Evaluating interval forecasts of high-frequency financial data

A number of methods of evaluating the validity of interval forecasts of financial data are analysed, and illustrated using intraday FTSE100 index futures returns. Some existing interval forecast evaluation techniques, such as the Markov chain approach of Christoffersen (1998), are shown to be inappropriate in the presence of periodic heteroscedasticity. Instead, we consider a regression-based test, and a modified version of Christoffersen's Markov chain test for independence, and analyse their properties when the financial time series exhibit periodic volatility. These approaches lead to different conclusions when interval forecasts of FTSE100 index futures returns generated by various GARCH(1,1) and periodic GARCH(1,1) models are evaluated.

Forecasting time series combining Holt-Winters and bootstrap approaches

Publicado em "AIP Conference Proceedings", Vol. 1648

Quantitative market and sales forecast accuracy analysis

The main objective of this master’s thesis was to quantitatively study the reliability of market and sales forecasts of a certain company by measuring bias, precision and accuracy of these forecasts by comparing forecasts against actual values. Secondly, the differences of bias, precision and accuracy between markets were explained by various macroeconomic variables and market characteristics. Accuracy and precision of the forecasts seems to vary significantly depending on the market that is being forecasted, the variable that is being forecasted, the estimation period, the length of the estimated period, the forecast horizon and the granularity of the data. High inflation, low income level and high year-on-year market volatility seems to be related with higher annual market forecast uncertainty and high year-on-year sales volatility with higher sales forecast uncertainty. When quarterly market size is forecasted, correlation between macroeconomic variables and forecast errors reduces. Uncertainty of the sales forecasts cannot be explained with macroeconomic variables. Longer forecasts are more uncertain, shorter estimated period leads to higher uncertainty, and usually more recent market forecasts are less uncertain. Sales forecasts seem to be more uncertain than market forecasts, because they incorporate both market size and market share risks. When lead time is more than one year, forecast risk seems to grow as a function of root forecast horizon. When lead time is less than year, sequential error terms are typically correlated, and therefore forecast errors are trending or mean-reverting. The bias of forecasts seems to change in cycles, and therefore the future forecasts cannot be systematically adjusted with it. The MASE cannot be used to measure whether the forecast can anticipate year-on-year volatility. Instead, we constructed a new relative accuracy measure to cope with this particular situation.

Valor en riesgo del portafolio de TES de los bancos colombianos

En este trabajo se realiza la medición del riesgo de mercado para el portafolio de TES de un banco colombiano determinado, abordando el pronóstico de valor en riesgo (VaR) mediante diferentes modelos multivariados de volatilidad: EWMA, GARCH ortogonal, GARCH robusto, así como distintos modelos de VaR con distribución normal y distribución t-student, evaluando su eficiencia con las metodologías de backtesting propuestas por Candelon et al. (2011) con base en el método generalizado de momentos, junto con los test de independencia y de cobertura condicional planteados por Christoffersen y Pelletier (2004) y por Berkowitz, Christoffersen y Pelletier (2010). Los resultados obtenidos demuestran que la mejor especificación del VaR para la medición del riesgo de mercado del portafolio de TES de los bancos colombianos, es el construido a partir de volatilidades EWMA y basado en la distribución normal, ya que satisface las hipótesis de cobertura no condicional, independencia y cobertura condicional, al igual que los requerimientos estipulados en Basilea II y en la normativa vigente en Colombia.

Forecast calibration and combination: a simple Bayesian approach for ENSO

This study presents a new simple approach for combining empirical with raw (i.e., not bias corrected) coupled model ensemble forecasts in order to make more skillful interval forecasts of ENSO. A Bayesian normal model has been used to combine empirical and raw coupled model December SST Niño-3.4 index forecasts started at the end of the preceding July (5-month lead time). The empirical forecasts were obtained by linear regression between December and the preceding July Niño-3.4 index values over the period 1950–2001. Coupled model ensemble forecasts for the period 1987–99 were provided by ECMWF, as part of the Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction (DEMETER) project. Empirical and raw coupled model ensemble forecasts alone have similar mean absolute error forecast skill score, compared to climatological forecasts, of around 50% over the period 1987–99. The combined forecast gives an increased skill score of 74% and provides a well-calibrated and reliable estimate of forecast uncertainty.

Bootstrap prediction intervals for autoregressive time series

The calculation of interval forecasts for highly persistent autoregressive (AR) time series based on the bootstrap is considered. Three methods are considered for countering the small-sample bias of least-squares estimation for processes which have roots close to the unit circle: a bootstrap bias-corrected OLS estimator; the use of the Roy–Fuller estimator in place of OLS; and the use of the Andrews–Chen estimator in place of OLS. All three methods of bias correction yield superior results to the bootstrap in the absence of bias correction. Of the three correction methods, the bootstrap prediction intervals based on the Roy–Fuller estimator are generally superior to the other two. The small-sample performance of bootstrap prediction intervals based on the Roy–Fuller estimator are investigated when the order of the AR model is unknown, and has to be determined using an information criterion.

Using irregularly spaced returns to estimate multi-factor models: application to Brazilian equity data

Multi-factor models constitute a useful tool to explain cross-sectional covariance in equities returns. We propose in this paper the use of irregularly spaced returns in the multi-factor model estimation and provide an empirical example with the 389 most liquid equities in the Brazilian Market. The market index shows itself significant to explain equity returns while the US$/Brazilian Real exchange rate and the Brazilian standard interest rate does not. This example shows the usefulness of the estimation method in further using the model to fill in missing values and to provide interval forecasts.

Traffic forecasts under uncertainty and capacity constraints

Traffic forecasts provide essential input for the appraisal of transport investment projects. However, according to recent empirical evidence, long-term predictions are subject to high levels of uncertainty. This paper quantifies uncertainty in traffic forecasts for the tolled motorway network in Spain. Uncertainty is quantified in the form of a confidence interval for the traffic forecast that includes both model uncertainty and input uncertainty. We apply a stochastic simulation process based on bootstrapping techniques. Furthermore, the paper proposes a new methodology to account for capacity constraints in long-term traffic forecasts. Specifically, we suggest a dynamic model in which the speed of adjustment is related to the ratio between the actual traffic flow and the maximum capacity of the motorway. This methodology is applied to a specific public policy that consists of suppressing the toll on a certain motorway section before the concession expires.

AFFINE INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS AND WANDERING INTERVALS

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips which have wandering intervals and are such that the support of the invariant measure is a Cantor set.

Determination of post-mortem interval using in situ tissue optical fluorescence

In this study we have used fluorescence spectroscopy to determine the post-mortem interval. Conventional methods in forensic medicine involve tissue or body fluids sampling and laboratory tests, which are often time demanding and may depend on expensive analysis. The presented method consists in using time-dependent variations on the fluorescence spectrum and its correlation with the time elapsed after regular metabolic activity cessation. This new approach addresses unmet needs for post-mortem interval determination in forensic medicine, by providing rapid and in situ measurements that shows improved time resolution relative to existing methods. (C) 2009 Optical Society of America

The Scientific Basis for High-Intensity Interval Training: Optimising Training Programmes and Maximising Performance in Highly Trained Endurance Athletes

While the physiological adaptations that occur following endurance training in previously sedentary and recreationally active individuals are relatively well understood, the adaptations to training in already highly trained endurance athletes remain unclear. While significant improvements in endurance performance and corresponding physiological markers are evident following submaximal endurance training in sedentary and recreationally active groups, an additional increase in submaximal training (i.e. volume) in highly trained individuals does not appear to further enhance either endurance performance or associated physiological variables [e.g. peak oxygen uptake (V-dot O2peak), oxidative enzyme activity]. It seems that, for athletes who are already trained, improvements in endurance performance can be achieved only through high-intensity interval training (HIT). The limited research which has examined changes in muscle enzyme activity in highly trained athletes, following HIT, has revealed no change in oxidative or glycolytic enzyme activity, despite significant improvements in endurance performance (p < 0.05). Instead, an increase in skeletal muscle buffering capacity may be one mechanism responsible for an improvement in endurance performance. Changes in plasma volume, stroke volume, as well as muscle cation pumps, myoglobin, capillary density and fibre type characteristics have yet to be investigated in response to HIT with the highly trained athlete. Information relating to HIT programme optimisation in endurance athletes is also very sparse. Preliminary work using the velocity at which V-dot O2max is achieved (Vmax) as the interval intensity, and fractions (50 to 75%) of the time to exhaustion at Vmax (Tmax) as the interval duration has been successful in eliciting improvements in performance in long-distance runners. However, Vmax and Tmax have not been used with cyclists. Instead, HIT programme optimisation research in cyclists has revealed that repeated supramaximal sprinting may be equally effective as more traditional HIT programmes for eliciting improvements in endurance performance. Further examination of the biochemical and physiological adaptations which accompany different HIT programmes, as well as investigation into the optimal HIT programme for eliciting performance enhancements in highly trained athletes is required.

Interval breast cancers in an Australian mammographic screening program

Objective: To determine the incidence of interval cancers which occurred in the first 12 months after mammographic screening at a mammographic screening service. Design: Retrospective analysis of data obtained by crossmatching the screening Service and the New South Wales Central Cancer Registry databases. Setting: The Central & Eastern Sydney Service of BreastScreen NSW. Participants: Women aged 40-69 years at first screen, who attended for their first or second screen between 1 March 1988 and 31 December 1992. Main outcome measures: Interval-cancer rates per 10 000 screens and as a proportion of the underlying incidence of breast cancer (as estimated by the underlying rate in the total NSW population). Results: The 12-month interval-cancer incidence per 10 000 screens was 4.17 for the 40-49 years age group (95% confidence interval [CI], 1.35-9.73) and 4.64 for the 50-69 years age group (95% CI, 2.47-7.94). Proportional incidence rates were 30.1% for the 40-49 years age group (95% CI, 9.8-70.3) and 22% for the 50-69 years age group (95% CI, 11.7-37.7). There was no significant difference between the proportional incidence rate for the 50-69 years age group for the Central & Eastern Sydney Service and those of major successful overseas screening trials. Conclusion: Screening quality was acceptable and should result in a significant mortality reduction in the screened population. Given the small number of cancers involved, comparison of interval-cancer statistics of mammographic screening programs with trials requires age-specific or age-adjusted data, and consideration of confidence intervals of both program and trial data.

Long range forecasts of the numbers of Helicoverpa punctigera and H-armigera (Lepidoptera : Noctuidae) in Australia using the Southern Oscillation Index and the Sea Surface Temperature

The use of long-term forecasts of pest pressure is central to better pest management. We relate the Southern Oscillation Index (SOI) and the Sea Surface Temperature (SST) to long-term light-trap catches of the two key moth pests of Australian agriculture, Helicoverpa punctigera (Wallengren) and H. armigera (Hubner), at Narrabri, New South Wales over 11 years, and for H. punctigera only at Turretfield, South Australia over 22 years. At Narrabri, the size of the first spring generation of both species was significantly correlated with the SOI in certain months, sometimes up to 15 months before the date of trapping. Differences in the SOI and SST between significant months were used to build composite variables in multiple regressions which gave fitted values of the trap catches to less than 25% of the observed values. The regressions suggested that useful forecasts of both species could be made 6-15 months ahead. The influence of the two weather variables on trap catches of H. punctigera at Turretfield were not as strong as at Narrabri, probably because the SOI was not as strongly related to rainfall in southern Australia as it is in eastern Australia. The best fits were again given by multiple regressions with SOI plus SST variables, to within 40% of the observed values. The reliability of both variables as predictors of moth numbers may be limited by the lack of stability in the SOI-rainfall correlation over the historical record. As no other data set is available to test the regressions, they can only be tested by future use. The use of long-term forecasts in pest management is discussed, and preliminary analyses of other long sets of insect numbers suggest that the Southern Oscillation Index may be a useful predictor of insect numbers in other parts of the world.

Impact of increasing the re-supply interval on the seasonality of subsidised prescription use in Australia

Objective: To evaluate the impact of increasing the minimum resupply period for prescriptions on the Pharmaceutical Benefits Scheme (PBS) in November 1994. The intervention was designed to reduce the stockpiling of medicines used for chronic medical conditions under the PBS safety net. Methods: Interrupted times series regression analyses were performed on 114 months of PBS drug utilisation data from January 1991 to June 2000. These analyses assessed whether there had been a significant interaction between the onset of the intervention in November 1994 and the extreme levels of drug utilisation in the months of December (peak utilisation) and January (lowest utilisation) respectively. Both serial and 12-month lag autocorrelations were controlled for. Results: The onset of the intervention was associated with a significant reduction in the December peak in drug utilisation; after the introduction of the policy there were 1,150,196 fewer proscriptions on average or that month (95% Cl 708,333-1,592,059). There was, however, no significant change in the low level of utilisation in January. The effect of the policy appears to be decreasing across successive postintervention years. though the odds of a prescription being dispensed in December remained significantly lower in 1999 compared to each of the pre-intervention years (11% vs. 14%) Conclusion: Analysis of the impact of increasing the re-supply period for PBS prescriptions showed that the magnitude of peak utilisation in December had been markedly reduced by the policy, though this effect appears to be decreasing over time. Continued monitoring and policy review is warranted in order to ensure that the initial effect of the intervention be maintained.