Testing for Co-Integration in Vector Autoregressions with Non-Stationary Volatility

Cavaliere, Giuseppe; Rahbek, Anders; Taylor, A. M. Robert

doi:10.2139/ssrn.1264907

Cited by 50 publications

(109 citation statements)

References 45 publications

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“…The key Assumption 2, which is due to Cavaliere et al (2010), models the volatility process σ t as a nonparametric function of time, thereby allows for a rich family of nonstationary dynamics 1 The methodologies developed in this paper could be extended to cover other trend models instead of a linear trend studied here. For instance, adding an indicator function of time trend in (1) and testing its coefficient cross-sectionally would lead to a common broken trend test at a given break point.…”

Section: Model Assumptions and Ols Estimationmentioning

confidence: 99%

“…in the innovation variance-covariance matrix; see Cavaliere et al (2010) for more discussions. The scalar version of Assumption 2 was employed by Cavaliere and Taylor (2007), Beare (2008) and Xu and Phillips (2008), inter alia, to analyze the effects of nonstationary volatility on the inference of univariate time series.…”

Section: Model Assumptions and Ols Estimationmentioning

confidence: 99%

“…The first weak convergence result in Lemma 1 appeared in Cavaliere et al (2010). The diffusion process W σ m (·) has the instantaneous covariance matrix σ −1 σ (·)σ ′ (·)σ −1 , and is equivalent in distribution to a vector time-changed Brownian motion (Davidson, 1994) if σ (·) can be rewritten as Υ 1 Υ 2 (·) where Υ 1 is a constant matrix while Υ 2 (·) is a diagonal matrix function.…”

Section: Model Assumptions and Ols Estimationmentioning

confidence: 99%

“…Note that the multivariate wild bootstrap scheme adopted here multiplies the same scalar to each element of  v t and was first used by Cavaliere et al (2010). The wild bootstrap seems more natural in our setting to account for the heteroskedasticity appeared in the data; see also Kilian (2004, 2007), Cavaliere and Taylor (2008) and Xu (2008) can be constructed.…”

Section: Bootstrapping the Multivariate Trend Testsmentioning

confidence: 99%

“…Robust inference under nonstationary volatility has attracted substantial attention recently in the econometrics literature; see Phillips and Xu (2006), Cavaliere and Taylor (2007), Cavaliere et al (2010), Beare (2008) and Xu and Phillips (2008). They mainly focus on the coefficients in the stable or unstable autoregressive models.…”

Section: Introductionmentioning

confidence: 99%

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Section: Model Assumptions and Ols Estimationmentioning

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Section: Model Assumptions and Ols Estimationmentioning

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Section: Bootstrapping the Multivariate Trend Testsmentioning

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2012

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

Barakchian

2013

Journal of Forecasting

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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 twocountry 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.

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Robust inference under time‐varying volatility: A real‐time evaluation of professional forecasters

Demetrescu

Hanck

Kruse

2022

J of Applied Econometrics

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Summary In many forecast evaluation applications, standard tests as well as tests allowing for time‐variation in relative forecast ability build on heteroskedasticity‐and‐autocorrelation consistent (HAC) covariance estimators. Yet, the finite‐sample performance of these asymptotics is often poor. “Fixed‐ b$$ b $$” asymptotics, used to account for long‐run variance estimation, improve finite‐sample performance under homoskedasticity, but lose asymptotic pivotality under time‐varying volatility. Moreover, loss of pivotality due to time‐varying volatility is found in the standard HAC framework in certain cases as well. We prove a wild bootstrap implementation to restore asymptotically pivotal inference for the above and new CUSUM‐ and Cramér‐von Mises‐based tests in a fairly general setup, allowing for estimation uncertainty from either a rolling window or a recursive approach when fixed‐ b$$ b $$ asymptotics are adopted to achieve good finite‐sample performance. We then investigate the (time‐varying) performance of professional forecasters relative to naive no‐change and model‐based predictions in real‐time. We exploit the Survey of Professional Forecasters (SPF) database and analyze nowcasts and forecasts at different horizons for output and inflation. We find that not accounting for time‐varying volatility seriously affects outcomes of tests for equal forecast ability: wild bootstrap inference typically yields convincing evidence for advantages of the SPF, while tests using non‐robust critical values provide remarkably less. Moreover, we find significant evidence for time‐variation of relative forecast ability, the advantages of the SPF weakening considerably after the “Great Moderation.”

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Testing for Co-Integration in Vector Autoregressions with Non-Stationary Volatility

Cited by 50 publications

References 45 publications

Robustifying multivariate trend tests to nonstationary volatility

Robustifying multivariate trend tests to nonstationary volatility

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

Robust inference under time‐varying volatility: A real‐time evaluation of professional forecasters

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