Space‐Time Model versus VAR Model: Forecasting Electricity demand in Japan

This paper examined the forecasting performance of disaggregated data with spatial dependency and applied it to forecasting electricity demand in Japan. We compared the performance of the spatial autoregressive ARMA (SAR‐ARMA) model with that of the vector autoregressive (VAR) model from a Bayesian perspective. With regard to the log marginal likelihood and log predictive density, the VAR(1) model performed better than the SAR‐ARMA( 1,1) model. In the case of electricity demand in Japan, we can conclude that the VAR model with contemporaneous aggregation had better forecasting performance than the SAR‐ARMA model. Copyright © 2011 John Wiley & Sons, Ltd.     

Hybrid Forecasting with Estimated Temporally Aggregated Linear Processes

We introduce a new strategy for the prediction of linear temporal aggregates; we call it ‘hybrid’ and study its performance using asymptotic theory. This scheme consists of carrying out model parameter estimation with data sampled at the highest available frequency and the subsequent prediction with data and models aggregated according to the forecasting horizon of interest. We develop explicit expressions that approximately quantify the mean square forecasting errors associated with the different prediction schemes and that take into account the estimation error component. These approximate estimates indicate that the hybrid forecasting scheme tends to outperform the so‐called ‘all‐aggregated’ approach and, in some instances, the ‘all‐disaggregated’ strategy that is known to be optimal when model selection and estimation errors are neglected. Unlike other related approximate formulas existing in the literature, those proposed in this paper are totally explicit and require neither assumptions on the second‐order stationarity of the sample nor Monte Carlo simulations for their evaluation. Copyright © 2014 John Wiley & Sons, Ltd.     

Theory and practice of multivariate arma forecasting

We compare univariate and multivariate forecasts based on ARMA models. In theory we cannot do worse by using a multivariate model instead of a univariate one, but we can risk getting no improvement. Conditions for no improvements are discussed as well as cases where large improvements occur. The effect of estimated parameters is examined and found to be small granted that a good method of estimation is used. However, multivariate models could be very sensitive to structural changes. This is illustrated via an example involving monetary data, where the multivariate forecasts perform considerably worse than the univariate ones. This seems to put a limitation on the use of multivariate ARMA forecasting models.     

A test of space-time arma modelling and forecasting of hotel data

This paper describes the application of space-time ARMA modelling to demand-related data from eight hotels from a single hotel chain in a large US city. Important spatial characteristics of the space-time process are incorporated into the model using a simple weighting matrix based on driving distances between the hotels. Using a hold-out sample, the forecasting performance of this space-time approach was found to be superior to eight separate univariate ARMA models.     

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.     

Econometric modelling for short‐term inflation forecasting in the euro area

This paper examines the problem of forecasting macro‐variables which are observed monthly (or quarterly) and result from geographical and sectorial aggregation. The aim is to formulate a methodology whereby all relevant information gathered in this context could provide more accurate forecasts, be frequently updated, and include a disaggregated explanation as useful information for decision‐making. The appropriate treatment of the resulting disaggregated data set requires vector modelling, which captures the long‐run restrictions between the different time series and the short‐term correlations existing between their stationary transformations. Frequently, due to a lack of degrees of freedom, the vector model must be restricted to a block‐diagonal vector model. This methodology is applied in this paper to inflation in the euro area, and shows that disaggregated models with cointegration restrictions improve accuracy in forecasting aggregate macro‐variables. Copyright © 2007 John Wiley & Sons, Ltd.     

The predictive value of temporally disaggregated volatility: evidence from index futures markets

This paper examines the benefits to forecasters of decomposing close-to-close return volatility into close-to-open (nighttime) and open-to-close (daytime) return volatility. Specifically, we consider whether close-to-close volatility forecasts based on the former type of (temporally aggregated) data are less accurate than corresponding forecasts based on the latter (temporally disaggregated) data. Results obtained from seven different US index futures markets reveal that significant increases in forecast accuracy are possible when using temporally disaggregated volatility data. This result is primarily driven by the fact that forecasts based on such data can be updated as more information becomes available (e.g., information flow from the preceding close-to-open/nighttime trading session). Finally, we demonstrate that the main findings of this paper are robust to the index futures market considered, the way in which return volatility is constructed, and the method used to assess forecast accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

The approximation of long‐memory processes by an ARMA model

A mean square error criterion is proposed in this paper to provide a systematic approach to approximate a long‐memory time series by a short‐memory ARMA(1, 1) process. Analytic expressions are derived to assess the effect of such an approximation. These results are established not only for the pure fractional noise case, but also for a general autoregressive fractional moving average long‐memory time series. Performances of the ARMA(1,1) approximation as compared to using an ARFIMA model are illustrated by both computations and an application to the Nile river series. Results derived in this paper shed light on the forecasting issue of a long‐memory process. Copyright © 2001 John Wiley & Sons, Ltd.     

ARMA Models and the Box–Jenkins Methodology

The purpose of this paper is to apply the Box–Jenkins methodology to ARIMA models and determine the reasons why in empirical tests it is found that the post-sample forecasting the accuracy of such models is generally worse than much simpler time series methods. The paper concludes that the major problem is the way of making the series stationary in its mean (i.e. the method of differencing) that has been proposed by Box and Jenkins. If alternative approaches are utilized to remove and extrapolate the trend in the data, ARMA models outperform the models selected through Box–Jenkins methodology. In addition, it is shown that using ARMA models to seasonally adjusted data slightly improves post-sample accuracies while simplifying the use of ARMA models. It is also confirmed that transformations slightly improve post-sample forecasting accuracy, particularly for long forecasting horizons. Finally, it is demonstrated that AR(1), AR(2) and ARMA(1,1) models can produce more accurate post-sample forecasts than those found through the application of Box–Jenkins methodology.© 1997 John Wiley & Sons, Ltd.     

Augmented Half‐Life Estimation Based on High‐Frequency Data

Half‐life estimation has been widely used to evaluate the speed of mean reversion for various economic and financial variables. However, half‐life estimation for the same variable are often different due to the length of the annual time series data used in alternative studies. To solve this issue, this paper extends the ARMA model and derives the half‐life estimation formula for high‐frequency monthly data. Our results indicate that half‐life estimation using short‐period monthly data is an effective approximation for that using long‐period annual data. Furthermore, by applying high‐frequency data, the required effective sample size can be reduced by at least 40% at the 95% confidence level. Copyright © 2015 John Wiley & Sons, Ltd.     

On Selecting a Power Transformation in Time-Series Analysis

The primary aim of this paper is to select an appropriate power transformation when we use ARMA models for a given time series. We propose a Bayesian procedure for estimating the power transformation as well as other parameters in time series models. The posterior distributions of interest are obtained utilizing the Gibbs sampler, a Markov Chain Monte Carlo (MCMC) method. The proposed methodology is illustrated with two real data sets. The performance of the proposed procedure is compared with other competing procedures. © 1997 John Wiley & Sons, Ltd.     

Municipal budget forecasting with multivariate ARMA models

In this paper multivariate ARMA models are applied to the problem of forecasting city budget variables. Unlike univariate time-series methods, multivariate models can use relationships among budget variables as well as relationships with economic and demographic indicators. Although available budget series are shorter than what is usually believed necessary for multivariate ARMA modelling, the forecasts seem to be of higher quality than those from univariate models.     

Forecasting high‐frequency financial data with the ARFIMA–ARCH model

Financial data series are often described as exhibiting two non‐standard time series features. First, variance often changes over time, with alternating phases of high and low volatility. Such behaviour is well captured by ARCH models. Second, long memory may cause a slower decay of the autocorrelation function than would be implied by ARMA models. Fractionally integrated models have been offered as explanations. Recently, the ARFIMA–ARCH model class has been suggested as a way of coping with both phenomena simultaneously. For estimation we implement the bias correction of Cox and Reid ( 1987 ). For daily data on the Swiss 1‐month Euromarket interest rate during the period 1986–1989, the ARFIMA–ARCH (5,d,2/4) model with non‐integer d is selected by AIC. Model‐based out‐of‐sample forecasts for the mean are better than predictions based on conditionally homoscedastic white noise only for longer horizons (τ > 40). Regarding volatility forecasts, however, the selected ARFIMA–ARCH models dominate. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

Forecasting non-normal time series

We look at the problem of forecasting time series which are not normally distributed. An overall approach is suggested which works both on simulated data and on real data sets. The idea is intuitively attractive and has the considerable advantage that it can readily be understood by non-specialists. Our approach is based on ARMA methodology and our models are estimated via a likelihood procedure which takes into account the non-normality of the data. We examine in some detail the circumstances in which taking explicit account of the nonnormality improves the forecasting process in a significant way. Results from several simulated and real series are included.     

Monthly Employment Indicators of the Euro Area and Larger Member States: Real‐Time Analysis of Indirect Estimates

The paper presents a comparative real‐time analysis of alternative indirect estimates relative to monthly euro area employment. In the experiment quarterly employment is temporally disaggregated using monthly unemployment as related series. The strategies under comparison make use of the contribution of sectoral data of the euro area and its six larger member states. The comparison is carried out among univariate temporal disaggregations of the Chow and Lin type and multivariate structural time series models of small and medium size. Specifications in logarithms are also systematically assessed. All multivariate set‐ups, up to 49 series modelled simultaneously, are estimated via the EM algorithm. Main conclusions are that mean revision errors of disaggregated estimates are overall small, a gain is obtained when the model strategy takes into account the information by both sector and member state and that larger multivariate set‐ups perform very well, with several advantages with respect to simpler models.Copyright © 2014 John Wiley & Sons, Ltd.     

Prediction of α‐stable GARCH and ARMA‐GARCH‐M models

The best prediction of generalized autoregressive conditional heteroskedasticity (GARCH) models with α‐stable innovations, α‐stable power‐GARCH models and autoregressive moving average (ARMA) models with GARCH in mean effects (ARMA‐GARCH‐M) are proposed. We present a sufficient condition for stationarity of α‐stable GARCH models. The prediction methods are easy to implement in practice. The proposed prediction methods are applied for predicting future values of the daily SP500 stock market and wind speed data.     

Disaggregation of annual flow data with multiplicative trends

Various methods based on smoothing or statistical criteria have been used for constructing disaggregated values compatible with observed annual totals. The present method is based on a time‐series model in a state space form and allows for a prescribed multiplicative trend. It is applied to US GNP data which have been used for comparing methods suggested for this purpose. The model can be extended to include quarterly series, related to the unknown disaggregated values. But as the estimation criteria are based on prediction errors of the aggregated values, the estimated form may not be optimal for reproducing high‐frequency variations of the disaggregated values. Copyright © 1999 John Wiley & Sons, Ltd.