Do seasonal unit roots matter for forecasting monthly industrial production?

We investigate the seasonal unit root properties of monthly industrial production series for 16 OECD countries within the context of a structural time series model. A basic version of this model assumes that there are 11 such seasonal unit roots. We propose to use model selection criteria (AIC and BIC) to examine if one or more of these are in fact stationary. We generally find that when these criteria indicate that a smaller number of seasonal unit roots can be assumed and hence that some seasonal roots are stationary, the corresponding model also gives more accurate one‐step‐ahead forecasts. Copyright © 2004 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.     

A nonparametric method for asymmetrically extending signal extraction filters

Two important problems in the X‐11 seasonal adjustment methodology are the construction of standard errors and the handling of the boundaries. We adapt the ‘implied model approach’ of Kaiser and Maravall to achieve both objectives in a nonparametric fashion. The frequency response function of an X‐11 linear filter is used, together with the periodogram of the differenced data, to define spectral density estimates for signal and noise. These spectra are then used to define a matrix smoother, which in turn generates an estimate of the signal that is linear in the data. Estimates of the signal are provided at all time points in the sample, and the associated time‐varying signal extraction mean squared errors are a by‐product of the matrix smoother theory. After explaining our method, it is applied to popular nonparametric filters such as the Hodrick–Prescott (HP), the Henderson trend, and ideal low‐pass and band‐pass filters, as well as X‐11 seasonal adjustment, trend, and irregular filters. Finally, we illustrate the method on several time series and provide comparisons with X‐12‐ARIMA seasonal adjustments. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

Asymmetries in conditional mean and variance: modelling stock returns by asMA‐asQGARCH

We propose a nonlinear time series model where both the conditional mean and the conditional variance are asymmetric functions of past information. The model is particularly useful for analysing financial time series where it has been noted that there is an asymmetric impact of good news and bad news on volatility (risk) transmission. We introduce a coherent framework for testing asymmetries in the conditional mean and the conditional variance, separately or jointly. To this end we derive both a Wald and a Lagrange multiplier test. Some of the new asymmetric model's moment properties are investigated. Detailed empirical results are given for the daily returns of the composite index of the New York Stock Exchange. There is strong evidence of asymmetry in both the conditional mean and the conditional variance functions. In a genuine out‐of‐sample forecasting experiment the performance of the best fitted asymmetric model, having asymmetries in both conditional mean and conditional variance, is compared with an asymmetric model for the conditional mean, and with no‐change forecasts. This is done both in terms of conditional mean forecasting as well as in terms of risk forecasting. Finally, the paper presents some evidence of asymmetries in the index stock returns of the Group of Seven (G7) industrialized countries. Copyright © 2004 John Wiley & Sons, Ltd.     

Dynamic harmonic regression

This paper describes in detail a flexible approach to nonstationary time series analysis based on a Dynamic Harmonic Regression (DHR) model of the Unobserved Components (UC) type, formulated within a stochastic state space setting. The model is particularly useful for adaptive seasonal adjustment, signal extraction and interpolation over gaps, as well as forecasting or backcasting. The Kalman Filter and Fixed Interval Smoothing algorithms are exploited for estimating the various components, with the Noise Variance Ratio and other hyperparameters in the stochastic state space model estimated by a novel optimization method in the frequency domain. Unlike other approaches of this general type, which normally exploit Maximum Likelihood methods, this optimization procedure is based on a cost function defined in terms of the difference between the logarithmic pseudo‐spectrum of the DHR model and the logarithmic autoregressive spectrum of the time series. The cost function not only seems to yield improved convergence characteristics when compared with the alternative ML cost function, but it also has much reduced numerical requirements. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

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 non‐Gaussian generalization of the Airline model for robust seasonal adjustment

In their seminal book Time Series Analysis: Forecasting and Control, Box and Jenkins (1976) introduce the Airline model, which is still routinely used for the modelling of economic seasonal time series. The Airline model is for a differenced time series (in levels and seasons) and constitutes a linear moving average of lagged Gaussian disturbances which depends on two coefficients and a fixed variance. In this paper a novel approach to seasonal adjustment is developed that is based on the Airline model and that accounts for outliers and breaks in time series. For this purpose we consider the canonical representation of the Airline model. It takes the model as a sum of trend, seasonal and irregular (unobserved) components which are uniquely identified as a result of the canonical decomposition. The resulting unobserved components time series model is extended by components that allow for outliers and breaks. When all components depend on Gaussian disturbances, the model can be cast in state space form and the Kalman filter can compute the exact log‐likelihood function. Related filtering and smoothing algorithms can be used to compute minimum mean squared error estimates of the unobserved components. However, the outlier and break components typically rely on heavy‐tailed densities such as the t or the mixture of normals. For this class of non‐Gaussian models, Monte Carlo simulation techniques will be used for estimation, signal extraction and seasonal adjustment. This robust approach to seasonal adjustment allows outliers to be accounted for, while keeping the underlying structures that are currently used to aid reporting of economic time series data. Copyright © 2006 John Wiley & Sons, Ltd.     

Finite sample prediction and interpolation for ARIMA models with missing data

A transformation which allows Cholesky decomposition to be used to evaluate the exact likelihood function of an ARIMA model with missing data has recently been suggested. This method is extended to allow calculation of finite sample predictions of future observations. The output from the exact likelihood evaluation may also be used to estimate missing series values. Copyright © 1999 John Wiley & Sons, Ltd.     

LASSO‐Type Penalties for Covariate Selection and Forecasting in Time Series

This paper studies some forms of LASSO‐type penalties in time series to reduce the dimensionality of the parameter space as well as to improve out‐of‐sample forecasting performance. In particular, we propose a method that we call WLadaLASSO (weighted lag adaptive LASSO), which assigns not only different weights to each coefficient but also further penalizes coefficients of higher‐lagged covariates. In our Monte Carlo implementation, the WLadaLASSO is superior in terms of covariate selection, parameter estimation precision and forecasting, when compared to both LASSO and adaLASSO, especially for a higher number of candidate lags and a stronger linear dependence between predictors. Empirical studies illustrate our approach for US risk premium and US inflation forecasting with good results. Copyright © 2016 John Wiley & Sons, Ltd.     

Bicorrelations and cross‐bicorrelations as non‐linearity tests and tools for exchange rate forecasting

This paper proposes and implements a new methodology for forecasting time series, based on bicorrelations and cross‐bicorrelations. It is shown that the forecasting technique arises as a natural extension of, and as a complement to, existing univariate and multivariate non‐linearity tests. The formulations are essentially modified autoregressive or vector autoregressive models respectively, which can be estimated using ordinary least squares. The techniques are applied to a set of high‐frequency exchange rate returns, and their out‐of‐sample forecasting performance is compared to that of other time series models. Copyright © 2001 John Wiley & Sons, Ltd.     

An Adaptive Multiscale Ensemble Learning Paradigm for Nonstationary and Nonlinear Energy Price Time Series Forecasting

For forecasting nonstationary and nonlinear energy prices time series, a novel adaptive multiscale ensemble learning paradigm incorporating ensemble empirical mode decomposition (EEMD), particle swarm optimization (PSO) and least square support vector machines (LSSVM) with kernel function prototype is developed. Firstly, the extrema symmetry expansion EEMD, which can effectively restrain the mode mixing and end effects, is used to decompose the energy price into simple modes. Secondly, by using the fine‐to‐coarse reconstruction algorithm, the high‐frequency, low‐frequency and trend components are identified. Furthermore, autoregressive integrated moving average is applicable to predicting the high‐frequency components. LSSVM is suitable for forecasting the low‐frequency and trend components. At the same time, a universal kernel function prototype is introduced for making up the drawbacks of single kernel function, which can adaptively select the optimal kernel function type and model parameters according to the specific data using the PSO algorithm. Finally, the prediction results of all the components are aggregated into the forecasting values of energy price time series. The empirical results show that, compared with the popular prediction methods, the proposed method can significantly improve the prediction accuracy of energy prices, with high accuracy both in the level and directional predictions. Copyright © 2016 John Wiley & Sons, Ltd.