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.

Selecting from amongst non–nested conditional variance models: information criteria and portfolio determination

We consider the finite sample properties of model selection by information criteria in conditionally heteroscedastic models. Recent theoretical results show that certain popular criteria are consistent in that they will select the true model asymptotically with probability 1. To examine the empirical relevance of this property, Monte Carlo simulations are conducted for a set of non–nested data generating processes (DGPs) with the set of candidate models consisting of all types of model used as DGPs. In addition, not only is the best model considered but also those with similar values of the information criterion, called close competitors, thus forming a portfolio of eligible models. To supplement the simulations, the criteria are applied to a set of economic and financial series. In the simulations, the criteria are largely ineffective at identifying the correct model, either as best or a close competitor, the parsimonious GARCH(1, 1) model being preferred for most DGPs. In contrast, asymmetric models are generally selected to represent actual data. This leads to the conjecture that the properties of parameterizations of processes commonly used to model heteroscedastic data are more similar than may be imagined and that more attention needs to be paid to the behaviour of the standardized disturbances of such models, both in simulation exercises and in empirical modelling.

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.

Forecasting exchange rate volatility using conditional variance models selected by information criteria

This paper uses appropriately modified information criteria to select models from the GARCH family, which are subsequently used for predicting US dollar exchange rate return volatility. The out of sample forecast accuracy of models chosen in this manner compares favourably on mean absolute error grounds, although less favourably on mean squared error grounds, with those generated by the commonly used GARCH(1, 1) model. An examination of the orders of models selected by the criteria reveals that (1, 1) models are typically selected less than 20% of the time.

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.

Separating skill from luck in REIT mutual funds

This study uses a bootstrap methodology to explicitly distinguish between skill and luck for 80 Real Estate Investment Trust Mutual Funds in the period January 1995 to May 2008. The methodology successfully captures non-normality in the idiosyncratic risk of the funds. Using unconditional, beta conditional and alpha-beta conditional estimation models, the results indicate that all but one fund demonstrates poor skill. Tests of robustness show that this finding is largely invariant to REIT market conditions and maturity.

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.

Autoregressive conditional kurtosis

This article proposes a new model for autoregressive conditional heteroscedasticity and kurtosis. Via a time-varying degrees of freedom parameter, the conditional variance and conditional kurtosis are permitted to evolve separately. The model uses only the standard Student’s t-density and consequently can be estimated simply using maximum likelihood. The method is applied to a set of four daily financial asset return series comprising U.S. and U.K. stocks and bonds, and significant evidence in favor of the presence of autoregressive conditional kurtosis is observed. Various extensions to the basic model are proposed, and we show that the response of kurtosis to good and bad news is not significantly asymmetric.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.