Initial distribution spread: A density forecasting approach

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model error limits the value of such efforts. This paper argues for choosing the initial ensemble in order to optimise forecasting performance rather than estimate the true state of the system. Density forecasting and choosing the initial ensemble are treated as one problem. Forecasting performance can be quantified by some scoring rule. In the case of the logarithmic scoring rule, theoretical arguments and empirical results are presented. It turns out that, if the underlying noise dominates model error, we can diagnose the noise spread.

The role of the log transformation in forecasting economic variables

For forecasting and economic analysis many variables are used in logarithms (logs). In time series analysis, this transformation is often considered to stabilize the variance of a series. We investigate under which conditions taking logs is beneficial for forecasting. Forecasts based on the original series are compared to forecasts based on logs. For a range of economic variables, substantial forecasting improvements from taking logs are found if the log transformation actually stabilizes the variance of the underlying series. Using logs can be damaging for the forecast precision if a stable variance is not achieved.

Forecasting annual inflation with seasonal monthly data: using levels versus logs of the underlying price index

This paper investigates whether using natural logarithms (logs) of price indices for forecasting inflation rates is preferable to employing the original series. Univariate forecasts for annual inflation rates for a number of European countries and the USA based on monthly seasonal consumer price indices are considered. Stochastic seasonality and deterministic seasonality models are used. In many cases, the forecasts based on the original variables result in substantially smaller root mean squared errors than models based on logs. In turn, if forecasts based on logs are superior, the gains are typically small. This outcome sheds doubt on the common practice in the academic literature to forecast inflation rates based on differences of logs.

Data uncertainty in real estate forecasting

The rapid expansion of the TMT sector in the late 1990s and more recent growing regulatory and corporate focus on business continuity and security have raised the profile of data centres. Data centres offer a unique blend of occupational, physical and technological characteristics compared to conventional real estate assets. Limited trading and heterogeneity of data centres also causes higher levels of appraisal uncertainty. In practice, the application of conventional discounted cash flow approaches requires information about a wide range of inputs that is difficult to derive from limited market signals or estimate analytically. This paper outlines an approach that uses pricing signals from similar traded cash flows is proposed. Based upon ‘the law of one price’, the method draws upon the premise that two identical future cash flows must have the same value now. Given the difficulties of estimating exit values, an alternative is that the expected cash flows of data centre are analysed over the life cycle of the building, with corporate bond yields used to provide a proxy for the appropriate discount rates for lease income. Since liabilities are quite diverse, a number of proxies are suggested as discount and capitalisation rates including indexed-linked, fixed interest and zero-coupon bonds. Although there are rarely assets that have identical cash flows and some approximation is necessary, the level of appraiser subjectivity is dramatically reduced.

Volatility persistence and time-varying betas in the UK real estate market

This paper investigates the degree of return volatility persistence and the time-varying behaviour of systematic risk (beta) for 31 market segments in the UK real estate market. The findings suggest that different property types exhibit differences in volatility persistence and time variability. There is also evidence that the volatility persistence of each market segment and its systematic risk are significantly positively related. Thus, the systematic risks of different property types tend to move in different directions during periods of increased market volatility. Finally, the market segments with systematic risks less than one tend to show negative time variability, while market segments with systematic risk greater than one generally show positive time variability, indicating a positive relationship between the volatility of the market and the systematic risk of individual market segments. Consequently safer and riskier market segments are affected differently by increases in market volatility.

An improvement in clear-air turbulence forecasting based on spontaneous imbalance theory: the ULTURB algorithm

Recent research has shown that Lighthill–Ford spontaneous gravity wave generation theory, when applied to numerical model data, can help predict areas of clear-air turbulence. It is hypothesized that this is the case because spontaneously generated atmospheric gravity waves may initiate turbulence by locally modifying the stability and wind shear. As an improvement on the original research, this paper describes the creation of an ‘operational’ algorithm (ULTURB) with three modifications to the original method: (1) extending the altitude range for which the method is effective downward to the top of the boundary layer, (2) adding turbulent kinetic energy production from the environment to the locally produced turbulent kinetic energy production, and, (3) transforming turbulent kinetic energy dissipation to eddy dissipation rate, the turbulence metric becoming the worldwide ‘standard’. In a comparison of ULTURB with the original method and with the Graphical Turbulence Guidance second version (GTG2) automated procedure for forecasting mid- and upper-level aircraft turbulence ULTURB performed better for all turbulence intensities. Since ULTURB, unlike GTG2, is founded on a self-consistent dynamical theory, it may offer forecasters better insight into the causes of the clear-air turbulence and may ultimately enhance its predictability.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Regularized logistic models for probabilistic forecasting and diagnostics

Logistic models are studied as a tool to convert dynamical forecast information (deterministic and ensemble) into probability forecasts. A logistic model is obtained by setting the logarithmic odds ratio equal to a linear combination of the inputs. As with any statistical model, logistic models will suffer from overfitting if the number of inputs is comparable to the number of forecast instances. Computational approaches to avoid overfitting by regularization are discussed, and efficient techniques for model assessment and selection are presented. A logit version of the lasso (originally a linear regression technique), is discussed. In lasso models, less important inputs are identified and the corresponding coefficient is set to zero, providing an efficient and automatic model reduction procedure. For the same reason, lasso models are particularly appealing for diagnostic purposes.

The concept of exchangeability in ensemble forecasting

A set of random variables is exchangeable if its joint distribution function is invariant under permutation of the arguments. The concept of exchangeability is discussed, with a view towards potential application in evaluating ensemble forecasts. It is argued that the paradigm of ensembles being an independent draw from an underlying distribution function is probably too narrow; allowing ensemble members to be merely exchangeable might be a more versatile model. The question is discussed whether established methods of ensemble evaluation need alteration under this model, with reliability being given particular attention. It turns out that the standard methodology of rank histograms can still be applied. As a first application of the exchangeability concept, it is shown that the method of minimum spanning trees to evaluate the reliability of high dimensional ensembles is mathematically sound.

Probabilistic forecasting: why model imperfection is a poison pill

This volume is a serious attempt to open up the subject of European philosophy of science to real thought, and provide the structural basis for the interdisciplinary development of its specialist fields, but also to provoke reflection on the idea of ‘European philosophy of science’. This efforts should foster a contemporaneous reflection on what might be meant by philosophy of science in Europe and European philosophy of science, and how in fact awareness of it could assist philosophers interpret and motivate their research through a stronger collective identity. The overarching aim is to set the background for a collaborative project organising, systematising, and ultimately forging an identity for, European philosophy of science by creating research structures and developing research networks across Europe to promote its development.

Forecasting extinction risk of ectotherms under climate warming: an evolutionary perspective

1. It has been postulated that climate warming may pose the greatest threat species in the tropics, where ectotherms have evolved more thermal specialist physiologies. Although species could rapidly respond to environmental change through adaptation, little is known about the potential for thermal adaptation, especially in tropical species. 2. In the light of the limited empirical evidence available and predictions from mutation-selection theory, we might expect tropical ectotherms to have limited genetic variance to enable adaptation. However, as a consequence of thermodynamic constraints, we might expect this disadvantage to be at least partially offset by a fitness advantage, that is, the ‘hotter-is-better’ hypothesis. 3. Using an established quantitative genetics model and metabolic scaling relationships, we integrate the consequences of the opposing forces of thermal specialization and thermodynamic constraints on adaptive potential by evaluating extinction risk under climate warming. We conclude that the potential advantage of a higher maximal development rate can in theory more than offset the potential disadvantage of lower genetic variance associated with a thermal specialist strategy. 4. Quantitative estimates of extinction risk are fundamentally very sensitive to estimates of generation time and genetic variance. However, our qualitative conclusion that the relative risk of extinction is likely to be lower for tropical species than for temperate species is robust to assumptions regarding the effects of effective population size, mutation rate and birth rate per capita. 5. With a view to improving ecological forecasts, we use this modelling framework to review the sensitivity of our predictions to the model’s underpinning theoretical assumptions and the empirical basis of macroecological patterns that suggest thermal specialization and fitness increase towards the tropics. We conclude by suggesting priority areas for further empirical research.

Futures basis, inventory and commodity price volatility: an empirical analysis

We employ a large dataset of physical inventory data on 21 different commodities for the period 1993–2011 to empirically analyze the behavior of commodity prices and their volatility as predicted by the theory of storage. We examine two main issues. First, we analyze the relationship between inventory and the shape of the forward curve. Low (high) inventory is associated with forward curves in backwardation (contango), as the theory of storage predicts. Second, we show that price volatility is a decreasing function of inventory for the majority of commodities in our sample. This effect is more pronounced in backwardated markets. Our findings are robust with respect to alternative inventory measures and over the recent commodity price boom.

The potential inefficiency of using marketing margins in applied commodity price analysis, forecasting and risk management

This paper examines the implications of using marketing margins in applied commodity price analysis. The marketing-margin concept has a long and distinguished history, but it has caused considerable controversy. This is particularly the case in the context of analyzing the distribution of research gains in multi-stage production systems. We derive optimal tax schemes for raising revenues to finance research and promotion in a downstream market, derive the rules for efficient allocation of the funds, and compare the rules with an without the marketing-margin assumption. Applying the methodology to quarterly time series on the Australian beef-cattle sector and, with several caveats, we conclude that, during the period 1978:2 - 1988:4, the Australian Meat and Livestock Corporation optimally allocated research resources.