ARIMA models of the price level: An assessment of the multilevel adaptive learning process in the USA

This paper estimates the ARIMA processes for the observed and expected price level corresponding to the three-level adaptive expectations model proposed by Jacobs and Jones (1980). These univariate processes are then compared with the best-fit ARIMA model. The results indicate that the best-fit model for the observed price level is a restricted version of the two-level adaptive learning process specified in terms of prices, suggesting a simple adaptive rule in the inflation rate. A comparison of the time-series forecasts from the best-fit model with the mean responses to the ASA-NBER survey shows no significant difference in their accuracy. The time-series forecasts are, however, conditionally efficient. The best-fit ARIMA model for expected prices measured by the ASA-NBER consensus forecasts does not correspond to any version of the Jacobs and Jones model.     

Sales forecasting using multi-equation transfer function models

The purpose of this study is first, to demonstrate how multivariate forecasting models can be effectively used to generate high performance forecasts for typical business applications. Second, this study compares the forecasts generated by a simultaneous transfer function model (STF) model and a white noise regression model with that of a univariate ARIMA model. The accuracy of these forecasting models is judged using their residual variances and forecasting errors in a post-sample period. It is found that ignoring the residual serial correlation can greatly degrade the forecasting performance of a multi-variable model, and in some situations, cause a multi-variable model to perform inferior to a univariate ARIMA model. This paper also demonstrates how a forecaster can use an STF model to compute both the multi-step ahead forecasts and their variances easily.     

A BVAR model for the connecticut economy

A Bayesian vector autoregressive (BVAR) model is developed for the Connecticut economy to forecast the unemployment rate, nonagricultural employment, real personal income, and housing permits authorized. The model includes both national and state variables. The Bayesian prior is selected on the basis of the accuracy of the out-of-sample forecasts. We find that a loose prior generally produces more accurate forecasts. The out-of-sample accuracy of the BVAR forecasts is also compared with that of forecasts from an unrestricted VAR model and of benchmark forecasts generated from univariate ARIMA models. The BVAR model generally produces the most accurate short- and long-term out-of-sample forecasts for 1988 through 1992. It also correctly predicts the direction of change.     

Level shifts,temporary changes and forecasting

The purpose of this paper is to analyze the effect of not treating Level Shift and Temporary Change outliers on the point forecasts and prediction intervals from ARIMA models. One of the principal conclusions is that the outliers of the type discussed here considerably increase the inaccuracy of point forecasts, although the latter depends not only on the time of occurrence of the outliers from the forecast origin but also on the type of ARIMA processes under consideration. However, regardless of the time of occurrence and of the type of ARIMA processes considered, Level Shifts and Temporary Changes significantly affect the width of the prediction intervals.     

Forecasting an aggregate of cointegrated disaggregates

This study examines the problem of forecasting an aggregate of cointegrated disaggregates. It first establishes conditions under which forecasts of an aggregate variable obtained from a disaggregate VECM will be equal to those from an aggregate, univariate time series model, and develops a simple procedure for testing those conditions. The paper then uses Monte Carlo simulations to show, for a finite sample, that the proposed test has good size and power properties and that whether a model satisfies the aggregation conditions is closely related to out‐of‐sample forecast performance. The paper then shows that ignoring cointegration and specifying the disaggregate model as a VAR in differences can significantly affect analyses of aggregation, with the VAR‐based test for aggregation possibly leading to faulty inference and the differenced VAR forecasts potentially understating the benefits of disaggregate information. Finally, analysis of an empirical problem confirms the basic results. Copyright © 2000 John Wiley & Sons, Ltd.     

Prior Information and ARIMA Forecasting

Using the method of ARIMA forecasting with benchmarks developed in this paper, it is possible to obtain forecasts which take into account the historical information of a series, captured by an ARIMA model (Box and Jenkins, 1970), as well as partial prior information about the forecasts. Prior information takes the form of benchmarks. These originate from the advice of experts, from forecasts of an annual econometric model or simply from pessimistic, realistic or optimistic scenarios contemplated by the analyst of the current economic situation. The benchmarks may represent annual levels to be achieved, neighbourhoods to be reached for a given time period, movements to be displayed or more generally any linear criteria to be satisfied by the forecasted values. The forecaster may then exercise his current economic evaluation and judgement to the fullest extent in deriving forecasts, since the laboriousness experienced without a systematic method is avoided.     

The Effect of Estimating Parameters on Long‐Term Forecasts for Cointegrated Systems

This paper concerns Long‐term forecasts for cointegrated processes. First, it considers the case where the parameters of the model are known. The paper analytically shows that neither cointegration nor integration constraint matters in Long‐term forecasts. It is an alternative implication of Long‐term forecasts for cointegrated processes, extending the results of previous influential studies. The appropriate Mote Carlo experiment supports our analytical result. Secondly, and more importantly, it considers the case where the parameters of the model are estimated. The paper shows that accuracy of the estimation of the drift term is crucial in Long‐term forecasts. Namely, the relative accuracy of various Long‐term forecasts depends upon the relative magnitude of variances of estimators of the drift term. It further experimentally shows that in finite samples the univariate ARIMA forecast, whose drift term is estimated by the simple time average of differenced data, is better than the cointegrated system forecast, whose parameters are estimated by the well‐known Johansen's ML method. Based upon finite sample experiments, it recommends the univariate ARIMA forecast rather than the conventional cointegrated system forecast in finite samples for its practical usefulness and robustness against model misspecifications. Copyright © 2011 John Wiley & Sons, Ltd.     

Linear constraints,robust-weighting and efficient composite modeling

Recent studies have shown that composite forecasting produces superior forecasts when compared to individual forecasts. This paper extends the existing literature by employing linear constraints and robust regression techniques in composite model building. Security analysts forecasts may be improved when combined with time series forecasts for a diversified sample of 261 firms with a 1980-1982 post-sample estimation period. The mean square error of analyst forecasts may be reduced by combining analyst and univariate time series model forecasts in constrained and unconstrained ordinary least squares regression models. These reductions are very interesting when one finds that the univariate time series model forecasts do not substantially deviate from those produced by ARIMA (0,1,1) processes. Moreover, security analysts' forecast errors may be significantly reduced when constrained and unconstrained robust regression analyses are employed.     

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.     

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.     

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.     

Forecast intervals of net migration: the case of the Netherlands

This study addresses problems concerning the forecasting of net migration in the preparation of population forecasts. "As the width of forecast intervals for migration in single years differs strongly from that of an interval for average migration during the forecast period, it is important that the forecaster indicates which type of interval is presented. A comparison of forecast intervals for net migration obtained from an ARIMA model to intervals in official Dutch national population forecasts shows that the uncertainty on migration has been underestimated in past official forecasts."     

An evaluation of quarterly national institute forecasts

This paper examines the quarterly forecasts by the U.K. National Institute of Economic and Social Research of the rate of inflation and the change in real gross domestic product and its components for horizons of one to four quarters ahead in the U.K. The forecasts are tested to see if they satisfy three implications of the rational expectations hypothesis: unbiasedness, efficiency and consistency. Explicit consideration is given to the information set available when the forecasts are made. In general, the data are consistent with the rational expectations hypothesis and our results provide encouragement for the view that aggregate expectations will meet the ex post requirements of rationality.     

Forecasting contemporaneous aggregates and the combination of forecasts: The case of the U.K. monetary aggregates

A number of papers in recent years have investigated the problems of forecasting contemporaneously aggregated time series and of combining alternative forecasts of a time series. This paper considers the integration of both approaches within the example of assessing the forecasting performance of models for two of the U.K. monetary aggregates, £M3 and MO. It is found that forecasts from a time series model for aggregate £M3 are superior to aggregated forecasts from individual models fitted to either the components or counterparts of £M3 and that an even better forecast is obtained by forming a linear combination of the three alternatives. For MO, however, aggregated forecasts from its components prove superior to either the forecast from the aggregate itself or from a linear combination of the two.     

Some comments on the initialization of exponential smoothing

It is shown that the traditional choice for the initial smoothed statistics in general exponential smoothing leads to the same forecasts as the equivalent ARIMA model, provided that one uses zero starting values for the initial shocks. In addition, an initialization which uses ‘backforecasts’ as initial smoothed statistics is considered, and its relationship to unconditional least squares is explored.     

Can cointegration‐based forecasting outperform univariate models? An application to Asian exchange rates

Conventional wisdom holds that restrictions on low‐frequency dynamics among cointegrated variables should provide more accurate short‐ to medium‐term forecasts than univariate techniques that contain no such information; even though, on standard accuracy measures, the information may not improve long‐term forecasting. But inconclusive empirical evidence is complicated by confusion about an appropriate accuracy criterion and the role of integration and cointegration in forecasting accuracy. We evaluate the short‐ and medium‐term forecasting accuracy of univariate Box–Jenkins type ARIMA techniques that imply only integration against multivariate cointegration models that contain both integration and cointegration for a system of five cointegrated Asian exchange rate time series. We use a rolling‐window technique to make multiple out of sample forecasts from one to forty steps ahead. Relative forecasting accuracy for individual exchange rates appears to be sensitive to the behaviour of the exchange rate series and the forecast horizon length. Over short horizons, ARIMA model forecasts are more accurate for series with moving‐average terms of order >1. ECMs perform better over medium‐term time horizons for series with no moving average terms. The results suggest a need to distinguish between ‘sequential’ and ‘synchronous’ forecasting ability in such comparisons. Copyright © 2002 John Wiley & Sons, Ltd.     

Forecasting growth and inflation in an enlarged euro area

We compare models for forecasting growth and inflation in the enlarged euro area. Forecasts are built from univariate autoregressive and single‐equation models. The analysis is undertaken for both individual countries and EU aggregate variables. Aggregate forecasts are constructed by both employing aggregate variables and by aggregating country‐specific forecasts. Using financial variables for country‐specific forecasts tends to add little to the predictive ability of a simple AR model. However, they do help to predict EU aggregates. Furthermore, forecasts from pooling individual country models usually outperform those of the aggregate itself, particularly for the EU25 grouping. This is particularly interesting from the perspective of the European Central Bank, who require forecasts of economic activity and inflation to formulate appropriate economic policy across the enlarged group. Copyright © 2008 John Wiley & Sons, Ltd.     

Seasonality in large-scale macroeconometric models

Macroeconomic indicators are typically appraised in seasonally adjusted form, and forecasts are often presented in a similar way (as annual changes, for example). Moreover, the quarterly macroeconomic models used in forecasting are commonly estimated from seasonally adjusted data. Nevertheless, these models can generate forecasts with seasonal patterns, and this paper assesses the cause and cure of this phenomenon. It is found that forecast seasonality is induced by seasonality in the various inputs: exogenous variables, residual adjustments, the dynamic specification of certain equations, and annual changes in policy variables. Series changing annually but observed quarterly are termed ‘intercalated series’, and are simple examples of periodic processes. Forecast seasonality can be removed by appropriate adjustment of all these inputs. Models containing explicit future expectations variables solved in a model-consistent manner are also considered: numerical sensitivity to the terminal quarter may result from terminal conditions that require adjustment when seasonality is present.     

Judgmental adjustment of earnings forecasts

Earnings forecasts have received a great deal of attention, much of which has centered on the comparative accuracy of judgmental and objective forecasting methods. Recently, studies have focused on the use of combinations of subjective and objective forecasts to improve forecast accuracy. This research offers an extension on this theme by subjectively modifying an objective forecast. Specifically, ARIMA forecasts are judgmentally adjusted by analysts using a structured approach based on Saaty's (1980) analytic hierarchy process. The results show that the accuracy of the unadjusted objective forecasts can be improved when judgmentally adjusted.     

Forecasting the federal budget with time-series models

The stochastic properties of conventionally denned federal expenditures and revenues are examined, and cointegration is found. Alternative time-series models-univariate ARIMA models, vector autoregressions in levels and differences, and an error correction model-are specified and estimated using quarterly data from 1955:1 through 1979:4. Updated forecasts for up to three years beyond the sample period are evaluated against actual expenditures, revenues and the deficit. The vector autoregression in levels shows evidence of nonstationarity, which leads to strong biases in the forecasts. The remaining models produce forecasts that are satisfactory by the mean squared error criterion, and the magnitudes of biases at the longer horizons are significantly smaller than those of the official forecasts.