The Stationary Bootstrap

Politis, Dimitris N.; Romano, Joseph P.

doi:10.1080/01621459.1994.10476870

Cited by 1,712 publications

(533 citation statements)

References 17 publications

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“…For example, it would be interesting to apply our diagnostic procedure to other estimator quality assessment methods [4,17,13] and to devise extensions of the diagnostic which are suitable for variants of the bootstrap designed to handle non-i.i.d. data [9,12,14,16,18]. Additionally, it should be possible to characterize theoretically the consistency of our diagnostic procedure, showing that its false positive and false negative rates approach zero as b1, .…”

Section: Resultsmentioning

confidence: 98%

A general bootstrap performance diagnostic

Kleiner

Talwalkar

Agarwal

et al. 2013

Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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As datasets become larger, more complex, and more available to diverse groups of analysts, it would be quite useful to be able to automatically and generically assess the quality of estimates, much as we are able to automatically train and evaluate predictive models such as classifiers. However, despite the fundamental importance of estimator quality assessment in data analysis, this task has eluded highly automatic solutions. While the bootstrap provides perhaps the most promising step in this direction, its level of automation is limited by the difficulty of evaluating its finite sample performance and even its asymptotic consistency. Thus, we present here a general diagnostic procedure which directly and automatically evaluates the accuracy of the bootstrap's outputs, determining whether or not the bootstrap is performing satisfactorily when applied to a given dataset and estimator. We show that our proposed diagnostic is effective via an extensive empirical evaluation on a variety of estimators and simulated and real datasets, including a real-world query workload from Conviva, Inc. involving 1.7TB of data (i.e., approximately 0.5 billion data points).

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Section: Resultsmentioning

confidence: 98%

A general bootstrap performance diagnostic

Kleiner

Talwalkar

Agarwal

et al. 2013

Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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“…Both methods generalize extremely well out-of-sample, and the shrinkage is only 0.12 and 0.16, corresponding to annualized returns of 23.3% and 19.9%. In order to asses the significance of these results, confidence intervals are constructed using the stationary bootstrap method, which is a superior alternative to well known block bootstrap procedure [17]. Instead of using a fixed block size, it varies probabilistically according to a geometric distribution.…”

Section: Resultsmentioning

confidence: 99%

Genetic Programming in Statistical Arbitrage

Saks

Maringer

2008

Lecture Notes in Computer Science

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Abstract. This paper employs genetic programming to discover statistical arbitrage strategies on the banking sector in the Euro Stoxx universe. Binary decision rules are evolved using two different representations. The first is the classical single tree approach, while the second is a dual tree structure where evaluation is contingent on the current market position. Hence, buy and sell rules are co-evolved. Both methods are capable of discovering significant statistical arbitrage strategies.

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“…evidenced by autocorrelation across several lags) this should also be clearly reflected by the bootstrap data in order to obtain a reasonable reference distribution under the null hypothesis of no lead-lag relations between the two series. This could be achieved by using the stationary bootstrap proposed by Politis and Romano (1994), which takes into account serial dependence.…”

Section: Impact Of Temporal Dependencementioning

confidence: 99%

Symmetric thermal optimal path and time-dependent lead-lag relationship: novel statistical tests and application to UK and US real-estate and monetary policies

Meng

Zhou

et al. 2016

Quantitative Finance

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We present the symmetric thermal optimal path (TOPS) method to determine the time-dependent lead-lag relationship between two stochastic time series. This novel version of the previously introduced TOP method alleviates some inconsistencies by imposing that the lead-lag relationship should be invariant with respect to a time reversal of the time series after a change of sign. This means that, if 'X comes before Y ', this transforms into 'Y comes before X' under a time reversal. We show that previously proposed bootstrap test lacks power and leads too often to a lack of rejection of the null that there is no lead-lag correlation when it is present. We introduce instead two novel tests. The first criterion, based on the free energy p-value ρ, quantifies the probability that a given lead-lag structure could be obtained from random time series with similar characteristics except for the lead-lag information. The second selfconsistent test embodies the idea that, for the lead-lag path to be significant, synchronizing the two time series using the time varying lead-lag path should lead to a statistically significant correlation. We perform intensive synthetic tests to demonstrate their performance and limitations. Finally, we apply the TOPS method with the two new tests to the time dependent lead-lag structures of house price and monetary policy of the United Kingdom (UK) and United States (US) from 1991 to 2011. We find that, for both countries, the TOPS paths indicate that interest rate changes were lagging behind house price index changes until the crisis in 2006-2007. The TOPS paths also suggest a catch up of the UK central bank and of the Federal Reserve still not being on top of the game during the crisis itself, as diagnosed by again the significant negative values of TOPS paths until 2008. Only later did the central banks interest rates as well as longer maturity rates lead the house price indices, confirming the occurrence of the transition to an era where the central bank is "causally" influencing the housing markets more than the reverse. The TOPS approach stresses the importance of accounting for change of regimes, so that similar pieces of information or policies may have drastically different impacts and developments, conditional on the economic, financial and geopolitical conditions. This study reinforces the view that the hypothesis of statistical stationarity in economics is highly questionable.

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The Stationary Bootstrap

Cited by 1,712 publications

References 17 publications

A general bootstrap performance diagnostic

A general bootstrap performance diagnostic

Genetic Programming in Statistical Arbitrage

Symmetric thermal optimal path and time-dependent lead-lag relationship: novel statistical tests and application to UK and US real-estate and monetary policies

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