Testing Density Forecasts, With Applications to Risk Management

Berkowitz, Jeremy

doi:10.1198/07350010152596718

Cited by 701 publications

(699 citation statements)

References 17 publications

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“…Considering the conditional and unconditional coverage tests (CC, UC), the under-rejection for the Laplace is significant in several cases, whereas the over-rejection for the Student's t setting is never significant. Kupiec [1995], the independence (ID) and Conditional Coverage (CC) test of Christoffersen [1998], and the Berkowitz [2001] To get an impression about the shape of the time-varying parameters, we plot σ 2 t , t , and ν t for the skewed Student's t model in Figure 2. We clearly see the increased volatility around the time of the financial crisis, as well as the higher volatility level during the European sovereign debt crisis (2010)(2011)(2012)(2013).…”

Section: Full Results For the Euro-dollar Ratementioning

confidence: 99%

Score Driven Exponentially Weighted Moving Average and Value-at-Risk Forecasting

Lucas

Zhang

2014

SSRN Journal

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Section: Full Results For the Euro-dollar Ratementioning

confidence: 99%

Score Driven Exponentially Weighted Moving Average and Value-at-Risk Forecasting

Lucas

Zhang

2014

SSRN Journal

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“…In practice, therefore, density evaluation with the pits requires application of tests for goodness-of-fit and independence at the end of the evaluation period. 7 The goodness-of-fit tests employed include the Likelihood Ratio (LR) test proposed by Berkowitz (2001). We use a three degrees-of-freedom variant with a test for independence, where under the alternative z τ,h follows an AR(1) process.…”

Section: Forecast Density Evaluationsmentioning

confidence: 99%

Real-Time Inflation Forecast Densities from Ensemble Phillips Curves

et al. 2010

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A popular macroeconomic forecasting strategy takes combinations across many models to hedge against model instabilities of unknown timing; see (among others) Stock and Watson (2004) and Clark and McCracken (2009). In this paper, we examine the effectiveness of recursive-weight and equal-weight combination strategies for density forecasting using a time-varying Phillips curve relationship between inflation and the output gap. The densities reflect the uncertainty across a large number of models using many statistical measures of the output gap, allowing for a single structural break of unknown timing. We use real-time data for the US, Australia, New Zealand and Norway. Our main finding is that the recursive-weight strategy performs well across the real-time data sets, consistently giving well-calibrated forecast densities. The equal-weight strategy generates poorly-calibrated forecast densities for the US and Australian samples. There is little difference between the two strategies for our New Zealand and Norwegian data. We also find that the ensemble modeling approach performs more consistently with real-time data than with revised data in all four countries.

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“…To test for standard normality of the z t values, a joint test involving the first four moments is employed using the likelihood ratio approach proposed by Berkowitz (2001). It is implemented as follows: Under the alternative hypothesis, we let z t be distributed according to the skewed exponential power distribution (SEP) of Fernandez, Osiewalski and Steel (1995), with…”

Section: Out-of-sample Performancementioning

confidence: 99%