Forecasting Interest Rates: An Application of the Stochastic Unit Root and Stochastic Cointegration Frameworks

Abstract This paper investigates forecasting U.S. Treasury bond and dollar Eurocurrency rates using the stochastic unit root (STUR) model of JEL classifications: C22, C53, G1

Detecting Regimes of Predictability in the U.S. Equity Premium

We investigate the stability of predictive regression models for the U.S. equity premium. A new approach for detecting regimes of temporary predictability is proposed using se- quential implementations of standard (heteroskedasticity-robust) regression t-statistics for predictability applied over relatively short time periods. Critical values for each test in the sequence are provided using subsampling methods. Our primary focus is to develop a real-time monitoring procedure for the emergence of predictive regimes using tests based on end-of-sample data in the sequential procedure, although the procedure could be used for an historical analysis of predictability. Our proposed method is robust to both the degree of persistence and endogeneity of the regressors in the predictive regression and to certain forms of heteroskedasticity in the shocks. We discuss how the detection procedure can be designed such that the false positive rate is pre-set by the practitioner at the start of the monitoring period. We use our approach to investigate for the presence of regime changes in the predictability of the U.S. equity premium at the one-month horizon by traditional macroeconomic and financial variables, and by binary technical analysis indicators. Our results suggest that the one-month ahead equity premium has temporarily been predictable (displaying so-called ‘pockets of predictability’), and that these episodes of predictability could have been detected in real-time by practitioners using our proposed methodology

Recursive right-tailed unit root tests for an explosive asset price bubble

In this article, we compare the local asymptotic and finite sample power of two recently proposed recursive right-tailed Dickey–Fuller-type tests for an explosive rational bubble in asset prices. It is shown that the power of the two tests can differ substantially depending on the location of the explosive regime, and whether such a regime ends in collapse. Since this information is typically unknown to the practitioner, we propose a union of rejections strategy that combines inference from the two individual tests. We find that, for a given specification of the explosive regime, the union of rejections strategy always attains power close to the better of the individual tests considered. An empirical illustration using the Nasdaq composite price index is also provided

Real-Time Detection of Regimes of Predictability in the U.S. Equity Premium

We propose new real-time monitoring procedures for the emergence of end-of-sample predictive regimes using sequential implementations of standard (heteroskedasticity-robust) regression t-statistics for predictability applied over relatively short time periods. The procedures we develop can also be used for detecting historical regimes of temporary predictability. Our proposed methods are robust to both the degree of persistence and endogeneity of the regressors in the predictive regression and to certain forms of heteroskedasticity in the shocks. We discuss how the monitoring procedures can be designed such that their false positive rate can be set by the practitioner at the start of the monitoring period using detection rules based on information obtained from the data in a training period. We use these new monitoring procedures to investigate the presence of regime changes in the predictability of the U.S. equity premium at the one-month horizon by traditional macroeconomic and financial variables, and by binary technical analysis indicators. Our results suggest that the one-month ahead equity premium has temporarily been predictable, displaying so-called 'pockets of predictability', and that these episodes of predictability could have been detected in real-time by practitioners using our proposed methodology

Improving the accuracy of asset price bubble start and end date estimators

Recent research has proposed using recursive right-tailed unit root tests to date the start and end of asset price bubbles. In this paper an alternative approach is proposed that utilises model-based minimum sum of squared residuals estimators combined with Bayesian Information Criterion model selection. Conditional on the presence of a bubble, the dating procedures suggested are shown to offer consistent estimation of the start and end dates of a fixed magnitude bubble, and can also be used to distinguish between different types of bubble process, i.e. a bubble that does or does not end in collapse, or a bubble that is ongoing at the end of the sample. Monte Carlo simulations show that the proposed dating approach out-performs the recursive unit root test methods for dating periods of explosive autoregressive behaviour in finite samples, particularly in terms of accurate identification of a bubble's end point. An empirical application involving Nasdaq stock prices is discussed

Tests for explosive financial bubbles in the presence of non-stationary volatility

This paper studies the impact of permanent volatility shifts in the innovation process on the performance of the test for explosive financial bubbles based on recursive right-tailed Dickey–Fuller-type unit root tests proposed by Phillips, Wu and Yu (2011). We show that, in this situation, their supremum-based test has a non-pivotal limit distribution under the unit root null, and can be quite severely over-sized, thereby giving rise to spurious indications of explosive behaviour. We investigate the performance of a wild bootstrap implementation of their test procedure for this problem, and show it is effective in controlling size, both asymptotically and in finite samples, yet does not sacrifice power relative to an (infeasible) size-adjusted version of their test, even when the shocks are homoskedastic. We also discuss an empirical application involving commodity price time series and find considerably less emphatic evidence for the presence of explosive bubbles in these data when using our proposed wild bootstrap implementation of the Phillips, Wu and Yu (2011) test

Testing for Co-explosive Behaviour in Financial Time Series

This article proposes a test to determine if two price series that each contain an explosive autoregressive regime consistent with the presence of a bubble are related in the sense that a linear combination of them is integrated of order zero. We refer to such a phenomenon as ‘co-explosive behaviour’, and propose a test based on a stationarity testing framework. The test allows the explosive episode in one series to lead (or lag) that in the other by a number of time periods. We establish the asymptotic properties of the test statistic and propose a wild bootstrap procedure for obtaining critical values that are robust to heteroskedasticity. Simulations show that the proposed test has good finite sample size and power performance. An empirical application to detect whether co-explosive behaviour exists among a set of precious and non-ferrous metals is presented

If Fibonacci was a Concrete Poet

Concrete poetry and lectur

Blackhorse Workshop

Graphic Identity, signage and graphic material produced for the Blackhorse Workshop, 1–2 Sutherland Rd Path, Walthamstow E17 6B