Hierarchical bayes forecasts of multinomial dirichlet data applied to coupon redemptions

This paper considers forecasting count data from a multinomial Dirichlet distribution. The forecasting procedure implements hierarchical Bayes methods in order to develop a prior distribution for a new series of data. The methodology is applied to the redemption of cents-off promotional coupons. In a forecasting experiment, early forecasts of new series are similar to those from pooling all redemptions from previous coupon promotions. However, the hierarchical Bayes model provides realistic estimates of forecasting errors, while those for the pooled forecasts are consistently optimistic. As the current series evolves, the hierarchical Bayes forecasts adapt more rapidly and are more accurate than pooled forecasts.     

Time series forecasts and extra-model information

Often a forecaster has supplementary information (e.g. field reports or forecasts from another source) that cannot be included directly in a time series model. Especially interesting are cases where this information is given at time intervals that are different from those of the time series model forecasts. Previous authors have considered a numerical and a model-based statistical method for combining extra-model information of this type with ARIMA model forecasts. This paper extends both methods to vector ARMA model forecasts and dynamic regression (transfer function) model forecasts. It is also shown that a Lagrange multiplier numerical procedure arises as a special case of the model-based procedure. An empirical example is given.     

Forecasting with missing data: application to coastal wave heights

This paper presents a comparative analysis of linear and mixed models for short‐term forecasting of a real data series with a high percentage of missing data. Data are the series of significant wave heights registered at regular periods of three hours by a buoy placed in the Bay of Biscay. The series is interpolated with a linear predictor which minimizes the forecast mean square error. The linear models are seasonal ARIMA models and the mixed models have a linear component and a non‐linear seasonal component. The non‐linear component is estimated by a non‐parametric regression of data versus time. Short‐term forecasts, no more than two days ahead, are of interest because they can be used by the port authorities to notify the fleet. Several models are fitted and compared by their forecasting behaviour. Copyright © 1999 John Wiley & Sons, Ltd.     

A hybrid forecasting approach for piece‐wise stationary time series

We consider the problem of forecasting a stationary time series when there is an unknown mean break close to the forecast origin. Based on the intercept‐correction methods suggested by Clements and Hendry (1998) and Bewley (2003), a hybrid approach is introduced, where the break and break point are treated in a Bayesian fashion. The hyperparameters of the priors are determined by maximizing the marginal density of the data. The distributions of the proposed forecasts are derived. Different intercept‐correction methods are compared using simulation experiments. Our hybrid approach compares favorably with both the uncorrected and the intercept‐corrected forecasts. Copyright © 2006 John Wiley & Sons, Ltd.     

Bayesian Assessment of Dynamic Quantile Forecasts

Bayesian methods for assessing the accuracy of dynamic financial value‐at‐risk (VaR) forecasts have not been considered in the literature. Such methods are proposed in this paper. Specifically, Bayes factor analogues of popular frequentist tests for independence of violations from, and for correct coverage of a time series of, dynamic quantile forecasts are developed. To evaluate the relevant marginal likelihoods, analytic integration methods are utilized when possible; otherwise multivariate adaptive quadrature methods are employed to estimate the required quantities. The usual Bayesian interval estimate for a proportion is also examined in this context. The size and power properties of the proposed methods are examined via a simulation study, illustrating favourable comparisons both overall and with their frequentist counterparts. An empirical study employs the proposed methods, in comparison with standard tests, to assess the adequacy of a range of forecasting models for VaR in several financial market data series. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting the Antwerp maritime steel traffic flow: A case study

This paper uses multivariate time series models to specify the maritime steel traffic flow in the port of Antwerp. The time series considered are the total outgoing and total incoming maritime steel traffic and the total steel production in the EEC. The obtained time series models provide useful insight into the general behaviour of the maritime steel traffic flow during the period 1971–82. In particular, they provide a quantitative interpretation of important changes which took place in the European steel industry during that period. The multivariate time series models produce forecasts which are a substantial improvement over those obtained by univariate time series models. This is especially the case for the series of total incoming maritime steel traffic in the port of Antwerp, when differencing and transformation of the original data are applied.     

Linking series generated at different frequencies

This is a report on our studies of the systematical use of mixed‐frequency datasets. We suggest that the use of high‐frequency data in forecasting economic aggregates can increase the accuracy of forecasts. The best way of using this information is to build a single model that relates the data of all frequencies, for example, an ARMA model with missing observations. As an application of linking series generated at different frequencies, we show that the use of a monthly industrial production index improves the predictability of the quarterly GNP. Copyright © 2008 John Wiley & Sons, Ltd.     

An evaluation of bayesian forecasting

‘Bayesian forecasting’ is a time series method of forecasting which (in the United Kingdom) has become synonymous with the state space formulation of Harrison and Stevens (1976). The approach is distinct from other time series methods in that it envisages changes in model structure. A disjoint class of models is chosen to encompass the changes. Each data point is retrospectively evaluated (using Bayes theorem) to judge which of the models held. Forecasts are then derived conditional on an assumed model holding true. The final forecasts are weighted sums of these conditional forecasts. Few empirical evaluations have been carried out. This paper reports a large scale comparison of time series forecasting methods including the Bayesian. The approach is two fold: a simulation study to examine parameter sensitivity and an empirical study which contrasts Bayesian with other time series methods.     

Multiple time-series modelling: Another look at the canadian money and income data

The practice of modelling the components of a vector time series to arrive at a joint model for the vector is considered. It is shown that in some cases this is not unreasonable. A vector ARMA model is used to model the Canadian money and income data. We also use these data to discuss the issue of differencing a multiple time series. Finally, models based on first and second differences are compared using forecasts.     

A model of an average recession and recovery

This paper proposes an Average Recession/Recovery Model (ARRM). It discusses the reasons why such a model is needed and how it can be developed. Major utilities of the model are (1) it is an extremely simple way to display complex forecasts to management graphically, (2) it can be applied to a single time series–with monthly or quarterly data–and is applicable to a large proportion of time series, both macro and micro, (3) it is easy to calculate, to understand, to program and to communicate with it and (4) it employs widely accepted statistical and economic methods.     

Henderson‐Trending of Macroeconomic Variables and Forecasting Accuracy

Using a structural time‐series model, the forecasting accuracy of a wide range of macroeconomic variables is investigated. Specifically of importance is whether the Henderson moving‐average procedure distorts the underlying time‐series properties of the data for forecasting purposes. Given the weight of attention in the literature to the seasonal adjustment process used by various statistical agencies, this study hopes to address the dearth of literature on ‘trending’ procedures. Forecasts using both the trended and untrended series are generated. The forecasts are then made comparable by ‘detrending’ the trended forecasts, and comparing both series to the realised values. Forecasting accuracy is measured by a suite of common methods, and a test of significance of difference is applied to the respective root mean square errors. It is found that the Henderson procedure does not lead to deterioration in forecasting accuracy in Australian macroeconomic variables on most occasions, though the conclusions are very different between the one‐step‐ahead and multi‐step‐ahead forecasts. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparison of two non‐parametric models for daily traffic forecasting in Hong Kong

The most up‐to‐date annual average daily traffic (AADT) is always required for transport model development and calibration. However, the current‐year AADT data are not always available. The short‐term traffic flow forecasting models can be used to predict the traffic flows for the current year. In this paper, two non‐parametric models, non‐parametric regression (NPR) and Gaussian maximum likelihood (GML), are chosen for short‐term traffic forecasting based on historical data collected for the annual traffic census (ATC) in Hong Kong. These models are adapted as they are more flexible and efficient in forecasting the daily vehicular flows in the Hong Kong ATC core stations (in total of 87 stations). The daily vehicular flows predicted by these models are then used to calculate the AADT of the current year, 1999. The overall prediction and comparison results show that the NPR model produces better forecasts than the GML model using the ATC data in Hong Kong. Copyright © 2006 John Wiley _ Sons, Ltd.     

Forecasting nonlinear time series with feed‐forward neural networks: a case study of Canadian lynx data

The forecasting capabilities of feed‐forward neural network (FFNN) models are compared to those of other competing time series models by carrying out forecasting experiments. As demonstrated by the detailed forecasting results for the Canadian lynx data set, FFNN models perform very well, especially when the series contains nonlinear and non‐Gaussian characteristics. To compare the forecasting accuracy of a FFNN model with an alternative model, Pitman's test is employed to ascertain if one model forecasts significantly better than another when generating one‐step‐ahead forecasts. Moreover, the residual‐fit spread plot is utilized in a novel fashion in this paper to compare visually out‐of‐sample forecasts of two alternative forecasting models. Finally, forecasting findings on the lynx data are used to explain under what conditions one would expect FFNN models to furnish reliable and accurate forecasts. Copyright © 2005 John Wiley & Sons, Ltd.     

Forecasting and trading strategies based on a price trend model

In this paper, we consider the price trend model in which it is assumed that the time series of a security's prices contain a stochastic trend component which remains constant on each of a sequence of time intervals, with each interval having random duration. A quasi‐maximum likelihood method is used to estimate the model parameters. Optimal one‐step‐ahead forecasts of returns are derived. The trading rule based on these forecasts is constructed and is found to bear similarity to a popular trading rule based on moving averages. When applying the methods to forecast the returns of the Hang Seng Index Futures in Hong Kong, we find that the performance of the newly developed trading rule is satisfactory. Copyright © 2000 John Wiley & Sons, Ltd.     

Linear combination of restrictions and forecasts in time series analysis

An important tool in time series analysis is that of combining information in an optimal way. Here we establish a basic combining rule of linear predictors and show that such problems as forecast updating, missing value estimation, restricted forecasting with binding constraints, analysis of outliers and temporal disaggregation can be viewed as problems of optimal linear combination of restrictions and forecasts. A compatibility test statistic is also provided as a companion tool to check that the linear restrictions are compatible with the forecasts generated from the historical data. Copyright © 2000 John Wiley & Sons, Ltd.     

Forecasting Death Rates Using Exogenous Determinants

Mortality models used for forecasting are predominantly based on the statistical properties of time series and do not generally incorporate an understanding of the forces driving secular trends. This paper addresses three research questions: Can the factors found in stochastic mortality‐forecasting models be associated with real‐world trends in health‐related variables? Does inclusion of health‐related factors in models improve forecasts? Do resulting models give better forecasts than existing stochastic mortality models? We consider whether the space spanned by the latent factor structure in mortality data can be adequately described by developments in gross domestic product, health expenditure and lifestyle‐related risk factors using statistical techniques developed in macroeconomics and finance. These covariates are then shown to improve forecasts when incorporated into a Bayesian hierarchical model. Results are comparable or better than benchmark stochastic mortality models. Copyright © 2014 John Wiley & Sons, Ltd.     

Short‐term prediction of motorway travel time using ANPR and loop data

Travel time is a good operational measure of the effectiveness of transportation systems. The ability to accurately predict motorway and arterial travel times is a critical component for many intelligent transportation systems (ITS) applications. Advanced traffic data collection systems using inductive loop detectors and video cameras have been installed, particularly for motorway networks. An inductive loop can provide traffic flow at its location. Video cameras with image‐processing software, e.g. Automatic Number Plate Recognition (ANPR) software, are able to provide travel time of a road section. This research developed a dynamic linear model (DLM) model to forecast short‐term travel time using both loop and ANPR data. The DLM approach was tested on three motorway sections in southern England. Overall, the model produced good prediction results, albeit large prediction errors occurred at congested traffic conditions due to the dynamic nature of traffic. This result indicated advantages of use of the both data sources. Copyright © 2008 John Wiley & Sons, Ltd.     

On SETAR non‐linearity and forecasting

We compare linear autoregressive (AR) models and self‐exciting threshold autoregressive (SETAR) models in terms of their point forecast performance, and their ability to characterize the uncertainty surrounding those forecasts, i.e. interval or density forecasts. A two‐regime SETAR process is used as the data‐generating process in an extensive set of Monte Carlo simulations, and we consider the discriminatory power of recently developed methods of forecast evaluation for different degrees of non‐linearity. We find that the interval and density evaluation methods are unlikely to show the linear model to be deficient on samples of the size typical for macroeconomic data. Copyright © 2003 John Wiley & Sons, Ltd.     

The Effects of Disaggregation on Forecasting Nonstationary Time Series

This paper focuses on the effects of disaggregation on forecast accuracy for nonstationary time series using dynamic factor models. We compare the forecasts obtained directly from the aggregated series based on its univariate model with the aggregation of the forecasts obtained for each component of the aggregate. Within this framework (first obtain the forecasts for the component series and then aggregate the forecasts), we try two different approaches: (i) generate forecasts from the multivariate dynamic factor model and (ii) generate the forecasts from univariate models for each component of the aggregate. In this regard, we provide analytical conditions for the equality of forecasts. The results are applied to quarterly gross domestic product (GDP) data of several European countries of the euro area and to their aggregated GDP. This will be compared to the prediction obtained directly from modeling and forecasting the aggregate GDP of these European countries. In particular, we would like to check whether long‐run relationships between the levels of the components are useful for improving the forecasting accuracy of the aggregate growth rate. We will make forecasts at the country level and then pool them to obtain the forecast of the aggregate. The empirical analysis suggests that forecasts built by aggregating the country‐specific models are more accurate than forecasts constructed using the aggregated data. Copyright © 2014 John Wiley & Sons, Ltd.     

Long‐memory forecasting of US monetary indices

Several studies have tested for long‐range dependence in macroeconomic and financial time series but very few have assessed the usefulness of long‐memory models as forecast‐generating mechanisms. This study tests for fractional differencing in the US monetary indices (simple sum and divisia) and compares the out‐of‐sample fractional forecasts to benchmark forecasts. The long‐memory parameter is estimated using Robinson's Gaussian semi‐parametric and multivariate log‐periodogram methods. The evidence amply suggests that the monetary series possess a fractional order between one and two. Fractional out‐of‐sample forecasts are consistently more accurate (with the exception of the M3 series) than benchmark autoregressive forecasts but the forecasting gains are not generally statistically significant. In terms of forecast encompassing, the fractional model encompasses the autoregressive model for the divisia series but neither model encompasses the other for the simple sum series. Copyright © 2006 John Wiley & Sons, Ltd.