A model selection test for non-nested misspecified diffusion models is developed by using a criterion based on the Kullback-Leibler information criterion in a new asymptotic framework that accounts for the relative significance of diffusion functions for high frequency data. The test examines the hypothesis that two competing models are equivalent in the criterion. Our approach differentiates the roles of diffusion and drift functions and shows the equivalence of models must be understood differently depending on the sampling frequencies; it is of primary importance for a model to have a diffusion function close to the true diffusion function for superiority when the sampling frequency is high, and we compare drift functions if the models can not be distinguished by the diffusion functions. As the sampling frequencies become higher, the diffusion functions are more important, and the informative signal for ranking the drift functions is weaker. The drift functions are useful only when we sample data for long enough. Our new asymptotics deals with the different rates of information in the diffusion and drift functions by considering both the sampling interval Δ and the sampling span T, and we show the sampling span must increase at a relative speed faster than Δ⁻² (or Δ²T→∞) to ensure sufficient information to be collected for distinguishing two models by their drift functions. The limiting distribution of the test statistic is normal, and we compare different asymptotic approximations to the sampling distribution of the test statistic using the sub-sampling, and the nonparametric block bootstrap methods, as well as the standard normal approximation for the test statistics standardized by the heteroskedasticity auto-correlation consistent variance estimators. We apply our test to the model selection problems for spot interest rate models and exchange rate models. We find that many popular models are observationally equivalent.
{"title":"Model Selection Testing for Diffusion Processes with Applications to Interest Rate and Exchange Rate Models","authors":"Hwan-sik Choi, Minsoo Jeong, Joon Y. Park","doi":"10.2139/ssrn.1491244","DOIUrl":"https://doi.org/10.2139/ssrn.1491244","url":null,"abstract":"A model selection test for non-nested misspecified diffusion models is developed by using a criterion based on the Kullback-Leibler information criterion in a new asymptotic framework that accounts for the relative significance of diffusion functions for high frequency data. The test examines the hypothesis that two competing models are equivalent in the criterion. Our approach differentiates the roles of diffusion and drift functions and shows the equivalence of models must be understood differently depending on the sampling frequencies; it is of primary importance for a model to have a diffusion function close to the true diffusion function for superiority when the sampling frequency is high, and we compare drift functions if the models can not be distinguished by the diffusion functions. As the sampling frequencies become higher, the diffusion functions are more important, and the informative signal for ranking the drift functions is weaker. The drift functions are useful only when we sample data for long enough. Our new asymptotics deals with the different rates of information in the diffusion and drift functions by considering both the sampling interval Δ and the sampling span T, and we show the sampling span must increase at a relative speed faster than Δ⁻² (or Δ²T→∞) to ensure sufficient information to be collected for distinguishing two models by their drift functions. The limiting distribution of the test statistic is normal, and we compare different asymptotic approximations to the sampling distribution of the test statistic using the sub-sampling, and the nonparametric block bootstrap methods, as well as the standard normal approximation for the test statistics standardized by the heteroskedasticity auto-correlation consistent variance estimators. We apply our test to the model selection problems for spot interest rate models and exchange rate models. We find that many popular models are observationally equivalent.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131193823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper analyses the constant elasticity of volatility (CEV) model suggested by [6]. The CEV model without mean reversion is shown to be the inverse Box-Cox transformation of integrated processes asymptotically. It is demonstrated that the maximum likelihood estimator of the power parameter has a nonstandard asymptotic distribution, which is expressed as an integral of Brownian motions, when the data generating process is not mean reverting. However, it is shown that the t-ratio follows a standard normal distribution asymptotically, so that the use of the conventional t-test in analyzing the power parameter of the CEV model is justified even if there is no mean reversion, as is often the case in empirical research. The model may applied to ultra high frequency data.
{"title":"Testing the Box-Cox Parameter in an Integrated Process","authors":"Jian Huang, Masahito Kobayashi, M. McAleer","doi":"10.2139/ssrn.1469098","DOIUrl":"https://doi.org/10.2139/ssrn.1469098","url":null,"abstract":"This paper analyses the constant elasticity of volatility (CEV) model suggested by [6]. The CEV model without mean reversion is shown to be the inverse Box-Cox transformation of integrated processes asymptotically. It is demonstrated that the maximum likelihood estimator of the power parameter has a nonstandard asymptotic distribution, which is expressed as an integral of Brownian motions, when the data generating process is not mean reverting. However, it is shown that the t-ratio follows a standard normal distribution asymptotically, so that the use of the conventional t-test in analyzing the power parameter of the CEV model is justified even if there is no mean reversion, as is often the case in empirical research. The model may applied to ultra high frequency data.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116667505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Seemingly absent from the arsenal of currently available "nearly efficient" testing procedures for the unit root hypothesis, i.e. tests whose asymptotic local power functions are virtually indistinguishable from the Gaussian power envelope, is a test admitting a (quasi-)likelihood ratio interpretation. We study the large sample properties of a quasi-likelihood ratio unit root test based on a Gaussian likelihood and show that this test is nearly efficient.
{"title":"Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis","authors":"Michael Jansson, M. Nielsen","doi":"10.2139/ssrn.1467526","DOIUrl":"https://doi.org/10.2139/ssrn.1467526","url":null,"abstract":"Seemingly absent from the arsenal of currently available \"nearly efficient\" testing procedures for the unit root hypothesis, i.e. tests whose asymptotic local power functions are virtually indistinguishable from the Gaussian power envelope, is a test admitting a (quasi-)likelihood ratio interpretation. We study the large sample properties of a quasi-likelihood ratio unit root test based on a Gaussian likelihood and show that this test is nearly efficient.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126015141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper re-examines the tests of the Sharpe-Lintner Capital Asset Pricing Model (CAPM). The null that the CAPM intercepts are zero is tested for ten size-based stock portfolios and for twenty five book-to-market sorted portfolios using five-year, ten-year and longer sub-periods during 1965-2004. The paper shows that the evidence for rejecting the CAPM on statistical grounds is weaker than the consensus view suggests, and highlights the pitfalls of testing multiple hypotheses with the conventional heteroskedasticity and autocorrelation robust (HAR) test with asymptotic P-values. The conventional test rejects the null for almost all sub-periods, which is consistent with the evidence in the literature. By contrast, the null is not rejected for most of the sub-periods by the new HAR tests developed by Kiefer et al. (2000), Kiefer and Vogelsang (2005), and Sun et al. (2008).
{"title":"Testing the CAPM Revisited","authors":"Surajit D. Ray, N. Savin, Ashish Tiwari","doi":"10.2139/ssrn.1364800","DOIUrl":"https://doi.org/10.2139/ssrn.1364800","url":null,"abstract":"This paper re-examines the tests of the Sharpe-Lintner Capital Asset Pricing Model (CAPM). The null that the CAPM intercepts are zero is tested for ten size-based stock portfolios and for twenty five book-to-market sorted portfolios using five-year, ten-year and longer sub-periods during 1965-2004. The paper shows that the evidence for rejecting the CAPM on statistical grounds is weaker than the consensus view suggests, and highlights the pitfalls of testing multiple hypotheses with the conventional heteroskedasticity and autocorrelation robust (HAR) test with asymptotic P-values. The conventional test rejects the null for almost all sub-periods, which is consistent with the evidence in the literature. By contrast, the null is not rejected for most of the sub-periods by the new HAR tests developed by Kiefer et al. (2000), Kiefer and Vogelsang (2005), and Sun et al. (2008).","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131158163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Whereas existing literature on inflation targeting has up to now focused on its impact on macroeconomic variables, this paper aims at investigating empirically whether the adoption of this framework has changed the preferences of the central banker. Using Markov-Switching VAR and Time Varying Parameters, we test the hypothesis that inflation targeting has constituted a switch towards a greater focus on inflation as conventional wisdom suggests. These two methods share the advantage of being nonlinear, of accounting for heteroskedasticity and of escaping the issue of choosing a date break. Our main results show that inflation targeting has not led to a stronger response to inflation and that the relative weight of inflation compared to output gap has decreased.
{"title":"Has Inflation Targeting Represented a Policy Switch? Evidence from Markov Switching-Var and Time-Varying Parameters","authors":"J. Creel, P. Hubert","doi":"10.2139/ssrn.1438010","DOIUrl":"https://doi.org/10.2139/ssrn.1438010","url":null,"abstract":"Whereas existing literature on inflation targeting has up to now focused on its impact on macroeconomic variables, this paper aims at investigating empirically whether the adoption of this framework has changed the preferences of the central banker. Using Markov-Switching VAR and Time Varying Parameters, we test the hypothesis that inflation targeting has constituted a switch towards a greater focus on inflation as conventional wisdom suggests. These two methods share the advantage of being nonlinear, of accounting for heteroskedasticity and of escaping the issue of choosing a date break. Our main results show that inflation targeting has not led to a stronger response to inflation and that the relative weight of inflation compared to output gap has decreased.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127883296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a test for the correct specification of a dynamic time-series model that is taken to be stationary about a deterministic linear trend function with no more than a finite number of discontinuities in the vector of trend coefficients. The test avoids the consideration of explicit alternatives to the null of trend stability. The proposal also does not involve the detailed modelling of the data-generating process of the stochastic component, which is simply assumed to satisfy a certain strong invariance principle for stationary causal processes taking a general form. As such, the resulting inference procedure is effectively an omnibus specification test for segmented linear trend stationarity. The test is of Wald-type, and is based on an asymptotically linear estimator of the vector of total-variation norms of the trend parameters whose influence function coincides with the efficient influence function. Simulations illustrate the utility of this procedure to detect discrete breaks or continuous variation in the trend parameter as well as alternatives where the trend coefficients change randomly each period. This paper also includes an application examining the adequacy of a linear trend-stationary specification with infrequent trend breaks for the historical evolution of U.S. real output.
{"title":"Efficient Semiparametric Detection of Changes in Trend","authors":"Chuan Goh","doi":"10.2139/ssrn.1142744","DOIUrl":"https://doi.org/10.2139/ssrn.1142744","url":null,"abstract":"This paper proposes a test for the correct specification of a dynamic time-series model that is taken to be stationary about a deterministic linear trend function with no more than a finite number of discontinuities in the vector of trend coefficients. The test avoids the consideration of explicit alternatives to the null of trend stability. The proposal also does not involve the detailed modelling of the data-generating process of the stochastic component, which is simply assumed to satisfy a certain strong invariance principle for stationary causal processes taking a general form. As such, the resulting inference procedure is effectively an omnibus specification test for segmented linear trend stationarity. The test is of Wald-type, and is based on an asymptotically linear estimator of the vector of total-variation norms of the trend parameters whose influence function coincides with the efficient influence function. Simulations illustrate the utility of this procedure to detect discrete breaks or continuous variation in the trend parameter as well as alternatives where the trend coefficients change randomly each period. This paper also includes an application examining the adequacy of a linear trend-stationary specification with infrequent trend breaks for the historical evolution of U.S. real output.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126495530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present results of an experiment on expectation formation in an asset market. Participants to our experiment must provide forecasts of the stock future return to computerized utility-maximizing investors, and are rewarded according to how well their forecasts perform in the market. In the Baseline treatment participants must forecast the stock return one period ahead; in the Volatility treatment, we also elicit subjective confidence intervals of forecasts, which we take as a measure of perceived volatility. The realized asset price is derived from a Walrasian market equilibrium equation with non-linear feedback from individual forecasts. Our experimental markets exhibit high volatility, fat tails and other properties typical of real financial data. Eliciting confidence intervals for predictions has the effect of reducing price fluctuations and increasing subjects' coordination on a common prediction strategy.
{"title":"Does Volatility Matter? Expectations of Price Return and Variability in an Asset Pricing Experiment","authors":"G. Bottazzi, Giovanna Devetag, F. Pancotto","doi":"10.2139/ssrn.1317345","DOIUrl":"https://doi.org/10.2139/ssrn.1317345","url":null,"abstract":"We present results of an experiment on expectation formation in an asset market. Participants to our experiment must provide forecasts of the stock future return to computerized utility-maximizing investors, and are rewarded according to how well their forecasts perform in the market. In the Baseline treatment participants must forecast the stock return one period ahead; in the Volatility treatment, we also elicit subjective confidence intervals of forecasts, which we take as a measure of perceived volatility. The realized asset price is derived from a Walrasian market equilibrium equation with non-linear feedback from individual forecasts. Our experimental markets exhibit high volatility, fat tails and other properties typical of real financial data. Eliciting confidence intervals for predictions has the effect of reducing price fluctuations and increasing subjects' coordination on a common prediction strategy.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131499889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We reassess the performance of market-timing rules when controlling for data-snooping biases. For the first time, a comprehensive set of simple and complex market-timing rules is examined and tested for statistical significance, using the White (2000) "Reality Check," the Hansen (2005) SPA test, as well as their stepwise extensions by Romano and Wolf (2005) and Hsu, Hsu, and Kuan (2010). Even though individual market-timing rules significantly outperform a buy-and-hold strategy at both daily and monthly frequencies when considered in isolation, their outperformance, generally, does not remain significant after correcting for data snooping. Relative to the alternative of investing in the risk-free rate, however, we find significant outperformance of the best rules, even after data-snooping adjustment, when testing at a monthly timing frequency. (JEL: G11, G14) Copyright The Author 2011. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.
{"title":"Data Snooping and Market-Timing Rule Performance","authors":"A. Neuhierl, Bernd Schlusche","doi":"10.2139/ssrn.1343896","DOIUrl":"https://doi.org/10.2139/ssrn.1343896","url":null,"abstract":"We reassess the performance of market-timing rules when controlling for data-snooping biases. For the first time, a comprehensive set of simple and complex market-timing rules is examined and tested for statistical significance, using the White (2000) \"Reality Check,\" the Hansen (2005) SPA test, as well as their stepwise extensions by Romano and Wolf (2005) and Hsu, Hsu, and Kuan (2010). Even though individual market-timing rules significantly outperform a buy-and-hold strategy at both daily and monthly frequencies when considered in isolation, their outperformance, generally, does not remain significant after correcting for data snooping. Relative to the alternative of investing in the risk-free rate, however, we find significant outperformance of the best rules, even after data-snooping adjustment, when testing at a monthly timing frequency. (JEL: G11, G14) Copyright The Author 2011. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131100774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper reviews the political economy view of economic growth in post-communist economies making the transition to free markets, focusing on the role of economic policy and institutions. We test the hypothesis that better institutions, measured in terms of economic freedom, contribute to growth. The empirical results from the cross-section of transition economies confirm this hypothesis. The paper concludes that non-linearities are present in the growth model and that differences arise depending on how economic well-being is defined.
{"title":"Economic Freedom as a Driver for Growth in Transition","authors":"Jenni Paakkonen","doi":"10.2139/ssrn.1341625","DOIUrl":"https://doi.org/10.2139/ssrn.1341625","url":null,"abstract":"This paper reviews the political economy view of economic growth in post-communist economies making the transition to free markets, focusing on the role of economic policy and institutions. We test the hypothesis that better institutions, measured in terms of economic freedom, contribute to growth. The empirical results from the cross-section of transition economies confirm this hypothesis. The paper concludes that non-linearities are present in the growth model and that differences arise depending on how economic well-being is defined.","PeriodicalId":425229,"journal":{"name":"ERN: Hypothesis Testing (Topic)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125376746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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