Time-series Properties and Forecasts of Crude Steel Consumption in the UK

This paper makes use of simple graphical techniques, a seasonal unit root test and a structural time-series model to obtain information on the time series properties of UK crude steel consumption. It shows that steel consumption has, after the removal of some quite substantial outliers, a fairly constant seasonal pattern, and a well-defined but stochastic business cycle. The long-run movement in steel consumption also appears to be stochastic in nature. These characteristics were used to identify a structural time-series model and the ex-post forecasts obtained from it performed reasonably well. Finally, this paper presents some ex-ante quarterly forecasts for crude steel consumption to the year 1999. © 1997 by John Wiley & Sons, Ltd.     

Robust exponential smoothing

The paper is devoted to robust modifications of exponential smoothing for time series with outliers or long-tailed distributions. Classical exponential smoothing applied to such time series is sensitive to the presence of outliers or long-tailed distributions and may give inadequate smoothing and forecasting results. First, simple and double exponential smoothing in the L₁ norm (i.e. based on the least absolute deviations) are discussed in detail. Then, general exponential smoothing is made robust, replacing the least squares approach by M-estimation in such a way that the recursive character of the final formulas is preserved. The paper gives simple algorithmic procedures which preserve advantageous features of classical exponential smoothing and, in addition, which are less sensitive to outliers. Robust versions are compared numerically with classical ones.     

Automatic monitoring of forecast errors

This paper evaluates a variety of automatic monitoring schemes to detect biased forecast errors. Backward cumulative sum (cusum) tracking signals have been recommended in previous research to monitor exponential smoothing models. This research shows that identical performance can be had with much simpler tracking signals. The smoothed-error signal is recommended for α = 0.1, although its performance deteriorates badly as α is increased. For higher α values, the simple cusum signal is recommended. A tracking signal based on the autocorrelation in errors is recommended for forecasting models other than exponential smoothing, with one exception. If the time series has a constant variance, the backward cusum should give better results.     

Quarterly liverpool model with current partial information: An exercise in forecasting

This paper applies an algorithm for the solution of partial current information in rational expectation models to the quarterly Liverpool macroeconomic model of the U.K. The algorithm is shown to produce marginally superior results in forecasts both in ex-post and ex-ante forecasts and can be viewed as an additional tool for the forecaster's kit-bag.     

Daily volatility forecasts: reassessing the performance of GARCH models

Volatility plays a key role in asset and portfolio management and derivatives pricing. As such, accurate measures and good forecasts of volatility are crucial for the implementation and evaluation of asset and derivative pricing models in addition to trading and hedging strategies. However, whilst GARCH models are able to capture the observed clustering effect in asset price volatility in‐sample, they appear to provide relatively poor out‐of‐sample forecasts. Recent research has suggested that this relative failure of GARCH models arises not from a failure of the model but a failure to specify correctly the ‘true volatility’ measure against which forecasting performance is measured. It is argued that the standard approach of using ex post daily squared returns as the measure of ‘true volatility’ includes a large noisy component. An alternative measure for ‘true volatility’ has therefore been suggested, based upon the cumulative squared returns from intra‐day data. This paper implements that technique and reports that, in a dataset of 17 daily exchange rate series, the GARCH model outperforms smoothing and moving average techniques which have been previously identified as providing superior volatility forecasts. Copyright © 2004 John Wiley & Sons, Ltd.     

Improving the Timeliness of Turning Signals for Business Cycles with Monthly Data

The conventional growth rate measures (such as month‐on‐month, year‐on‐year growth rates and 6‐month smoothed annualized rate adopted by the US Bureau of Labor Statistics and Economic Cycle Research Institute) are popular and can be easily obtained by computing the growth rate for monthly data based on a fixed comparison benchmark, although they do not make good use of the information underlying the economic series. By focusing on the monthly data, this paper proposes the k‐month kernel‐weighted annualized rate (k‐MKAR), which includes most existing growth rate measures as special cases. The proposed k‐MKAR measure involves the selection of smoothing parameters that are associated with the accuracy and timeliness for detecting the change in business turning points. That is, the comparison base is flexible and is likely to vary for different series under consideration. A data‐driven procedure depending upon the stepwise multiple reality check test for choosing the smoothing parameters is also suggested in this paper. The simple numerical evaluation and Monte Carlo experiment are conducted to confirm that our measures (in particular the two‐parameter k‐MKAR) improve the timeliness subject to a certain degree of accuracy. The business cycle signals issued by the Council for Economic Planning and Development over the period from 1998 to 2009 in Taiwan are taken as an example to illustrate the empirical application of our method. The empirical results show that the k‐MKAR‐based score lights are more capable of reflecting turning points earlier than the conventional year‐on‐year measure without sacrificing accuracy. Copyright © 2016 John Wiley & Sons, Ltd.     

A non‐Gaussian generalization of the Airline model for robust seasonal adjustment

In their seminal book Time Series Analysis: Forecasting and Control, Box and Jenkins (1976) introduce the Airline model, which is still routinely used for the modelling of economic seasonal time series. The Airline model is for a differenced time series (in levels and seasons) and constitutes a linear moving average of lagged Gaussian disturbances which depends on two coefficients and a fixed variance. In this paper a novel approach to seasonal adjustment is developed that is based on the Airline model and that accounts for outliers and breaks in time series. For this purpose we consider the canonical representation of the Airline model. It takes the model as a sum of trend, seasonal and irregular (unobserved) components which are uniquely identified as a result of the canonical decomposition. The resulting unobserved components time series model is extended by components that allow for outliers and breaks. When all components depend on Gaussian disturbances, the model can be cast in state space form and the Kalman filter can compute the exact log‐likelihood function. Related filtering and smoothing algorithms can be used to compute minimum mean squared error estimates of the unobserved components. However, the outlier and break components typically rely on heavy‐tailed densities such as the t or the mixture of normals. For this class of non‐Gaussian models, Monte Carlo simulation techniques will be used for estimation, signal extraction and seasonal adjustment. This robust approach to seasonal adjustment allows outliers to be accounted for, while keeping the underlying structures that are currently used to aid reporting of economic time series data. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating and Predicting the General Random Effects Model

This paper extends the ‘remarkable property’ of Breusch (Journal of Econometrics 1987; 36 : 383–389) and Baltagi and Li (Journal of Econometrics 1992; 53 : 45–51) to the three‐way random components framework. Indeed, like its one‐way and two‐way counterparts, the three‐way random effects model maximum likelihood estimation can be obtained as an iterated generalized least squares procedure through an appropriate algorithm of monotonic sequences of some variance components ratios, θ_i (i = 2, 3, 4). More specifically, a search over θ_iwhile iterating on the regression coefficients estimates β and the other θ_jwill guard against the possibility of multiple local maxima of the likelihood function. In addition, the derivations of related prediction functions are obtained based on complete as well as incomplete panels. Finally, an application to international trade issues modeling is presented. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Forecasting with balanced state space representations of multivariate distributed lag models

A procedure for estimating state space models for multivariate distributed lag processes is described. It involves singular value decomposition techniques and yields an internally balanced state space representation which has attractive properties. Following the specifications of a forecasting competition, the approach is applied to generate ex-post forecasts for US real GNP growth rates. The forecasts of the estimated state space model are compared to those of twelve econometric models and an ARIMA model.     

Esterase activity in the hepatopancreas ofMacrobrachium lamarrei (Crustacea: Decapoda)

Summary The activity of the hepatopancreatic esterase of the fresh water prawnMacrobrachium lamarrei was optimal at pH 7.4 and temperature 40°C. The activity increased with the increase in incubation period and enzyme concentration. The Michaelis constant (K_m) of the enzyme was 2.1×10^–3M.The investigations are a part of the thesis presented to University of Lucknow, India.Acknowledgments. The authors are grateful to the University Grants Commission, India for the award of a Junior Research Fellowship.     

The combining of forecasts using recursive techniques with non-stationary weights

This paper evaluates six optimal and four ad hoc recursive combination methods on five actual data sets. The performance of all methods is compared to the mean and recursive least squares. A modification to one method is proposed and evaluated. The recursive methods were found to be very effective from start-up on two of the data sets. Where the optimal methods worked well so did the ad hoc ones, suggesting that often combination methods allowing ‘local bias’ adjustment may be preferable to the mean forecast and comparable to the optimal methods.     

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.     

Sources of error in forecasts and expectations: U.K. economic models, 1984–8

This paper presents a comparative analysis of the sources of error in forecasts for the UK economy published over a recent four-year period by four independent groups. This analysis rests on the archiving at the ESRC Macroeconomic Modelling Bureau of the original forecasts together with all their accompanying assumptions and adjustments. A method of decomposing observed forecast errors so as to distinguish the contributions of forecaster and model is set out; the impact of future expectations treated in a ‘model-consistent’ or ‘rational’ manner is specifically considered. The results show that the forecaster's adjustments make a substantial contribution to forecast performance, a good part of which comes from adjustments that bring the model on track at the start of the forecast period. The published ex-ante forecasts are usually superior to pure model-based ex-post forecasts, whose performance indicates some misspecification of the underlying models.     

Forecasting air pollution PM2.5 in Beijing using weather data and multiple kernel learning

PM_2.5 mass concentration prediction is an important research issue because of the increasing impact of air pollution on the urban environment. In this paper, a PM_2.5 forecasting framework incorporating meteorological factors based on multiple kernel learning (MKL) is proposed to forecast the near future PM_2.5. In addition, we develop a novel two-step algorithm for solving the primal MKL problem. Compared with most existing MKL 2-step algorithms, the proposed algorithm does not require the optimal step size for updating kernel combination coefficients by linear search. To demonstrate the performance of the proposed forecasting framework, its performance is compared to single kernel-based support vector regression (SVR). Data sets of an inland city Beijing acquired from UCI are used to train and validate both of two methods. Experiments show that our proposed method outperforms the SVR.     

Multi‐step forecasting for long‐memory processes

In this paper we present results of a simulation study to assess and compare the accuracy of forecasting techniques for long‐memory processes in small sample sizes. We analyse differences between adaptive ARMA(1,1) L‐step forecasts, where the parameters are estimated by minimizing the sum of squares of L‐step forecast errors, and forecasts obtained by using long‐memory models. We compare widths of the forecast intervals for both methods, and discuss some computational issues associated with the ARMA(1,1) method. Our results illustrate the importance and usefulness of long‐memory models for multi‐step forecasting. Copyright © 1999 John Wiley & Sons, Ltd.     

Time Series of Zero‐Inflated Counts and their Coherent Forecasting

Poisson integer‐valued auto‐regressive process of order 1 (PINAR(1)) due to Al‐Osh and Alzaid (Journal of Time Series Analysis 1987; 8 (3): 261–275) and McKenzie (Advances in Applied Probability 1988; 20 (4): 822–835) has received a significant attention in modelling low‐count time series during the last two decades because of its simplicity. But in many practical scenarios, the process appears to be inadequate, especially when data are overdispersed in nature. This overdispersion occurs mainly for three reasons: presence of some extreme values, large number of zeros, and presence of both extreme values with a large number of zeros. In this article, we develop a zero‐inflated Poisson INAR(1) process as an alternative to the PINAR(1) process when the number of zeros in the data is larger than the expected number of zeros by the Poisson process. We investigate some important properties such as stationarity, ergodicity, autocorrelation structure, and conditional distribution, with a detailed study on h‐step‐ahead coherent forecasting. A comparative study among different methods of parameter estimation is carried out using some simulated data. One real dataset is analysed for practical illustration. Copyright © 2015 John Wiley & Sons, Ltd.     

Statistical estimation of optimal portfolios for non‐Gaussian dependent returns of assets

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector‐valued non‐Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ? for non‐Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ?. First, it is shown that there are some cases when the asymptotic variance of ? under non‐Gaussianity can be smaller than that under Gaussianity. The result shows that non‐Gaussianity of the returns does not always affect the efficiency badly. Second, we give a necessary and sufficient condition for ? to be asymptotically efficient when the return process is Gaussian, which shows that ? is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. Furthermore, we investigate the problem of predicting the one‐step‐ahead optimal portfolio return by the estimated portfolio based on ? and examine the mean squares prediction error. Copyright © 2008 John Wiley & Sons, Ltd.     

Inflation forecasting for aggregates of the EU-7 and EU-14 with Bayesian VAR models

This article applies the Bayesian Vector Auto-Regressive (BVAR) model to key economic aggregates of the EU-7, consisting of the former narrow-band ERM members plus Austria, and the EU-14. This model appears to be useful as an additional forecasting tool besides structural macroeconomic models, as is shown both by absolute forecasting performance and by a comparison of ex-post BVAR forecasts with forecasts by the OECD. A comparison of the aggregate models to single-country models reveals that pooling has a strong impact on forecast errors. If forecast errors are interpreted as shocks, shocks appear to be—at least in part—asymmetric, or countries react differently to shocks. © 1998 John Wiley & Sons, Ltd.     

Robust modelling of ARCH models

The autoregressive conditional heteroscedastic (ARCH) model and its extensions have been widely used in modelling changing variances in financial time series. Since the asset return distributions frequently display tails heavier than normal distributions, it is worth while studying robust ARCH modelling without a specific distribution assumption. In this paper, rather than modelling the conditional variance, we study ARCH modelling for the conditional scale. We examine the L₁‐estimation of ARCH models and derive the limiting distributions of the estimators. A robust standardized absolute residual autocorrelation based on least absolute deviation estimation is proposed. Then a robust portmanteau statistic is constructed to test the adequacy of the model, especially the specification of the conditional scale. We obtain their asymptotic distributions under mild conditions. Examples show that the suggested L₁‐norm estimators and the goodness‐of‐fit test are robust against error distributions and are accurate for moderate sample sizes. This paper provides a useful tool in modelling conditional heteroscedastic time series data. Copyright © 2001 John Wiley & Sons, Ltd.