derive four principles.

Modelling multinational telecommunications demand with limited data

Abstract Forecasting the diffusion of innovations in the telecommunications sector is a constantly recurring problem for national providers. The problem is characterised by short data series making the estimation of model parameters unreliable. However, the same innovation will be diffusing simultaneously in other national markets, although with a different start date. The use of this cross-sectional data in constructing innovation diffusion models is investigated here. Four models for pooling the cross-sectional data are described and two diffusion models are discussed although only one, the Gompertz model is used throughout. Three innovation data sets are used in the evaluation of the models: digital cellular telephones, ISDN connections and fax connections. The pooled diffusion forecasts proved to be more accurate in several comparisons relative to a naive benchmark and to individual forecasts when available.

Evidence for the selection of forecasting methods

Reid (1972) was among the first to argue that the relative accuracy of forecasting methods changes according to the properties of the time series. Comparative analyses of forecasting performance such as the M-Competition tend to support this argument. The issue addressed here is the usefulness of statistics summarizing the data available in a time series in predicting the relative accuracy of different forecasting methods. Nine forecasting methods are described and the literature suggesting summary statistics for choice of forecasting method is summarized. Based on this literature and further argument a set of these statistics is proposed for the analysis. These statistics are used as explanatory variables in predicting the relative performance of the nine methods using a set of simulated time series with known properties. These results are evaluated on observed data sets, the M-Competition data and Fildes Telecommunications data. The general conclusion is that the summary statistics can be used to select a good forecasting method (or set of methods) but not necessarily the best. Copyright