Bootstrapping prediction intervals for autoregressive models

Methods of improving the coverage of Box–Jenkins prediction intervals for linear autoregressive models are explored. These methods use bootstrap techniques to allow for parameter estimation uncertainty and to reduce the small-sample bias in the estimator of the models’ parameters. In addition, we also consider a method of bias-correcting the non-linear functions of the parameter estimates that are used to generate conditional multi-step predictions.

Forecasting with vector autoregressive models of data vintages: US output growth and inflation

Vintage-based vector autoregressive models of a single macroeconomic variable are shown to be a useful vehicle for obtaining forecasts of different maturities of future and past observations, including estimates of post-revision values. The forecasting performance of models which include information on annual revisions is superior to that of models which only include the first two data releases. However, the empirical results indicate that a model which reflects the seasonal nature of data releases more closely does not offer much improvement over an unrestricted vintage-based model which includes three rounds of annual revisions.

Real-time forecasting of inflation and output growth with autoregressive models in the presence of data revisions

We examine how the accuracy of real-time forecasts from models that include autoregressive terms can be improved by estimating the models on ‘lightly revised’ data instead of using data from the latest-available vintage. The benefits of estimating autoregressive models on lightly revised data are related to the nature of the data revision process and the underlying process for the true values. Empirically, we find improvements in root mean square forecasting error of 2–4% when forecasting output growth and inflation with univariate models, and of 8% with multivariate models. We show that multiple-vintage models, which explicitly model data revisions, require large estimation samples to deliver competitive forecasts. Copyright © 2012 John Wiley & Sons, Ltd.

Improving real-time estimates of output and inflation gaps with multiple-vintage models

Real-time estimates of output gaps and inflation gaps differ from the values that are obtained using data available long after the event. Part of the problem is that the data on which the real-time estimates are based is subsequently revised. We show that vector-autoregressive models of data vintages provide forecasts of post-revision values of future observations and of already-released observations capable of improving estimates of output and inflation gaps in real time. Our findings indicate that annual revisions to output and inflation data are in part predictable based on their past vintages.

Evidence for the chaotic origin of Northern Annular Mode variability

Exponential spectra are found to characterize variability of the Northern Annular Mode (NAM) for periods less than 36 days. This corresponds to the observed rounding of the autocorrelation function at lags of a few days. The characteristic persistence timescales during winter and summer is found to be ∼5 days for these high frequencies. Beyond periods of 36 days the characteristic decorrelation timescale is ∼20 days during winter and ∼6 days in summer. We conclude that the NAM cannot be described by autoregressive models for high frequencies; the spectra are more consistent with low-order chaos. We also propose that the NAM exhibits regime behaviour, however the nature of this has yet to be identified.

Business cycle asymmetries: characterisation and testing based on Markov-switching autoregressions

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.

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

Robust approaches to forecasting

We investigate alternative robust approaches to forecasting, using a new class of robust devices, contrasted with equilibrium-correction models. Their forecasting properties are derived facing a range of likely empirical problems at the forecast origin, including measurement errors, impulses, omitted variables, unanticipated location shifts and incorrectly included variables that experience a shift. We derive the resulting forecast biases and error variances, and indicate when the methods are likely to perform well. The robust methods are applied to forecasting US GDP using autoregressive models, and also to autoregressive models with factors extracted from a large dataset of macroeconomic variables. We consider forecasting performance over the Great Recession, and over an earlier more quiescent period.

Real-time factor model forecasting and the effects of instability

Factor forecasting models are shown to deliver real-time gains over autoregressive models for US real activity variables during the recent period, but are less successful for nominal variables. The gains are largely due to the Financial Crisis period, and are primarily at the shortest (one quarter ahead) horizon. Excluding the pre-Great Moderation years from the factor forecasting model estimation period (but not from the data used to extract factors) results in a marked fillip in factor model forecast accuracy, but does the same for the AR model forecasts. The relative performance of the factor models compared to the AR models is largely unaffected by whether the exercise is in real time or is pseudo out-of-sample.

The housing market channel of monetary policy transmission in the Euro area

Purpose – The purpose of this paper is to explore the role of the housing market in the monetary policy transmission to consumption among euro area member states. It has been argued that the housing market in one country is then important when its mortgage market is well developed. The countries in the euro area follow unitary monetary policy, however, their housing and mortgage markets show some heterogeneity, which may lead to different policy effects on aggregate consumption through the housing market. Design/methodology/approach – The housing market can act as a channel of monetary policy shocks to household consumption through changes in house prices and residential investment – the housing market channel. We estimate vector autoregressive models for each country and conduct a counterfactual analysis in order to disentangle the housing market channel and assess its importance across the euro area member states. Findings – We find little evidence for heterogeneity of the monetary policy transmission through house prices across the euro area countries. Housing market variations in the euro area seem to be better captured by changes in residential investment rather than by changes in house prices. As a result we do not find significantly large house price channels. For some of the countries however, we observe a monetary policy channel through residential investment. The existence of a housing channel may depend on institutional features of both the labour market or with institutional factors capturing the degree of household debt as is the LTV ratio. Originality/value – The study contributes to the existing literature by assessing whether a unitary monetary policy has a different impact on consumption across the euro area countries through their housing and mortgage markets. We disentangle monetary-policy-induced effects on consumption associated with variations on the housing markets due to either house price variations or residential investment changes. We show that the housing market can play a role in the monetary transmission mechanism even in countries with less developed mortgage markets through variations in residential investment.

Threshold autoregressive and Markov switching models: an application to commercial real estate

Although financial theory rests heavily upon the assumption that asset returns are normally distributed, value indices of commercial real estate display significant departures from normality. In this paper, we apply and compare the properties of two recently proposed regime switching models for value indices of commercial real estate in the US and the UK, both of which relax the assumption that observations are drawn from a single distribution with constant mean and variance. Statistical tests of the models' specification indicate that the Markov switching model is better able to capture the non-stationary features of the data than the threshold autoregressive model, although both represent superior descriptions of the data than the models that allow for only one state. Our results have several implications for theoretical models and empirical research in finance.

Comparison of subspace and ARX models of a waveguide's terahertz transient response after optimal wavelet filtering

A quasi-optical deembedding technique for characterizing waveguides is demonstrated using wide-band time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time-domain responses were discretized and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an AutoRegressive with eXogenous input (ARX), as well as with a state-space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize both signal distortion, as well as the noise propagating in the ARX and subspace models. The optimal filtering procedure used in the wavelet domain for the recorded time-domain signatures is described in detail. The effect of filtering prior to the identification procedures is elucidated with the aid of pole-zero diagrams. Models derived from measurements of terahertz transients in a precision WR-8 waveguide adjustable short are presented.

The cross-currency hedging performance of implied versus statistical forecasting models

This article examines the ability of several models to generate optimal hedge ratios. Statistical models employed include univariate and multivariate generalized autoregressive conditionally heteroscedastic (GARCH) models, and exponentially weighted and simple moving averages. The variances of the hedged portfolios derived using these hedge ratios are compared with those based on market expectations implied by the prices of traded options. One-month and three-month hedging horizons are considered for four currency pairs. Overall, it has been found that an exponentially weighted moving-average model leads to lower portfolio variances than any of the GARCH-based, implied or time-invariant approaches.

Forecasting models of retail rents

The authors model retail rents in the United Kingdom with use of vector-autoregressive and time-series models. Two retail rent series are used, compiled by LaSalle Investment Management and CB Hillier Parker, and the emphasis is on forecasting. The results suggest that the use of the vector-autoregression and time-series models in this paper can pick up important features of the data that are useful for forecasting purposes. The relative forecasting performance of the models appears to be subject to the length of the forecast time-horizon. The results also show that the variables which were appropriate for inclusion in the vector-autoregression systems differ between the two rent series, suggesting that the structure of optimal models for predicting retail rents could be specific to the rent index used. Ex ante forecasts from our time-series suggest that both LaSalle Investment Management and CB Hillier Parker real retail rents will exhibit an annual growth rate above their long-term mean.