Short‐term forecasting of GDP using large datasets: a pseudo real‐time forecast evaluation exercise

This paper performs a large‐scale forecast evaluation exercise to assess the performance of different models for the short‐term forecasting of GDP, resorting to large datasets from ten European countries. Several versions of factor models are considered and cross‐country evidence is provided. The forecasting exercise is performed in a simulated real‐time context, which takes account of publication lags in the individual series. In general, we find that factor models perform best and models that exploit monthly information outperform models that use purely quarterly data. However, the improvement over the simpler, quarterly models remains contained. Copyright © 2009 John Wiley & Sons, Ltd.     

Modeling and forecasting time series with a general non-normal distribution

We propose a model for time series with a general marginal distribution given by the Johnson family of distributions. We investigate for which Johnson distributions forecasting using the model is likely to be most effective compared to using a linear model. Monte Carlo simulation is used to assess the reliability of methods for determining which of the three Johnson forms is most appropriate for a given series. Finally, we give model fitting and forecasting results using the modeling procedure on a selection of simulated and real time series.     

On tests for non-linearity in time series analysis

We have developed a new test for non-linearity in time series data in discrete time. A comparative study has been conducted on Subba Rao, Gabr and Hinich's test, Keenan's test, Petruccelli and Davies test, and the new test. Both simulated and real data are used in the study. The implication for forecasting is briefly discussed.     

Forecasting real‐time data allowing for data revisions

A modeling approach to real‐time forecasting that allows for data revisions is shown. In this approach, an observed time series is decomposed into stochastic trend, data revision, and observation noise in real time. It is assumed that the stochastic trend is defined such that its first difference is specified as an AR model, and that the data revision, obtained only for the latest part of the time series, is also specified as an AR model. The proposed method is applicable to the data set with one vintage. Empirical applications to real‐time forecasting of quarterly time series of US real GDP and its eight components are shown to illustrate the usefulness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Forecasting non-seasonal time series with missing observations

Most forecasting methods are based on equally spaced data. In the case of missing observations the methods have to be modified. We have considered three smoothing methods: namely, simple exponential smoothing; double exponential smoothing; and Holt's method. We present a new, unified approach to handle missing data within the smoothing methods. This approach is compared with previously suggested modifications. The comparison is done on 12 real, non-seasonal time series, and shows that the smoothing methods, properly modified, usually perform well if the time series have a moderate number of missing observations.     

Signal Diffusion Mapping: Optimal Forecasting with Time‐Varying Lags

We introduce a new methodology for forecasting, which we call signal diffusion mapping. Our approach accommodates features of real‐world financial data which have been ignored historically in existing forecasting methodologies. Our method builds upon well‐established and accepted methods from other areas of statistical analysis. We develop and adapt those models for use in forecasting. We also present tests of our model on data in which we demonstrate the efficacy of our approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Forecasting Call Centre Arrivals

This article presents a novel neural network?based approach to the intra?day forecasting of call arrivals in call centres. We apply the method to individual time series of arrivals for different customer call groups. To train the model, we use historical call data from three months and, for each day, we aggregate the call volume in 288 intervals of 5 minutes. With these data, our method can be used for predicting the call volume in the next 5?minute interval using either previous real data or previous predictions to iteratively produce multi?step?ahead forecasts. We compare our approach with other conventional forecasting techniques. Experimental results provide factual evidence in favour of our approach. Copyright © 2013 John Wiley & Sons, Ltd.     

The forecasting attributes of trend- and difference-stationary representations for macroeconomic time series

We analyse the forecasting attributes of trenc and diffence-stationary representations of the U.S. macroeconomic time series sudied by Nelson and Plosser (1982). Predictive densities based on models estimated for these series (which terminate in 1970) are compared with subsequent realizations compiled by Schotman and van Dijk (1991) which terminate in (1988). Predictive densities obtained using the, extended series are also derived to assess the impact of the subsequent realization on long-range forecasts. Of particular interest are comparisons of the average intervals of predictive densities corresponding to the competing specifications In general, we find that coverage intervals based on diference-stationary specifications are far wider than those based or. trend-stationary specifications for the real series, and slightly wider for the nominal series. This additional width is often a virtue in forecasting nuninal series over the 1971-1988 period, as the inflation experienced durnig this time was unprecedented in the 1900s. However, the evolution of the real series has been relatively stable in the 1900s, hence the uncertainty associated with difference-stationary specifications generally seems excessive for these data.     

Evidence for the selection of forecasting methods

Reid (1972) was among the first to argue that the relative accuracy of forecasting methods changes according to the properties of the time series. Comparative analyses of forecasting performance such as the M‐Competition tend to support this argument. The issue addressed here is the usefulness of statistics summarizing the data available in a time series in predicting the relative accuracy of different forecasting methods. Nine forecasting methods are described and the literature suggesting summary statistics for choice of forecasting method is summarized. Based on this literature and further argument a set of these statistics is proposed for the analysis. These statistics are used as explanatory variables in predicting the relative performance of the nine methods using a set of simulated time series with known properties. These results are evaluated on observed data sets, the M‐Competition data and Fildes Telecommunications data. The general conclusion is that the summary statistics can be used to select a good forecasting method (or set of methods) but not necessarily the best. Copyright © 2000 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.     

Bayesian Forecasting for Time Series of Categorical Data

Time series of categorical data is not a widely studied research topic. Particularly, there is no available work on the Bayesian analysis of categorical time series processes. With the objective of filling that gap, in the present paper we consider the problem of Bayesian analysis including Bayesian forecasting for time series of categorical data, which is modelled by Pegram's mixing operator, applicable for both ordinal and nominal data structures. In particular, we consider Pegram's operator‐based autoregressive process for the analysis. Real datasets on infant sleep status are analysed for illustrations. We also illustrate that the Bayesian forecasting is more accurate than the corresponding frequentist's approach when we intend to forecast a large time gap ahead. Copyright © 2016 John Wiley & Sons, Ltd.     

Covariance estimation for multivariate conditionally Gaussian dynamic linear models

In multivariate time series, estimation of the covariance matrix of observation innovations plays an important role in forecasting as it enables computation of standardized forecast error vectors as well as the computation of confidence bounds of forecasts. We develop an online, non‐iterative Bayesian algorithm for estimation and forecasting. It is empirically found that, for a range of simulated time series, the proposed covariance estimator has good performance converging to the true values of the unknown observation covariance matrix. Over a simulated time series, the new method approximates the correct estimates, produced by a non‐sequential Monte Carlo simulation procedure, which is used here as the gold standard. The special, but important, vector autoregressive (VAR) and time‐varying VAR models are illustrated by considering London metal exchange data consisting of spot prices of aluminium, copper, lead and zinc. Copyright © 2007 John Wiley & Sons, Ltd.     

A Comparison of Box—Jenkins and objective methods for determining the order of a non-seasonal ARMA Model

This paper evaluates different procedures for selecting the order of a non-seasonal ARMA model. Specifically, it compares the forecasting accuracy of models developed by the personalized Box-Jenkins (BJ) methodology with models chosen by numerous automatic procedures. The study uses real series modelled by experts (textbook authors) in the BJ approach. Our results show that many objective selection criteria provide structures equal or superior to the time-consuming BJ method. For the sets of data used in this study, we also examine the influence of parsimony in time-series forecasting. Defining what models are too large or too small is sensitive to the forecast horizon. Automatic techniques that select the best models for forecasting are similar in size to BJ models although they often disagree on model order.     

Subset selection of autoregressive time series models

We propose a solution to select promising subsets of autoregressive time series models for further consideration which follows up on the idea of the stochastic search variable selection procedure in George and McCulloch (1993). It is based on a Bayesian approach which is unconditional on the initial terms. The autoregression stepup is in the form of a hierarchical normal mixture model, where latent variables are used to identify the subset choice. The framework of our procedure is utilized by the Gibbs sampler, a Markov chain Monte Carlo method. The advantage of the method presented is computational: it is an alternative way to search over a potentially large set of possible subsets. The proposed method is illustrated with a simulated data as well as a real data. Copyright © 1999 John Wiley & Sons, Ltd.     

A hybrid approach with step-size aggregation to forecasting hierarchical time series

Hierarchical time series arise in various fields such as manufacturing and services when the products or services can be hierarchically structured. “Top-down” and “bottom-up” forecasting approaches are often used for forecasting such hierarchical time series. In this paper, we develop a new hybrid approach (HA) with step-size aggregation for hierarchical time series forecasting. The new approach is a weighted average of the two classical approaches with the weights being optimally chosen for all the series at each level of the hierarchy to minimize the variance of the forecast errors. The independent selection of weights for all the series at each level of the hierarchy makes the HA inconsistent while aggregating suitably across the hierarchy. To address this issue, we introduce a step-size aggregate factor that represents the relationship between forecasts of the two consecutive levels of the hierarchy. The key advantage of the proposed HA is that it captures the structure of the hierarchy inherently due to the combination of the hierarchical approaches instead of independent forecasts of all the series at each level of the hierarchy. We demonstrate the performance of the new approach by applying it to the monthly data of ‘Industrial’ category of M3-Competition as well as on Pakistan energy consumption data.     

Fitting of growth curves over time when the data are obtained from a single realization

This paper focuses on the general problem of forecasting the maximum value of a time series which by the nature of the data must approach an asymptotic value. Examples of such series include the growth of organisms, the concentration of a chemical reagent during a reaction occurring over time or the amount of a fossil fuel resource which has been discovered or produced as a function of time. The approach taken below differs from the usual models for this type of data in that it assumes that an unobserved time series is actually driving the process, and that the observed data series is a function of the unobserved process. In the case of fossil fuels the unobserved series might be a measure of the exploratory drilling, the number of production days in a given time period or even the amount of fiscal resources devoted to exploratory activities. A maximum likelihood method is developed for estimating the parameters of the process, especially the maximum S, and the covariance structure of the estimators is developed. The methodology is illustrated on an example of oil production. Finally, methods are developed for forecasting the data into the near future.     

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.     

The Role of Survey Data in Nowcasting Euro Area GDP Growth

This paper evaluates the impact of new releases of financial, real activity and survey data on nowcasting euro area gross domestic product (GDP). We show that all three data categories positively impact on the accuracy of GDP nowcasts, whereby the effect is largest in the case of real activity data. When treating variables as if they were all published at the same time and without any time lag, financial series lose all their significance, while survey data remain an important ingredient for the nowcasting exercise. The subsequent analysis shows that the sectoral coverage of survey data, which is broader than that of timely available real activity data, as well as their information content stemming from questions focusing on agents' expectations, are the main sources of the ‘genuine’ predictive power of survey data. When the forecast period is restricted to the 2008–09 financial crisis, the main change is an enhanced forecasting role for financial data. Copyright © 2015 John Wiley & Sons, Ltd.     

Methods for backcasting,nowcasting and forecasting using factor‐MIDAS: With an application to Korean GDP

We utilize mixed‐frequency factor‐MIDAS models for the purpose of carrying out backcasting, nowcasting, and forecasting experiments using real‐time data. We also introduce a new real‐time Korean GDP dataset, which is the focus of our experiments. The methodology that we utilize involves first estimating common latent factors (i.e., diffusion indices) from 190 monthly macroeconomic and financial series using various estimation strategies. These factors are then included, along with standard variables measured at multiple different frequencies, in various factor‐MIDAS prediction models. Our key empirical findings as follows. (i) When using real‐time data, factor‐MIDAS prediction models outperform various linear benchmark models. Interestingly, the “MSFE‐best” MIDAS models contain no autoregressive (AR) lag terms when backcasting and nowcasting. AR terms only begin to play a role in “true” forecasting contexts. (ii) Models that utilize only one or two factors are “MSFE‐best” at all forecasting horizons, but not at any backcasting and nowcasting horizons. In these latter contexts, much more heavily parametrized models with many factors are preferred. (iii) Real‐time data are crucial for forecasting Korean gross domestic product, and the use of “first available” versus “most recent” data “strongly” affects model selection and performance. (iv) Recursively estimated models are almost always “MSFE‐best,” and models estimated using autoregressive interpolation dominate those estimated using other interpolation methods. (v) Factors estimated using recursive principal component estimation methods have more predictive content than those estimated using a variety of other (more sophisticated) approaches. This result is particularly prevalent for our “MSFE‐best” factor‐MIDAS models, across virtually all forecast horizons, estimation schemes, and data vintages that are analyzed.     

When are Direct Multi‐step and Iterative Forecasts Identical?

Although both direct multi‐step‐ahead forecasting and iterated one‐step‐ahead forecasting are two popular methods for predicting future values of a time series, it is not clear that the direct method is superior in practice, even though from a theoretical perspective it has lower mean squared error (MSE). A given model can be fitted according to either a multi‐step or a one‐step forecast error criterion, and we show here that discrepancies in performance between direct and iterative forecasting arise chiefly from the method of fitting, and is dictated by the nuances of the model's misspecification. We derive new formulas for quantifying iterative forecast MSE, and present a new approach for assessing asymptotic forecast MSE. Finally, the direct and iterative methods are compared on a retail series, which illustrates the strengths and weaknesses of each approach. Copyright © 2015 John Wiley & Sons, Ltd.