Functional methods for time series prediction: a nonparametric approach

The problem of prediction in time series using nonparametric functional techniques is considered. An extension of the local linear method to regression with functional explanatory variable is proposed. This forecasting method is compared with the functional Nadaraya–Watson method and with finite‐dimensional nonparametric predictors for several real‐time series. Prediction intervals based on the bootstrap and conditional distribution estimation for those nonparametric methods are also compared. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Forecasting Australia's real house price index: A comparison of time series and machine learning methods

We employ 47 different algorithms to forecast Australian log real house prices and growth rates, and compare their ability to produce accurate out-of-sample predictions. The algorithms, which are specified in both single- and multi-equation frameworks, consist of traditional time series models, machine learning (ML) procedures, and deep learning neural networks. A method is adopted to compute iterated multistep forecasts from nonlinear ML specifications. While the rankings of forecast accuracy depend on the length of the forecast horizon, as well as on the choice of the dependent variable (log price or growth rate), a few generalizations can be made. For one- and two-quarter-ahead forecasts we find a large number of algorithms that outperform the random walk with drift benchmark. We also report several such outperformances at longer horizons of four and eight quarters, although these are not statistically significant at any conventional level. Six of the eight top forecasts (4 horizons × 2 dependent variables) are generated by the same algorithm, namely a linear support vector regressor (SVR). The other two highest ranked forecasts are produced as simple mean forecast combinations. Linear autoregressive moving average and vector autoregression models produce accurate olne-quarter-ahead predictions, while forecasts generated by deep learning nets rank well across medium and long forecast horizons.     

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.     

A semi‐parametric time series approach in modeling hourly electricity loads

In this paper we develop a semi‐parametric approach to model nonlinear relationships in serially correlated data. To illustrate the usefulness of this approach, we apply it to a set of hourly electricity load data. This approach takes into consideration the effect of temperature combined with those of time‐of‐day and type‐of‐day via nonparametric estimation. In addition, an ARIMA model is used to model the serial correlation in the data. An iterative backfitting algorithm is used to estimate the model. Post‐sample forecasting performance is evaluated and comparative results are presented. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimation procedures for structural time series models

A univariate structural time series model based on the traditional decomposition into trend, seasonal and irregular components is defined. A number of methods of computing maximum likelihood estimators are then considered. These include direct maximization of various time domain likelihood function. The asymptotic properties of the estimators are given and a comparison between the various methods in terms of computational efficiency and accuracy is made. The methods are then extended to models with explanatory variables.     

ARIMA model building and the time series analysis approach to forecasting

This paper reviews the approach to forecasting based on the construction of ARIMA time series models. Recent developments in this area are surveyed, and the approach is related to other forecasting methodologies.     

Highest-density forecast regions for nonlinear and non-normal time series models

Forecast regions are a common way to summarize forecast accuracy. They usually consist of an interval symmetric about the forecast mean. However, symmetric intervals may not be appropriate forecast regions when the forecast density is not symmetric and unimodal. With many modern time series models, such as those which are non-linear or have non-normal errors, the forecast densities are often asymmetric or multimodal. The problem of obtaining forecast regions in such cases is considered and it is proposed that highest-density forecast regions be used. A graphical method for presenting the results is discussed.     

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.     

Selection and estimation of component models for seasonal time series

We present a method for investigating the evolution of trend and seasonality in an observed time series. A general model is fitted to a residual spectrum, using components to represent the seasonality. We show graphically how well the fitted spectrum captures the evidence for evolving seasonality associated with the different seasonal frequencies. We apply the method to model two time series and illustrate the resulting forecasts and seasonal adjustment for one series. Copyright © 2000 John Wiley & Sons, Ltd.     

ARARMA models for time series analysis and forecasting

Methods of time series forecasting are proposed which can be applied automatically. However, they are not rote formulae, since they are based on a flexible philosophy which can provide several models for consideration. In addition it provides diverse diagnostics for qualitatively and quantitatively estimating how well one can forecast a series. The models considered are called ARARMA models (or ARAR models) because the model fitted to a long memory time series (t) is based on sophisticated time series analysis of AR (or ARMA) schemes (short memory models) fitted to residuals Y(t) obtained by parsimonious‘best lag’non-stationary autoregression. Both long range and short range forecasts are provided by an ARARMA model Section 1 explains the philosophy of our approach to time series model identification. Sections 2 and 3 attempt to relate our approach to some standard approaches to forecasting; exponential smoothing methods are developed from the point of view of prediction theory (section 2) and extended (section 3). ARARMA models are introduced (section 4). Methods of ARARMA model fitting are outlined (sections 5,6). Since‘the proof of the pudding is in the eating’, the methods proposed are illustrated (section 7) using the classic example of international airline passengers.     

A state-dependent linear recurrent formula with application to time series with structural breaks

An underlying assumption in Multivariate Singular Spectrum Analysis (MSSA) is that the time series are governed by a linear recurrent continuation. However, in the presence of a structural break, multiple series can be transferred from one homogeneous state to another over a comparatively short time breaking this assumption. As a consequence, forecasting performance can degrade significantly. In this paper, we propose a state-dependent model to incorporate the movement of states in the linear recurrent formula called a State-Dependent Multivariate SSA (SD-MSSA) model. The proposed model is examined for its reliability in the presence of a structural break by conducting an empirical analysis covering both synthetic and real data. Comparison with standard MSSA, BVAR, VAR and VECM models shows the proposed model outperforms all three models significantly.     

Moving average threshold heterogeneous autoregressive (MAT-HAR) models

We propose moving average threshold heterogeneous autoregressive (MAT-HAR) models as a novel combination of heterogeneous autoregression (HAR) and threshold autoregression (TAR). The MAT-HAR has multiple groups of lags of a target series, and a threshold term can appear in each group. The threshold is a moving average of lagged target series, which guarantees time-varying thresholds and simple estimation via least squares. We show via Monte Carlo simulations that the MAT-HAR has sharp in-sample and out-of-sample performance. An empirical application on the industrial production of Japan suggests that significant threshold effects exist, and the MAT-HAR has a higher forecast accuracy than the HAR.     

A hybrid forecasting approach for piece‐wise stationary time series

We consider the problem of forecasting a stationary time series when there is an unknown mean break close to the forecast origin. Based on the intercept‐correction methods suggested by Clements and Hendry (1998) and Bewley (2003), a hybrid approach is introduced, where the break and break point are treated in a Bayesian fashion. The hyperparameters of the priors are determined by maximizing the marginal density of the data. The distributions of the proposed forecasts are derived. Different intercept‐correction methods are compared using simulation experiments. Our hybrid approach compares favorably with both the uncorrected and the intercept‐corrected forecasts. Copyright © 2006 John Wiley & Sons, Ltd.     

Order series method for forecasting non‐Gaussian time series

A new forecasting non‐Gaussian time series method based on order series transformation properties has been proposed. The proposed method improves Yu's method without using Hermite polynomial expansion to process nonlinear instantaneous transformations and provides acceptable forecasting accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

The versatility of spectrum analysis for forecasting financial time series

The versatility of the one‐dimensional discrete wavelet analysis combined with wavelet and Burg extensions for forecasting financial times series with distinctive properties is illustrated with market data. Any time series of financial assets may be decomposed into simpler signals called approximations and details in the framework of the one‐dimensional discrete wavelet analysis. The simplified signals are recomposed after extension. The final output is the forecasted time series which is compared to observed data. Results show the pertinence of adding spectrum analysis to the battery of tools used by econometricians and quantitative analysts for the forecast of economic or financial time series.     

Variance estimation for multivariate dynamic linear models

The problem of estimating unknown observational variances in multivariate dynamic linear models is considered. Conjugate procedures are possible for univariate models and also for special very restrictive common components models but they are not generally applicable. However, for clarity of operation and in order to avoid numerical integration, it is desirable to have conjugacy or approximate conjugacy. Such an approximate procedure is proposed based upon a simple analytic approximation. It is exact for the sub-class of conjugate models and improves on a previous procedure based upon the Robust filter.     

Neural network versus econometric models in forecasting inflation

Artificial neural network modelling has recently attracted much attention as a new technique for estimation and forecasting in economics and finance. The chief advantages of this new approach are that such models can usually find a solution for very complex problems, and that they are free from the assumption of linearity that is often adopted to make the traditional methods tractable. In this paper we compare the performance of Back‐Propagation Artificial Neural Network (BPN) models with the traditional econometric approaches to forecasting the inflation rate. Of the traditional econometric models we use a structural reduced‐form model, an ARIMA model, a vector autoregressive model, and a Bayesian vector autoregression model. We compare each econometric model with a hybrid BPN model which uses the same set of variables. Dynamic forecasts are compared for three different horizons: one, three and twelve months ahead. Root mean squared errors and mean absolute errors are used to compare quality of forecasts. The results show the hybrid BPN models are able to forecast as well as all the traditional econometric methods, and to outperform them in some cases. Copyright © 2000 John Wiley & Sons, Ltd.     

Ex post and ex ante prediction of unobserved multivariate time series: a structural‐model based approach

A methodology for estimating high‐frequency values of an unobserved multivariate time series from low‐frequency values of and related information to it is presented in this paper. This is an optimal solution, in the multivariate setting, to the problem of ex post prediction, disaggregation, benchmarking or signal extraction of an unobservable stochastic process. Also, the problem of extrapolation or ex ante prediction is optimally solved and, in this context, statistical tests are developed for checking online the ocurrence of extreme values of the unobserved time series and consistency of future benchmarks with the present and past observed information. The procedure is based on structural or unobserved component models, whose assumptions and specification are validated with the data alone. Copyright © 2007 John Wiley & Sons, Ltd.     

Forecasting with latent structure time series models: an application to nominal interest rates

In this paper we develop a latent structure extension of a commonly used structural time series model and use the model as a basis for forecasting. Each unobserved regime has its own unique slope and variances to describe the process generating the data, and at any given time period the model predicts a priori which regime best characterizes the data. This is accomplished by using a multinomial logit model in which the primary explanatory variable is a measure of how consistent each regime has been with recent observations. The model is especially well suited to forecasting series which are subject to frequent and/or major shocks. An application to nominal interest rates shows that the behaviour of the three‐month US Treasury bill rate is adequately explained by three regimes. The forecasting accuracy is superior to that produced by a traditional single‐regime model and a standard ARIMA model with a conditionally heteroscedastic error. Copyright © 1999 John Wiley & Sons, Ltd.