Forecasting economic time series that require a power transformation: Case of state tax receipts

In this study, time series analysis is applied to the problem of forecasting state income tax receipts. The data series is of special interest since it exhibits a strong trend with a high multiplicative seasonal component. An appropriate model is identified by simultaneous estimation of the parameters of the power transformation and the ARMA model using the Schwarz (1978) Bayesian information criterion. The forecasting performance of the time series model obtained from this procedure is compared with alternative time series and regression models. The study illustrates how an information criterion can be employed for identifying time series models that require a power transformation, as exemplified by state tax receipts. It also establishes time series analysis as a viable technique for forecasting state tax receipts.     

A forecasting procedure for nonlinear autoregressive time series models

Forecasting for nonlinear time series is an important topic in time series analysis. Existing numerical algorithms for multi‐step‐ahead forecasting ignore accuracy checking, alternative Monte Carlo methods are also computationally very demanding and their accuracy is difficult to control too. In this paper a numerical forecasting procedure for nonlinear autoregressive time series models is proposed. The forecasting procedure can be used to obtain approximate m‐step‐ahead predictive probability density functions, predictive distribution functions, predictive mean and variance, etc. for a range of nonlinear autoregressive time series models. Examples in the paper show that the forecasting procedure works very well both in terms of the accuracy of the results and in the ability to deal with different nonlinear autoregressive time series models. Copyright © 2005 John Wiley & Sons, Ltd.     

A hybrid model considering cointegration for interval-valued pork price forecasting in China

Compared with point forecasting, interval forecasting is believed to be more effective and helpful in decision making, as it provides more information about the data generation process. Based on the well-established “linear and nonlinear” modeling framework, a hybrid model is proposed by coupling the vector error correction model (VECM) with artificial intelligence models which consider the cointegration relationship between the lower and upper bounds (Coin-AIs). VECM is first employed to fit the original time series with the residual error series modeled by Coin-AIs. Using pork price as a research sample, the empirical results statistically confirm the superiority of the proposed VECM-CoinAIs over other competing models, which include six single models and six hybrid models. This result suggests that considering the cointegration relationship is a workable direction for improving the forecast performance of the interval-valued time series. Moreover, with a reasonable data transformation process, interval forecasting is proven to be more accurate than point forecasting.     

A Neuro‐wavelet Model for the Short‐Term Forecasting of High‐Frequency Time Series of Stock Returns

We propose a wavelet neural network (neuro‐wavelet) model for the short‐term forecast of stock returns from high‐frequency financial data. The proposed hybrid model combines the capability of wavelets and neural networks to capture non‐stationary nonlinear attributes embedded in financial time series. A comparison study was performed on the predictive power of two econometric models and four recurrent neural network topologies. Several statistical measures were applied to the predictions and standard errors to evaluate the performance of all models. A Jordan net that used as input the coefficients resulting from a non‐decimated wavelet‐based multi‐resolution decomposition of an exogenous signal showed a consistent superior forecasting performance. Reasonable forecasting accuracy for the one‐, three‐ and five step‐ahead horizons was achieved by the proposed model. The procedure used to build the neuro‐wavelet model is reusable and can be applied to any high‐frequency financial series to specify the model characteristics associated with that particular series. Copyright © 2013 John Wiley & Sons, Ltd.     

Using CAViaR Models with Implied Volatility for Value‐at‐Risk Estimation

This paper proposes value‐at risk (VaR) estimation methods that are a synthesis of conditional autoregressive value at risk (CAViaR) time series models and implied volatility. The appeal of this proposal is that it merges information from the historical time series and the different information supplied by the market's expectation of risk. Forecast‐combining methods, with weights estimated using quantile regression, are considered. We also investigate plugging implied volatility into the CAViaR models—a procedure that has not been considered in the VaR area so far. Results for daily index returns indicate that the newly proposed methods are comparable or superior to individual methods, such as the standard CAViaR models and quantiles constructed from implied volatility and the empirical distribution of standardised residuals. We find that the implied volatility has more explanatory power as the focus moves further out into the left tail of the conditional distribution of S&P 500 daily returns. Copyright © 2012 John Wiley & Sons, Ltd.     

Detection of regime switches between stationary and nonstationary processes and economic forecasting

It often occurs that no model may be exactly right, and that different portions of the data may favour different models. The purpose of this paper is to propose a new procedure for the detection of regime switches between stationary and nonstationary processes in economic time series and to show its usefulness in economic forecasting. In the proposed procedure, time series observations are divided into several segments, and a stationary or nonstationary autoregressive model is fitted to each segment. The goodness of fit of the global model composed of these local models is evaluated using the corresponding information criterion, and the division which minimizes the information criterion defines the best model. Simulation and forecasting results show the efficacy and limitations of the proposed procedure. Copyright © 2005 John Wiley & Sons, Ltd.     

A non‐linear dynamic model for multiplicative seasonal‐trend decomposition

A non‐linear dynamic model is introduced for multiplicative seasonal time series that follows and extends the X‐11 paradigm where the observed time series is a product of trend, seasonal and irregular factors. A selection of standard seasonal and trend component models used in additive dynamic time series models are adapted for the multiplicative framework and a non‐linear filtering procedure is proposed. The results are illustrated and compared to X‐11 and log‐additive models using real data. In particular it is shown that the new procedures do not suffer from the trend bias present in log‐additive models. Copyright © 2002 John Wiley & Sons, Ltd.     

Time series forecasting models involving power transformations

In this paper we discuss procedures for overcoming some of the problems involved in fitting autoregressive integrated moving average forecasting models to time series data, when the possibility of incorporating an instantaneous power transformation of the data into the analysis is contemplated. The procedures are illustrated using series of quarterly observations on corporate earnings per share.     

Deletion diagnostics for transformations of time series

Deletion diagnostics are derived for the effect of individual observations on the estimated transformation of a time series. The paper uses the modified power transformation of Box and Cox to provide a parametric family of transformations. Inference about the transformation parameter is made through regression on a constructed variable. The effect of deletion of observations on residuals and on the estimate of the regression parameter are obtained. Index plots of the diagnostic quantities are shown to be highly informative. Structural time series modelling is used, so that the results readily extend to inference about regression on other explanatory variables.     

On a robust test for SETAR‐type nonlinearity in time series analysis

There has been growing interest in exploiting potential forecast gains from the nonlinear structure of self‐exciting threshold autoregressive (SETAR) models. Statistical tests have been proposed in the literature to help analysts check for the presence of SETAR‐type nonlinearities in observed time series. However, previous studies show that classical nonlinearity tests are not robust to additive outliers. In practice, time series outliers are not uncommonly encountered. It is important to develop a more robust test for SETAR‐type nonlinearity in time series analysis and forecasting. In this paper we propose a new robust nonlinearity test and the asymptotic null distribution of the test statistic is derived. A Monte Carlo experiment is carried out to compare the power of the proposed test with other existing tests under the influence of time series outliers. The effects of additive outliers on nonlinearity tests with misspecification of the autoregressive order are also studied. The results indicate that the proposed method is preferable to the classical tests when the observations are contaminated with outliers. Finally, we provide illustrative examples by applying the statistical tests to three real datasets. Copyright © 2009 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.     

Building neural network models for time series: a statistical approach

This paper is concerned with modelling time series by single hidden layer feedforward neural network models. A coherent modelling strategy based on statistical inference is presented. Variable selection is carried out using simple existing techniques. The problem of selecting the number of hidden units is solved by sequentially applying Lagrange multiplier type tests, with the aim of avoiding the estimation of unidentified models. Misspecification tests are derived for evaluating an estimated neural network model. All the tests are entirely based on auxiliary regressions and are easily implemented. A small‐sample simulation experiment is carried out to show how the proposed modelling strategy works and how the misspecification tests behave in small samples. Two applications to real time series, one univariate and the other multivariate, are considered as well. Sets of one‐step‐ahead forecasts are constructed and forecast accuracy is compared with that of other nonlinear models applied to the same series. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Forecasting daily foreign exchange rates using genetically optimized neural networks

Forecasting currency exchange rates is an important financial problem that has received much attention especially because of its intrinsic difficulty and practical applications. The statistical distribution of foreign exchange rates and their linear unpredictability are recurrent themes in the literature of international finance. Failure of various structural econometric models and models based on linear time series techniques to deliver superior forecasts to the simplest of all models, the simple random walk model, have prompted researchers to use various non‐linear techniques. A number of non‐linear time series models have been proposed in the recent past for obtaining accurate prediction results, in an attempt to ameliorate the performance of simple random walk models. In this paper, we use a hybrid artificial intelligence method, based on neural network and genetic algorithm for modelling daily foreign exchange rates. A detailed comparison of the proposed method with non‐linear statistical models is also performed. The results indicate superior performance of the proposed method as compared to the traditional non‐linear time series techniques and also fixed‐geometry neural network models. Copyright © 2002 John Wiley & Sons, Ltd.     

A Robust Test for Threshold‐Type Nonlinearity in Multivariate Time Series Analysis

There is growing interest in exploring potential forecast gains from the nonlinear structure of multivariate threshold autoregressive (MTAR) models. A least squares‐based statistical test has been proposed in the literature. However, previous studies on univariate time series analysis show that classical nonlinearity tests are often not robust to additive outliers. The outlier problem is expected to pose similar difficulties for multivariate nonlinearity tests. In this paper, we propose a new and robust MTAR‐type nonlinearity test, and derive the asymptotic null distribution of the test statistic. A Monte Carlo experiment is carried out to compare the power of the proposed test with that of the least squares‐based test under the influence of additive time series outliers. The results indicate that the proposed method is preferable to the classical test when observations are contaminated by outliers. Finally, we provide illustrative examples by applying the statistical tests to two real datasets. Copyright © 2015 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.     

Short‐term forecasting of industrial electricity consumption in Brazil

This paper presents short‐term forecasting methods applied to electricity consumption in Brazil. The focus is on comparing the results obtained after using two distinct approaches: dynamic non‐linear models and econometric models. The first method, that we propose, is based on structural statistical models for multiple time series analysis and forecasting. It involves non‐observable components of locally linear trends for each individual series and a shared multiplicative seasonal component described by dynamic harmonics. The second method, adopted by the electricity power utilities in Brazil, consists of extrapolation of the past data and is based on statistical relations of simple or multiple regression type. To illustrate the proposed methodology, a numerical application is considered with real data. The data represents the monthly industrial electricity consumption in Brazil from the three main power utilities: Eletropaulo, Cemig and Light, situated at the major energy‐consuming states, Sao Paulo, Rio de Janeiro and Minas Gerais, respectively, in the Brazilian Southeast region. The chosen time period, January 1990 to September 1994, corresponds to an economically unstable period just before the beginning of the Brazilian Privatization Program. Implementation of the algorithms considered in this work was made via the statistical software S‐PLUS. Copyright © 1999 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.     

A linear benchmark for forecasting GDP growth and inflation?

Predicting the future evolution of GDP growth and inflation is a central concern in economics. Forecasts are typically produced either from economic theory‐based models or from simple linear time series models. While a time series model can provide a reasonable benchmark to evaluate the value added of economic theory relative to the pure explanatory power of the past behavior of the variable, recent developments in time series analysis suggest that more sophisticated time series models could provide more serious benchmarks for economic models. In this paper we evaluate whether these complicated time series models can outperform standard linear models for forecasting GDP growth and inflation. We consider a large variety of models and evaluation criteria, using a bootstrap algorithm to evaluate the statistical significance of our results. Our main conclusion is that in general linear time series models can hardly be beaten if they are carefully specified. However, we also identify some important cases where the adoption of a more complicated benchmark can alter the conclusions of economic analyses about the driving forces of GDP growth and inflation. Copyright © 2008 John Wiley & Sons, Ltd.     

A Dynamic Model Selection Procedure to Forecast Using Multi-Process Models

Multi-process models are particularly useful when observations appear extreme relative to their forecasts, because they allow for explanations of any behaviour of a time series, considering more generating sources simultaneously. In this paper, the multi-process approach is extended by developing a dynamic procedure to assess the weights of the various sources, alias the prior probabilities of the rival models, that compete in the collection to make forecasts. The new criterion helps the forecasting system to learn about the most plausible scenarios for the time series, considering all the combinations of consecutive models to be a function of the magnitude of the one-step-ahead forecast error. Throughout the paper, the different treatments of outliers and structural changes are highlighted using the concepts of robustness and sensitivity. Finally, the dynamic selection procedure is tested on the CP6 dataset, showing an effective improvement in the overall predictive ability of multi-process models whenever anomalous observations occur. © 1997 John Wiley & Sons, Ltd.