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.     

Modeling European industrial production with multivariate singular spectrum analysis: A cross‐industry analysis

In this paper, an optimized multivariate singular spectrum analysis (MSSA) approach is proposed to find leading indicators of cross‐industry relations between 24 monthly, seasonally unadjusted industrial production (IP) series for German, French, and UK economies. Both recurrent and vector forecasting algorithms of horizontal MSSA (HMSSA) are considered. The results from the proposed multivariate approach are compared with those obtained via the optimized univariate singular spectrum analysis (SSA) forecasting algorithm to determine the statistical significance of each outcome. The data are rigorously tested for normality, seasonal unit root hypothesis, and structural breaks. The results are presented such that users can not only identify the most appropriate model based on the aim of the analysis, but also easily identify the leading indicators for each IP variable in each country. Our findings show that, for all three countries, forecasts from the proposed MSSA algorithm outperform the optimized SSA algorithm in over 70% of cases. Accordingly, this new approach succeeds in identifying leading indicators and is a viable option for selecting the SSA choices L and r, which minimizes a loss function.     

Forecasting Multivariate Time Series with the Theta Method

In this study building on earlier work on the properties and performance of the univariate Theta method for a unit root data‐generating process we: (a) derive new theoretical formulations for the application of the method on multivariate time series; (b) investigate the conditions for which the multivariate Theta method is expected to forecast better than the univariate one; (c) evaluate through simulations the bivariate form of the method; and (d) evaluate this latter model in real macroeconomic and financial time series. The study provides sufficient empirical evidence to illustrate the suitability of the method for vector forecasting; furthermore it provides the motivation for further investigation of the multivariate Theta method for higher dimensions. Copyright © 2015 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.     

Multivariate Forecasting with BVARs and DSGE Models

In this paper I assess the ability of Bayesian vector autoregressions (BVARs) and dynamic stochastic general equilibrium (DSGE) models of different size to forecast comovements of major macroeconomic series in the euro area. Both approaches are compared to unrestricted VARs in terms of multivariate point and density forecast accuracy measures as well as event probabilities. The evidence suggests that BVARs and DSGE models produce accurate multivariate forecasts even for larger datasets. I also detect that BVARs are well calibrated for most events, while DSGE models are poorly calibrated for some. In sum, I conclude that both are useful tools to achieve parameter dimension reduction. Copyright © 2016 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 time series with increasing seasonal variation

Four options for modeling and forecasting time series data containing increasing seasonal variation are discussed, including data transformations, double seasonal difference models and two kinds of transfer function-type ARIMA models employing seasonal dummy variables. An explanation is given for the typical ARIMA model identification analysis failing to identify double seasonal difference models for this kind of data. A logical process of selecting one option for a particular case is outlined, focusing on issues of linear versus non-linear increasing seasonal variation, and the level of stochastic versus deterministic behavior in a time series. Example models for the various options are presented for six time series, with point forecast and interval forecast comparisons. Interval forecasts from data-transformation models are found to generally be too wide and sometimes illogical in the dependence of their width on the point forecast level. Suspicion that maximum likelihood estimation of ARIMA models leads to excessive indications of unit roots in seasonal moving-average operators is reported.     

Forecasting volatility with noisy jumps: an application to the Dow Jones Industrial Average stocks

Empirical high‐frequency data can be used to separate the continuous and the jump components of realized volatility. This may improve on the accuracy of out‐of‐sample realized volatility forecasts. A further improvement may be realized by disentangling the two components using a sampling frequency at which the market microstructure effect is negligible, and this is the objective of the paper. In particular, a significant improvement in the accuracy of volatility forecasts is obtained by deriving the jump information from time intervals at which the noise effect is weak. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting Temperature Indices Density with Time‐Varying Long‐Memory Models

The hedging of weather risks has become extremely relevant in recent years, promoting the diffusion of weather‐derivative contracts. The pricing of such contracts requires the development of appropriate models for the prediction of the underlying weather variables. Within this framework, a commonly used specification is the ARFIMA‐GARCH. We provide a generalization of such a model, introducing time‐varying memory coefficients. Our model satisfies the empirical evidence of the changing memory level observed in average temperature series, and provides useful improvements in the forecasting, simulation, and pricing issues related to weather derivatives. We present an application related to the forecast and simulation of a temperature index density, which is then used for the pricing of weather options. Copyright © 2011 John Wiley & Sons, Ltd.     

Forecasting the US Term Structure of Interest Rates Using Nonparametric Functional Data Analysis

In this paper we consider a novel procedure to forecasting the US zero coupon bond yields for a continuum of maturities by using the methodology of nonparametric functional data analysis (NP‐FDA). We interpret the US yields as curves since the term structure of interest rates defines a relation between the yield of a bond and its maturity. Within the NP‐FDA approach, each curve is viewed as a functional random variable and the dynamics present in the sample are modeled without imposing any parametric structure. In order to evaluate forecast the performance of the proposed estimator, we consider forecast horizons h = 1,3,6,12… months and the results are compared with widely known benchmark models. Our estimates with NP‐FDA present predictive performance superior to its competitors in many situations considered, especially for short‐term maturities. Copyright © 2016 John Wiley & Sons, Ltd.     

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 the Effects of a Canada–US Currency Union on Output and Prices: A Counterfactual Analysis

This paper is a counterfactual analysis investigating the consequences of the formation of a currency union for Canada and the USA: whether outputs increase and prices decrease if these countries form a currency union. We use a two‐country cointegrated model to conduct the counterfactual analysis, where the conditional forecasts are generated based on the Gaussian assumption. To deal with structural breaks and model uncertainty, conditional forecasts are generated from different models/estimation windows and the model‐averaging technique is used to combine the forecasts. We also examine the robustness of our results to parameter uncertainty using the wild bootstrap method. The results show that forming the currency union would probably boost the Canadian economy, whereas it would not have significant effects on US output or Canadian and US price levels. Copyright © 2013 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.     

Policy‐Oriented Macroeconomic Forecasting with Hybrid DGSE and Time‐Varying Parameter VAR Models

Micro‐founded dynamic stochastic general equilibrium (DSGE) models appear to be particularly suited to evaluating the consequences of alternative macroeconomic policies. Recently, increasing efforts have been undertaken by policymakers to use these models for forecasting, although this proved to be problematic due to estimation and identification issues. Hybrid DSGE models have become popular for dealing with some of the model misspecifications and the trade‐off between theoretical coherence and empirical fit, thus allowing them to compete in terms of predictability with VAR models. However, DSGE and VAR models are still linear and they do not consider time variation in parameters that could account for inherent nonlinearities and capture the adaptive underlying structure of the economy in a robust manner. This study conducts a comparative evaluation of the out‐of‐sample predictive performance of many different specifications of DSGE models and various classes of VAR models, using datasets for the real GDP, the harmonized CPI and the nominal short‐term interest rate series in the euro area. Simple and hybrid DSGE models were implemented, including DSGE‐VAR and factor‐augmented DGSE, and tested against standard, Bayesian and factor‐augmented VARs. Moreover, a new state‐space time‐varying VAR model is presented. The total period spanned from 1970:Q1 to 2010:Q4 with an out‐of‐sample testing period of 2006:Q1–2010:Q4, which covers the global financial crisis and the EU debt crisis. The results of this study can be useful in conducting monetary policy analysis and macro‐forecasting in the euro area. Copyright © 2016 John Wiley & Sons, Ltd.