Forecasting from non-linear models in practice

If a simple non-linear autoregressive time-series model is suggested for a series, it is not straightforward to produce multi-step forecasts from it. Several alternative theoretical approaches are discussed and then compared with a simulation study only for the two-step case. It is suggested that fitting a new model for each forecast horizon may be a satisfactory strategy.     

Dynamic relationship analysis of us gasoline and crude oil prices

This paper studies the dynamic relationships between US gasoline prices, crude oil prices, and the stock of gasoline. Using monthly data between January 1973 and December 1987, we find that the US gasoline price is mainly influenced by the price of crude oil. The stock of gasoline has little or no influence on the price of gasoline during the period before the second energy crisis, and seems to have some influence during the period after. We also find that the dynamic relationship between the prices of gasoline and crude oil changes over time, shifting from a longer lag response to a shorter lag response. Box-Jenkins ARIMA and transfer function models are employed in this study. These models are estimated using estimation procedure with and without outlier adjustment. For model estimation with outlier adjustment, an iterative procedure for the joint estimation of model parameters and outlier effects is employed. The forecasting performance of these models is carefully examined. For the purpose of illustration, we also analyze these time series using classical white-noise regression models. The results show the importance of using appropriate time-series methods in modeling and forecasting when the data are serially correlated. This paper also demonstrates the problems of time-series modeling when outliers are present.     

Recursive estimation and forecasting of non-stationary time series

The paper presents a unified, fully recursive approach to the modelling and forecasting of non-stationary time-series. The basic time-series model, which is based on the well-known ‘component’ or ‘structuraL’ form, is formulated in state-space terms. A novel spectral decomposition procedure, based on the exploitation of recursive smoothing algorithms, is then utilized to simplify the procedures of model identification and estimation. Finally, the fully recursive formulation allows for conventional or self-adaptive implementation of state-space forecasting and seasonal adjustment. Although the paper is restricted to the consideration of univariate time series, the basic approach can be extended to handle explanatory variables or full multivariable (vector) series.     

Forecasting accounting data: A multiple time-series analysis

This paper examines the relative forecasting performance of multivariate time-series analysis. One hundred consecutive monthly observations for three accounting series were obtained from a manufacturing division of a large corporation. Regression, univariate time-series, transfer-function, and multiple time-series models were identified, estimated, and used to forecast each accounting series. The multiple time-series model yielded the smallest forecast variances.     

Going Up–Going Down: How Good Are People at Forecasting Trends and Changes in Trends?

Prior studies of judgemental time-series forecasting have found that people have problems with downward-sloping series. This laboratory-based study presents a controlled experiment of series direction and it investigates the problems of changing trends. Results confirm that people have significant difficulties in dealing with downward-sloping series and that behaviour is consistent with a general tendency to anticipate that downward series will reverse themselves. There is a significantly less tendency to do so for upward series. Results are discussed in terms of systematic and unsystematic error.© 1997 John Wiley & Sons, Ltd.     

Variance intervention

Variance intervention is a simple state-space approach to handling sharp discontinuities of level or slope in the states or parameters of models for non-stationary time-series. It derives from earlier procedures used in the 1960s for the design of self-adaptive, state variable feedback control systems. In the alternative state-space forecasting context considered in the present paper, it is particularly useful when applied to structural time series models. The paper compares the variance intervention procedure with the related ‘subjective intervention’ approach proposed by West and Harrison in a recent issue of the Journal of Forecasting, and demonstrates it efficacy by application to various time-series data, including those used by West and Harrison.     

The usefulness of heuristic N(E)RLS algorithms for combining forecasts

There exists theoretical and empirical evidence on the efficiency and robustness of Non-negativity Restricted Least Squares combinations of forecasts. However, the computational complexity of the method hinders its widespread use in practice. We examine various optimizing and heuristic computational algorithms for estimating NRLS combination models and provide certain CPU-time reducing implementations. We empirically compare the combination weights identified by the alternative algorithms and their computational demands based on a total of more than 66,000 models estimated to combine the forecasts of 37 firm-specific accounting earnings series. The ex ante prediction accuracies of combined forecasts from the optimizing versus heuristic algorithms are compared. The effects of fit sample size, model specification, multicollinearity, correlations of forecast errors, and series and forecast variances on the relative accuracy of the optimizing versus heuristic algorithms are analysed. The results reveal that, in general, the computationally simple heuristic algorithms perform as well as the optimizing algorithms. No generalizable conclusions could be reached, however, about which algorithm should be used based on series and forecast characteristics. © 1997 John Wiley & Sons, Ltd.     

Non-Gaussian seasonal adjustment: X-12-ARIMA versus robust structural models

This study compares X-12-ARIMA and MING, two new seasonal adjustment methods designed to handle outliers and structural changes in a time series. X-12-ARIMA is a successor to the X-11-ARIMA seasonal adjustment method, and is being developed at the US Bureau of the Census. MING is a ‘Mixture based Non-Gaussian’ method for seasonal adjustment using time series structural models and is implemented as a function in the S-Plus language. The procedures are compared using 29 macroeconomic time series from the US Bureau of the Census. These series have both outliers and structural changes, providing a good testbed for comparing non-Gaussian methods. For the 29 series, the X-12-ARIMA decomposition consistently leads to smoother seasonal factors which are as or more ‘flexible’ than the MING seasonal component. On the other hand, MING is more stable, particularly in the way it handles outliers and level shifts. This study relies heavily on graphical tools for comparing seasonal adjustment methods.     

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.     

Using the bootstrap for improved ARIMA model identification

This paper presents a new method of identifying ARIMA time-series models. We use the bootstrap technique in estimating the distribution of sample autocorrelations both separately and in a simultaneous inference setting. The bootstrap has the advantage of being nonparametric and thus free of reliance on asymptotic normality, which may not hold for short or medium-size series. The simultaneous procedure is unique, as it has no feasible parametric alternatives. An application to exchange rates illustrates our methodology. In the example chosen, we are able to produce better forecasts using the model identified via the bootstrap technique.     

The role of prices in models of innovation diffusion

When evaluating the launch of a new product or service, forecasts of the diffusion path and the effects of the marketing mix are critically important. Currently no unified framework exists to provide guidelines on the inclusion and specification of marketing mix variables into models of innovation diffusion. The objective of this research is to examine empirically the role of prices in diffusion models, in order to establish whether price can be incorporated effectively into the simpler time-series models. Unlike existing empirical research which examines the models' fit to historical data, we examine the predictive validity of alternative models. Only if the incorporation of prices improves the predictive performance of diffusion models can it be argued that these models have validity. A series of diffusion models which include prices are compared against a number of well-accepted diffusion models, including the Bass (1969) model, and more recently developed ‘flexible’ diffusion models. For short data series and long-lead time forecasting, the situation typical of practical situations, price rarely added to the forecasting capability of simpler time-series models. Copyright © 1998 John Wiley & Sons, Ltd.     

Periodically integrated subset autoregressions for dutch industrial production and money stock

The univariate quarterly Dutch series of industrial production and money stock are both modelled with a periodically integrated subset autoregression (PISA). This model for a non-stationary series allows the lag orders, the values of the parameters and the cyclical patterns to vary over the seasons. The PISA models are found by applying a general-to-simple specification strategy, which deals with non-stationarity and periodicity simultaneously. It is found that the two series show a common asymmetric cyclical behaviour. This paper further proposes a test for periodicity in the errors, with which it is argued that a non-periodic model for the industrial production and money stock is misspecified and that seasonal adjustment does not remove periodicity in the autocorrelation function.     

Simulating the European economies under alternative monetary policy assumptions

This paper examines the implications of alternative monetary policy rules for economic stabilization within Europe, using the OECD world model, INTERLINK. The results suggest that policy linkage through the Exchange Rate Mechanism will have differing effects on the effectiveness of stabilization policies depending on the nature of economic shocks. For demand shocks, the choice of monetary rule in the country of the ‘anchor’ currency is of more consequence than the flexibility of exchange rates. For supply shocks, exchange rate rigidity is likely to have more problematic effects on economic adjustment. Spillover effects are also important when the shock is felt primarily by the ‘anchor’ economy.     

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.     

When and how to use scenario planning: A heuristic approach with illustration

This paper offers a step-by-step analysis of a heuristic approach to scenario planning, taking a managerial perspective. The scenario method is contrasted in general with more traditional planning techniques, which tend to perform less well when faced with high uncertainty and complexity. An actual case involving a manufacturing company is used to illustrate the main steps of the proposed heuristic. Its essence is to identify relevant trends and uncertainties, and blend them into scenarios that are internally consistent. In addition, the scenarios should bound the range of plausible uncertainties and challenge managerial thinking. Links to decision making are examined next, including administrative policies as well as integrative techniques. At the strategic level, a key-success-factor matrix is proposed for integrating scenarios, competitor analysis and strategic vision. At the operational level, Monte Carlo simulation is suggested and illustrated as one useful technique for combining scenario thinking with formal project evaluation (after appropriate translations). The paper concludes with a general discussion of scenario planning, to place it in a broader perspective.     

Forecasting volatility in commodity markets

This paper uses recent advances in time-series modeling to derive long-horizon forecasts of commodity price volatility which incorporate investors' expectations of volatility. Our results are promising. We compare several different forecasts of commodity price volatility, which we divide into three categories: (1) forecasts using only expectations derived from options prices; (2) forecasts using only time-series modeling; and (3) forecasts which combine market expectations and time-series methods. The forecasts in (1) and (2) are used extensively in the literature, while those in (3) are new in this paper. On comparing these different forecasts, we find that our proposed forecasts from category (3) outperform both market expectations forecasts and time-series forecasts. This result holds both in and out of sample for virtually all commodities considered.     

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.     

Time-series analysis supported by power transformations

This paper presents some procedures aimed at helping an applied time-series analyst in the use of power transformations. Two methods are proposed for selecting a variance-stabilizing transformation and another for bias-reduction of the forecast in the original scale. Since these methods are essentially model-independent, they can be employed with practically any type of time-series model. Some comparisons are made with other methods currently available and it is shown that those proposed here are either easier to apply or are more general, with a performance similar to or better than other competing procedures.     

Model uncertainty and forecast accuracy

In time-series analysis, a model is rarely pre-specified but rather is typically formulated in an iterative, interactive way using the given time-series data. Unfortunately the properties of the fitted model, and the forecasts from it, are generally calculated as if the model were known in the first place. This is theoretically incorrect, as least squares theory, for example, does not apply when the same data are used to formulates and fit a model. Ignoring prior model selection leads to biases, not only in estimates of model parameters but also in the subsequent construction of prediction intervals. The latter are typically too narrow, partly because they do not allow for model uncertainty. Empirical results also suggest that more complicated models tend to give a better fit but poorer ex-ante forecasts. The reasons behind these phenomena are reviewed. When comparing different forecasting models, the BIC is preferred to the AIC for identifying a model on the basis of within-sample fit, but out-of-sample forecasting accuracy provides the real test. Alternative approaches to forecasting, which avoid conditioning on a single model, include Bayesian model averaging and using a forecasting method which is not model-based but which is designed to be adaptable and robust.     

Structural Time-series Modelling of Monetary Aggregates: A Case Study for Eleven European Countries

Monetary aggregates for eleven European countries are analysed using the structural time-series methodology, paying special attention to unit root issues. Estimation of the parameters of the models is carried out by applying the asymptotic least squares (ALS) procedure. A comparison with the maximum likelihood estimates obtained via the Kalman filter shows that ALS is an alternative to Kalman filter estimation. The empirical results show that for only a small number of series the four variance parameters of the basic structural model are strictly positive. For the majority of the series the variance of the irregular component is equal to 0.©1997 John Wiley & Sons, Ltd.