Inferring the Predictability Induced by a Persistent Regressor in a Predictive Threshold Model

Abstract

We develop tests for detecting possibly episodic predictability induced by a persistent predictor. Our framework is that of a predictive regression model with threshold effects and our goal is to develop operational and easily implementable inferences when one does not wish to imposeà priori restrictions on the parameters of the model other than the slopes corresponding to the persistent predictor. Differently put our tests for the null hypothesis of no predictability against threshold predictability remain valid without the need to know whether the remaining parameters of the model are characterised by threshold effects or not (e.g. shifting versus non-shifting intercepts). One interesting feature of our setting is that our test statistics remain unaffected by whether some nuisance parameters are identified or not. We subsequently apply our methodology to the predictability of aggregate stock returns with valuation ratios and document a robust countercyclicality in the ability of some valuation ratios to predict returns.

Endogeneity in Semiparametric Threshold Regression

“…Our final test statistic is defined as W n (γ). Motivated by Gonzalo and Pitarakis (2016), we will show that W n (γ) has the same limit distribution under the null hypothesis regardless…”

Uncovering Regimes in Out of Sample Forecast Errors from Predictive Regressions*

“…Assumption A1 mimics closely the environment considered in Gonzalo and Pitarakis (2012, 2017) and excluding the probabilistic properties of has been the operating standard in the linear predictive regression literature. Both and are allowed to display a rich dependence structure while is restricted to be a conditionally homoskedastic martingale difference sequence.…”

“…The issue is of great practical importance as the presence of regime specificity in prediction errors would call for a reassessment of the models used to generate forecasts and in particular motivate a switch to nonlinear specifications that are explicitly able to capture episodic predictability as for instance in Gonzalo and Pitarakis (2012, 2017) where the authors considered the inclusion of threshold effects within predictive regressions driven by a single highly persistent predictor. Such piecewise linear structures are particularly convenient as they allow the forecaster to control the particular indicator used for proxying economic times or more generally sentiment.…”

“…We view the testing procedures introduced in this paper as useful practical diagnostic tools that can be used to motivate the explicit inclusion of regime dependence within the predictive model itself. Although postdiagnostic re‐evaluation issues are beyond the scope of this paper such specifications have been shown to lead to considerable gains in prediction accuracy as demonstrated in an in‐sample and single predictor based equity premium forecasting context in Gonzalo and Pitarakis (2012, 2017). More recent research by Farmer, Schmidt and Timmermann (2018) also explores the idea of pockets of predictability by proposing novel non‐parametric methods to model and detect such behaviour and offering interesting insights and formal evidence on its causes in the context of stock returns.…”

Differences Between Short‐ and Long‐Term Risk Aversion: An Optimal Asset Allocation Perspective

“…In our setting, we introduce a risk aversion function that, in order to guarantee the positiveness of the relative risk aversion coefficient, is defined aswhere Z t + j =(1, Z 1, t + j ,…, Z n −1, t + j ) ′ denotes a vector of n −1 macroeconomic and financial variables reflecting all the information available to the investor at time t + j ; γ and η are the corresponding vectors of model parameters. This piecewise linear formulation follows the spirit of Gonzalo and Pitarakis () on threshold predictive regression and Perron () and Andrews () on structural breaks. More compactly, the multiperiod utility function becomes…”