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.

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Wave scattering by an axisymmetric ice floe of varying thickness

The problem of water wave scattering by a circular ice floe, floating in fluid of finite depth, is formulated and solved numerically. Unlike previous investigations of such situations, here we allow the thickness of the floe (and the fluid depth) to vary axisymmetrically and also incorporate a realistic non-zero draught. A numerical approximation to the solution of this problem is obtained to an arbitrary degree of accuracy by combining a Rayleigh–Ritz approximation of the vertical motion with an appropriate variational principle. This numerical solution procedure builds upon the work of Bennets et al. (2007, J. Fluid Mech., 579, 413–443). As part of the numerical formulation, we utilize a Fourier cosine expansion of the azimuthal motion, resulting in a system of ordinary differential equations to solve in the radial coordinate for each azimuthal mode. The displayed results concentrate on the response of the floe rather than the scattered wave field and show that the effects of introducing the new features of varying floe thickness and a realistic draught are significant.

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.

Accessing extremes of mid-latitudinal wave activity: methodology and application

A statistical methodology is proposed and tested for the analysis of extreme values of atmospheric wave activity at mid-latitudes. The adopted methods are the classical block-maximum and peak over threshold, respectively based on the generalized extreme value (GEV) distribution and the generalized Pareto distribution (GPD). Time-series of the ‘Wave Activity Index’ (WAI) and the ‘Baroclinic Activity Index’ (BAI) are computed from simulations of the General Circulation Model ECHAM4.6, which is run under perpetual January conditions. Both the GEV and the GPD analyses indicate that the extremes ofWAI and BAI areWeibull distributed, this corresponds to distributions with an upper bound. However, a remarkably large variability is found in the tails of such distributions; distinct simulations carried out under the same experimental setup provide sensibly different estimates of the 200-yr WAI return level. The consequences of this phenomenon in applications of the methodology to climate change studies are discussed. The atmospheric configurations characteristic of the maxima and minima of WAI and BAI are also examined.