Forecasting for the generation of trading signals in financial markets

In this paper we show that optimal trading results can be achieved if we can forecast a key summary statistic of future prices. Consider the following optimization problem. Let the return r_i (over time i=1, 2, ..., n) for the ith day be given and the investor has to make investment decision d_i on the ith day with d_i=1 representing a ‘long' position and d_i=0 a ‘neutral' position. The investment return is given by r=Σⁿ_i=1r_id_i−cΣⁿ⁺¹_i=1∣d_i−d_i−1∣, where c is the transaction cost. The mathematical programming problem of choosing d₁, ..., d_n to maximize r under a given transaction cost c is shown to have an analytic solution, which is a function of a key summary statistic called the largest change before reversal. The largest change before reversal is recommended to be used as an output in a neural network for the generation of trading signals. When neural network forecasting is applied to a dataset of Hang Seng Index Futures Contract traded in Hong Kong, it is shown that forecasting the largest change before reversal outperforms the k‐step‐ahead forecast in achieving higher trading profits. Copyright © 2000 John Wiley & Sons, Ltd.     

A dynamic linear model approach for disaggregating time series data

An approach is proposed for obtaining estimates of the basic (disaggregated) series, x_i, when only an aggregate series, y_t, of k period non-overlapping sums of x_i's is available. The approach is based on casting the problem in a dynamic linear model form. Then estimates of x_i can be obtained by application of the Kalman filtering techniques. An ad hoc procedure is introduced for deriving a model form for the unobserved basic series from the observed model of the aggregates. An application of this approach to a set of real data is given.     

Analysis of many short time sequences: Forecast improvements achieved by shrinkage

Credibility models in actuarial science deal with multiple short time series where each series represents claim amounts of different insurance groups. Commonly used credibility models imply shrinkage of group-specific estimates towards their average. In this paper we model the claim size yu in group i and at time t as the sum of three independent components: y_it = μ_r + δ_i + ?_it. The first component, μt = μ_t?1 + m_t, represents time-varying levels that are common to all groups. The second component, δ_i, represents random group offsets that are the same in all periods, and the third component represents independent measurement errors. In this paper we show how to obtain forecasts from this model and we discuss the nature of the forecasts, with particular emphasis on shrinkage. We also assess the forecast improvements that can be expected from such a model. Finally, we discuss an extension of the above model which also allows the group offsets to change over time. We assume that the offsets for different groups follow independent random walks.     

Sensitivity of univariate AR(1) time‐series forecasts near the unit root

We consider the linear time‐series model y_t=d_t+u_t(t=1,...,n), where d_t is the deterministic trend and u_t the stochastic term which follows an AR(1) process; u_t=θu_t−1+ϵ_t, with normal innovations ϵ_t. Various assumptions about the start‐up will be made. Our main interest lies in the behaviour of the l‐period‐ahead forecast y_n+1 near θ=1. Unlike in other studies of the AR(1) unit root process, we do not wish to ask the question whether θ=1 but are concerned with the behaviour of the forecast estimate near and at θ=1. For this purpose we define the sth (s=1,2) order sensitivity measure λ_l^(s) of the forecast y_n+1 near θ=1. This measures the sensitivity of the forecast at the unit root. In this study we consider two deterministic trends: d_t=β_t and d_t=β_t+β_tt. The forecast will be the Best Linear Unbiased forecast. We show that, when d_t=β_t, the number of observations has no effect on forecast sensitivity. When the deterministic trend is linear, the sensitivity is zero. We also develop a large‐sample procedure to measure the forecast sensitivity when we are uncertain whether to include the linear trend. Our analysis suggests that, depending on the initial conditions, it is better to include a linear trend for reduced sensitivity of the medium‐term forecast. Copyright © 2001 John Wiley & Sons, Ltd.     

Semiparametric forecast intervals

Consider forecasting the economic variable Y_t+h with predictors X _t, where h is the forecast horizon. This paper introduces a semiparametric method that generates forecast intervals of Y_t+h| X _t from point forecast models. First, the point forecast model is estimated, thereby taking advantage of its predictive power. Then, nonparametric estimation of the conditional distribution function (CDF) of the forecast error conditional on X _t builds the rest of the forecast distribution around the point forecast, from which symmetric and minimum‐length forecast intervals for Y_t+h| X _t can be constructed. Under mild regularity conditions, asymptotic analysis shows that (1) regardless of the quality of the point forecast model (i.e., it may be misspecified), forecast quantiles are consistent and asymptotically normal; (2) minimum length forecast intervals are consistent. Proposals for bandwidth selection and dimension reduction are made. Three sets of simulations show that for reasonable point forecast models the method has significant advantages over two existing approaches to interval forecasting: one that requires the point forecast model to be correctly specified, and one that is based on fully nonparametric CDF estimate of Y_t+h| X _t. An application to exchange rate forecasting is presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Polarographic determination of the reaction rate of the second step in an SN1 displacement

Zusammenfassung Die Zeitabhängigkeit des polarographischen Stromes, welche man bei der gemäss SN1 verlaufenden Hydrolyse vonp-Methoxy-2-phenylpropylchlorid beobachtet, ermöglicht die Bestimmung der Geschwindigkeitskonstantenk ₁ der Gesamtreaktion sowie auch der Geschwindigkeitskonstantenk ₂ des zweiten raschen Schrittes, welcher nach pseudo-erster Ordnung verläuft. Fürk ₂ ergibt sich in Aceton, das 5% Wasser enthält, bei 25°Ck ₂=2,0×10³ sec^–1.

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We would like to thank the N.R.C. for provision of a grant to purchase the Electrochemical System and the University of New Brunswick for a Fellowship for one of us (D.B.).     

Effects of pCai and pHi on cell-to-cell coupling

Summary Internal longitudinal resistance (r_i), a determinant of cardiac conduction, is affected by changes in intracellular calcium and protons. However, the role and mechanism by which H⁺ and Ca²⁺ may modulate r_i is uncertain. Cable analysis was performed in cardiac Purkinje fibers to measure r_i during various interventions. In some experiments, intracellular pH (pH_i) was recorded simultaneously to study the pH_i-r_i relation. Both intracellular Ca²⁺ and H⁺ independently modified r_i. However, internal resistance of cardiac fibers was insensitive to pH_i changes compared to other tissues. A latent period preceded the pH_i-related changes in r_i and the amount of change depended upon methodology. The results suggest that direct action of protons on r_i may be subordinate to other regulatory processes. Ionic regulation of internal longitudinal resistance may occur by more than one mechanism: i) direct cationic binding to sites on junctional membrane proteins; and ii) H⁺- or Ca²⁺-dependent phosphorylation of junctional proteins.     

Transformations and dynamic linear models

The dynamic linear model (DLM) with additive Gaussian errors provides a useful statistical tool that is easily implemented because of the simplicity of updating a normal model that has a natural conjugate prior. If the model is not linear or if it does not have additive Gaussian errors, then numerical methods are usually required to update the distributions of the unknown parameters. If the dimension of the parameter space is small, numerical methods are feasible. However, as the number of unknown parameters increases, the numerial methods rapidly grow in complexity and cost. This article addresses the situation where a state dependent transformation of the observations follows the DLM, but a priori the appropriate transformation is not known. The Box-Cox family, which is indexed by a single parameter, illustrates the methodology. A prior distribution is constructed over a grid of points for the transformation parameter. For each value of the grid the relevant parameter esitmates and forecasts are obtained for the transformed series. These quantities are then integrated by the current distribution of the transformation parameter. When a new observation becomes available, parallel Kalman filters are used to update the distributions of the unknown parameters and to compute the likelihood of the transformation parameter at each grid point. The distribution of the transformation parameter is then updated.     

Nouvelles données sur la cytogénétique et la spéciation des Leggada (Mammalia-Rodentia-Muridae)

Summary To the 237 pigmy-mice studies in his previous papers, the author brings new data concerning the cytogenetics of 25 Leggada. One first set of 12 mice from Nigeria belongs to the same polymorphic series containing themusculoides from the Ivory Coast and the Central African Republic.A small sample from Ippy (Central African Republic), although the individuals are morphologically all alike and referable tomusculoides, shows an amazing diversity: /259.2N=28, N.F.=36, sex chromosomes of the translocated type (TR). We meet here a new robertsonian combination in the polymorphic series, 34/33/32/31 ... 28/... 22/... 19/18./260.2N=32, N.F.=36, sex chromosomesTR. Both big biarmed autosomes are metacentric — submetacentric with a centromeric index of about 0.25 by the typicalmusculoides having the same diploid number./261.2N=19, N.F.=36, sex chromosomesX/Y ₁ Y ₂. The first occurrence of such sex chromosomes by the Leggada. By themusculoides from Rhodesia we were dealing with the typeX ₁ X ₂ /Y. /262.2N=18, N.F.=36, sex chromosomesX/X. Very likely the female of /261.In the complexminutoides-musculoides, we meet many different caryotypes and it is obvious that the chromosomal mutations play here the part of a primary factor of isolation, previous to the gene mutations which later will allow the taxonomic determination of the species actually in statu nascendi.     

Cell-to-cell coupling studied in isolated ventricular cell pairs

Summary Cell pairs isolated from adult rat and guinea pig ventricles were used to study the electrical properties of the nexal membrane. Each cell of a pair was connected to a voltage-clamp system so as to enable whole-cell, tight-seal recording. The current-voltage relationship of the nexal membrane was found to be linear, revealing a resistance r_n of 2–4 M. r_n was insensitive to the sarcolemmal membrane potential (range:–90 to +30 mV), and exerted no time-dependent gating behavior (range: 0.1 to 10 s). Lowering pH_i yielded a small increase in r_n. Vigorous elevations in [Ca²⁺]_i gave rise to an increase in r_n which was associated with a cell shortening. Uncoupling caused by aliphatic alcohols or halothane did not produce cell shortening. Cell pairs were also used to study action potential transfer.     

Misspecified prediction for time series

Let {X_t} be a stationary process with spectral density g(λ).It is often that the true structure g(λ) is not completely specified. This paper discusses the problem of misspecified prediction when a conjectured spectral density f_θ(λ), θ∈Θ, is fitted to g(λ). Then, constructing the best linear predictor based on f_θ(λ), we can evaluate the prediction error M(θ). Since θ is unknown we estimate it by a quasi‐MLE . The second‐order asymptotic approximation of is given. This result is extended to the case when X_t contains some trend, i.e. a time series regression model. These results are very general. Furthermore we evaluate the second‐order asymptotic approximation of for a time series regression model having a long‐memory residual process with the true spectral density g(λ). Since the general formulae of the approximated prediction error are complicated, we provide some numerical examples. Then we illuminate unexpected effects from the misspecification of spectra. Copyright © 2001 John Wiley & Sons, Ltd.     

Synthesis Ca3Y2Ge3O12

Zusammenfassung Ca₃Y₂Ge₃O₁₂ wurde in chemisch homogener Form auf hydrothermalem Weg hergestellt. Es besitzt eine Garnet-Struktur mit dem Gitterparametera ₀=12,804 Å.     

Intraluminal pressure and equivalent arterial wall tension

Résumé P=T/r, une loi de Laplace, est d'habitude appliquée pour exprimer la relation entre la pression intraluminale (P) et la tension intramurale (T) d'un vaisseau de rayonr. Sur un segment tubulaire, et sur une bande hélicale de l'aorte du lapin, nous avons mesuré deux valeurs équivalentes,P _50% etT _50%, obtenues lorsque la contraction causée par la noradrénaline est réduite de moitié. Ainsi la valeur der, calculée en utilisant l'equationP=T/r, est environ 75% de la valeur mesurée.     

A new parsimonious recurrent forecasting model in singular spectrum analysis

Singular spectrum analysis (SSA) is a powerful nonparametric method in the area of time series analysis that has shown its capability in different applications areas. SSA depends on two main choices: the window length L and the number of eigentriples used for grouping r. One of the most important issues when analyzing time series is the forecast of new observations. When using SSA for time series forecasting there are several alternative algorithms, the most widely used being the recurrent forecasting model, which assumes that a given observation can be written as a linear combination of the L?1 previous observations. However, when the window length L is large, the forecasting model is unlikely to be parsimonious. In this paper we propose a new parsimonious recurrent forecasting model that uses an optimal m(<L?1) coefficients in the linear combination of the recurrent SSA. Our results support the idea of using this new parsimonious recurrent forecasting model instead of the standard recurrent SSA forecasting model.     

Application of the linear partial information model to forecasting the Swiss timber market

Most often, statistical analyses only provide partial information about the appropriateness of different models, structures and parameters which may underlie the dynamic process that has generated a time series. Linear partial information (LPI), in particular, consists of linear restrictions such as LPI: p_a> p_b, p_a> p_c where p_a denotes the probability that structure a holds. Fuzzy information of this type can be put to use for decision-making by LPI analysis. In this paper, LPI analysis is applied to answer the question of whether subsidizing price, given an abnormal disturbance on the timber market, would contribute to continuous forest management, a stated goal of Swiss environmental policy.     

Sopra un caso particolare della superficie F 4 (3) di M. Noether

Summary The Noetherian surfaceF ₄ ⁽³⁾ , which is represented on a plane by a linear ³ system ofC ₉(A ₁ ³ A ₂ ³ A ₃ ³ A ₄ ³ A ₅ ³ A ₆ ³ A ₇ ³ A ₈ ³ A ₉ ² A ₁₀), possesses generally only one linear pencil of elliptic cubics. IfA _i (i=1, 2, , 9) are the basis points of aHalphen pencil ofC ₉,A ₁₀ is infinitely near toA ₉, and in this caseF ₄ ⁽³⁾ is a not trivial example of such a surface with two pencils of elliptic cubics.     

Exact test for opposite trends of probability changes in one or several 3×2 tables

Zusammenfassung Der «Likelihood»-Quotiententest wird auf einer 3×2-Kontigenztafel mit unbekannten Wahrscheinlichkeitenp _ij (i=1,2,3;j=1,2) angewandt, um die Hypothese H₀:p _i1=p _i2 (i=1,2,3) gegen die alternative Hypothese H₁:p ₁₁>p ₁₂ p ₃₁<p ₃₂ zuprüfen, und zwar wenn kleine Stichproben vorhanden sind. Ausserdem wird die Kombination solcher Tests behandelt. Als Beispiel wird diese Testtheorie beim Wahlverhalten des Kabeljaus im Dressurversuch über akustische Lokalisation in zwei Stimulussituationen verwendet.

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The close cooperation with Drs.E. Meelis, Institute of Theoretical Biology Leyden, The Netherlands, in applying the likelihood ratio test to this case is gratefully acknowledged.

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The author is greatly indebted to Dr.J. Oosterhoff, Mathematical Institute, University of Nijmegen, The Netherlands, for introducing the subclasses 1b and 1c in the computation of vector and for the explicit expressions in these cases which eliminated the need for a numerical optimization. Further more valuable remarks regarding the combination problem were obtained.     

Forecasting temporally aggregated vector ARMA processes

If interest centres on forecasting a temporally aggregated multiple time series and the generation process of the disaggregate series is a known vector ARMA (autoregressive moving average) process then forecasting the disaggregate series and temporally aggregating the forecasts is at least as efficient, under a mean squared error measure, as forecasting the aggregated series directly. Necessary and sufficient conditions for equality of the two forecasts are given. In practice the data generation process is usually unknown and has to be determined from the available data. Using asymptotic theory it is shown that also in this case aggregated forecasts from the disaggregate process will usually be superior to forecasts obtained from the aggregated process.     

On the usefulness of macroeconomic forecasts as inputs to forecasting models

A forecasting model for y_t based on its relationship to exogenous variables (e.g. x?_t) must use x?_t, the forecast of x?_t. An example is given where commercially available x?_t's are sufficiently inaccurate that a univariate model for y_t appears preferable. For a variety of types of models inclusion of an exogenous variable x?_t is shown to worsen the y_t forecasts whenever x?_t must itself be forecast by x?_t and MSE (x?_t) > Var (x?_t). Tests with forecasts from a variety of sources indicate that, with a few notable exceptions, MSE (x?_t) > Var (x?_t) is common for macroeconomic forecasts more than a quarter or two ahead. Thus, either:

• (a) available medium range forecasts for many macroeconomic variables (e.g. the GNP growth rate) are not an improvement over the sample mean (so that such variables are not useful explanatory variables in forecasting models), and/or
• (b) the suboptimization involved in directly replacing x?_t by x?_t is a luxury that we cannot afford.