A new parsimonious recurrent forecasting model in singular spectrum analysis

Singular spectrum analysis (SSA) is a powerful nonparametric method in the area of time series analysis that has shown its capability in different applications areas. SSA depends on two main choices: the window length L and the number of eigentriples used for grouping r. One of the most important issues when analyzing time series is the forecast of new observations. When using SSA for time series forecasting there are several alternative algorithms, the most widely used being the recurrent forecasting model, which assumes that a given observation can be written as a linear combination of the L?1 previous observations. However, when the window length L is large, the forecasting model is unlikely to be parsimonious. In this paper we propose a new parsimonious recurrent forecasting model that uses an optimal m(<L?1) coefficients in the linear combination of the recurrent SSA. Our results support the idea of using this new parsimonious recurrent forecasting model instead of the standard recurrent SSA forecasting model.     

Modeling interval trendlines: Symbolic singular spectrum analysis for interval time series

In this article we propose an extension of singular spectrum analysis for interval-valued time series. The proposed methods can be used to decompose and forecast the dynamics governing a set-valued stochastic process. The resulting components on which the interval time series is decomposed can be understood as interval trendlines, cycles, or noise. Forecasting can be conducted through a linear recurrent method, and we devised generalizations of the decomposition method for the multivariate setting. The performance of the proposed methods is showcased in a simulation study. We apply the proposed methods so to track the dynamics governing the Argentina Stock Market (MERVAL) in real time, in a case study over a period of turbulence that led to discussions of the government of Argentina with the International Monetary Fund.     

Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis

In recent years the singular spectrum analysis (SSA) technique has been further developed and applied to many practical problems. The aim of this research is to extend and apply the SSA method, using the UK Industrial Production series. The performance of the SSA and multivariate SSA (MSSA) techniques was assessed by applying it to eight series measuring the monthly seasonally unadjusted industrial production for the main sectors of the UK economy. The results are compared with those obtained using the autoregressive integrated moving average and vector autoregressive models. We also develop the concept of causal relationship between two time series based on the SSA techniques. We introduce several criteria which characterize this causality. The criteria and tests are based on the forecasting accuracy and predictability of the direction of change. The proposed tests are then applied and examined using the UK industrial production series. Copyright © 2012 John Wiley & Sons, Ltd.     

Singular spectrum analysis for value at risk in stochastic volatility models

Estimation of the value at risk (VaR) requires prediction of the future volatility. Whereas this is a simple task in ARCH and related models, it becomes much more complicated in stochastic volatility (SV) processes where the volatility is a function of a latent variable that is not observable. In-sample (present and past values) and out-of-sample (future values) predictions of that unobservable variable are thus necessary. This paper proposes singular spectrum analysis (SSA), which is a fully nonparametric technique that can be used for both purposes. A combination of traditional forecasting techniques and SSA is also considered to estimate the VaR. Their performance is assessed in an extensive Monte Carlo and with an application to a daily series of S&P500 returns.     

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.     

Asymmetry in the link between the yield spread and industrial production: threshold effects and forecasting

We analyse the nonlinear behaviour of the information content in the spread for future real economic activity. The spread linearly predicts one‐year‐ahead real growth in nine industrial production sectors of the USA and four of the UK over the last 40 years. However, recent investigations on the spread–real activity relation have questioned both its linear nature and its time‐invariant framework. Our in‐sample empirical evidence suggests that the spread–real activity relationship exhibits asymmetries that allow for different predictive power of the spread when past spread values were above or below some threshold value. We then measure the out‐of‐sample forecast performance of the nonlinear model using predictive accuracy tests. The results show that significant improvement in forecasting accuracy, at least for one‐step‐ahead forecasts, can be obtained over the linear model. Copyright © 2004 John Wiley & Sons, Ltd.     

Energy consumption,survey data and the prediction of industrial production in Italy: a comparison and combination of different models

We investigate the prediction of italian industrial production and first specify a model based on electricity consumption showing that the cubic trend in such a model mostly captures the evolution over time of the electricity coefficient, which can be well approximated by a smooth transition model, with no gains in predictive power. We also analyse the performance of models based on data of two different business surveys. According to the standard statistics of forecasting accuracy, the linear energy‐based model is not outperformed by any other model, nor by a combination of forecasts. However, a more comprehensive set of evaluation criteria sheds light on the relative merit of each individual model. A modelling strategy which makes full use of all information available is proposed. Copyright © 2000 John Wiley & Sons, Ltd.     

A leading indicator approach to predicting short‐term shifts in demand for business travel by air to and from the UK

This paper uses the probit model to examine whether leading indicator information could be used for the purpose of predicting short‐term shifts in demand for business travel by air to and from the UK. Leading indicators considered include measures of business expectations, availability of funds for corporate travel and some well‐known macroeconomic indicators. The model performance is evaluated on in‐ and out‐of‐sample basis, as well as against a linear leading indicator model, which is used to mimic the current forecasting practice in the air transport industry. The estimated probit model is shown to provide timely predictions of the early 1980s and 1990s industry recessions and is shown to be more accurate than the benchmark linear model. Copyright © 2005 John Wiley & Sons, Ltd.     

A large Bayesian VAR with a block-specific shrinkage: A forecasting application for Italian industrial production

This paper proposes a Bayesian vector autoregression (BVAR) model with the Kalman filter to forecast the Italian industrial production index in a pseudo real-time experiment. Minnesota priors are adopted as a general framework, but a different shrinkage pattern is imposed for both the VAR coefficients and the Kalman gain, depending on the informative contribution of each variable investigated at frequency level. Both a time-varying and a constant selection for the shrinkage are proposed. Overall, the new BVAR models significantly improve the forecasting performance in comparison with the more traditional versions based on standard Minnesota priors with a single shrinkage, equal for all the variables, and selected on the basis of some optimal criteria. Very promising results come out in terms of density forecasting as well.     

Signal Extraction and Forecasting of the UK Tourism Income Time Series: A Singular Spectrum Analysis Approach

We present and apply singular spectrum analysis (SSA), a relatively new, non‐parametric and data‐driven method for signal extraction (trends, seasonal and business cycle components) and forecasting of UK tourism income. Our results show that SSA slightly outperforms SARIMA and time‐varying‐parameter state space models in terms of root mean square error, mean absolute error and mean absolute percentage error forecasting criteria. Copyright © 2011 John Wiley & Sons, Ltd.     

Out‐of‐sample equity premium prediction: A scenario analysis approach

We propose two methods of equity premium prediction with single and multiple predictors respectively and evaluate their out‐of‐sample performance using US stock data with 15 popular predictors for equity premium prediction. The first method defines three scenarios in terms of the expected returns under the scenarios and assumes a Markov chain governing the occurrence of the scenarios over time. It employs predictive quantile regressions of excess return on a predictor for three quantiles to estimate the occurrence of the scenarios over an in‐sample period and the transition probabilities of the Markov chain, predicts the expected returns under the scenarios, and generates an equity premium forecast by combining the predicted expected returns under three scenarios with the estimated transition probabilities. The second method generates an equity premium forecast by combining the individual forecasts from the first method across all predictors. For most of predictors, the first method outperforms the benchmark method of historical average and the traditional predictive linear regression with a single predictor both statistically and economically, and the second method consistently performs better than several competing methods used in the literature. The performance of our methods is further examined under different scenarios and economic conditions, and is robust for two different out‐of‐sample periods and specifications of the scenarios.     

Short‐Term Forecasts of French GDP: A Dynamic Factor Model with Targeted Predictors

In recent years, factor models have received increasing attention from both econometricians and practitioners in the forecasting of macroeconomic variables. In this context, Bai and Ng (Journal of Econometrics 2008; 146 : 304–317) find an improvement in selecting indicators according to the forecast variable prior to factor estimation (targeted predictors). In particular, they propose using the LARS‐EN algorithm to remove irrelevant predictors. In this paper, we adapt the Bai and Ng procedure to a setup in which data releases are delayed and staggered. In the pre‐selection step, we replace actual data with estimates obtained on the basis of past information, where the structure of the available information replicates the one a forecaster would face in real time. We estimate on the reduced dataset the dynamic factor model of Giannone et al. (Journal of Monetary Economics 2008; 55 : 665–676) and Doz et al. (Journal of Econometrics 2011; 164 : 188–205), which is particularly suitable for the very short‐term forecast of GDP. A pseudo real‐time evaluation on French data shows the potential of our approach. Copyright © 2013 John Wiley & Sons, Ltd.