A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models

This article considers constructing confidence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the performance of various procedures in terms of exact coverage rates and lengths of the confidence intervals. These include the procedures of Bai (1997 Bai, J. (1997). Estimation of a change point in multiple regressions. Review of Economics and Statistics 79:551–563.) based on the asymptotic distribution under a shrinking shift framework, Elliott and Müller (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) based on inverting a test locally invariant to the magnitude of break, Eo and Morley (2015 Eo, Y., Morley, J. (2015). Likelihood-ratio-based confidence sets for the timing of structural breaks. Quantitative Economics 6:463–497.[Crossref], [Web of Science ®], [Google Scholar]) based on inverting a likelihood ratio test, and various bootstrap procedures. On the basis of achieving an exact coverage rate that is closest to the nominal level, Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) approach is by far the best one. However, this comes with a very high cost in terms of the length of the confidence intervals. When the errors are serially correlated and dealing with a change in intercept or a change in the coefficient of a stationary regressor with a high signal-to-noise ratio, the length of the confidence interval increases and approaches the whole sample as the magnitude of the change increases. The same problem occurs in models with a lagged dependent variable, a common case in practice. This drawback is not present for the other methods, which have similar properties. Theoretical results are provided to explain the drawbacks of Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) method

A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models

This article considers constructing confidence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the performance of various procedures in terms of exact coverage rates and lengths of the confidence intervals. These include the procedures of Bai (1997 Bai, J. (1997). Estimation of a change point in multiple regressions. Review of Economics and Statistics 79:551–563.) based on the asymptotic distribution under a shrinking shift framework, Elliott and Müller (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) based on inverting a test locally invariant to the magnitude of break, Eo and Morley (2015 Eo, Y., Morley, J. (2015). Likelihood-ratio-based confidence sets for the timing of structural breaks. Quantitative Economics 6:463–497.) based on inverting a likelihood ratio test, and various bootstrap procedures. On the basis of achieving an exact coverage rate that is closest to the nominal level, Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.) approach is by far the best one. However, this comes with a very high cost in terms of the length of the confidence intervals. When the errors are serially correlated and dealing with a change in intercept or a change in the coefficient of a stationary regressor with a high signal-to-noise ratio, the length of the confidence interval increases and approaches the whole sample as the magnitude of the change increases. The same problem occurs in models with a lagged dependent variable, a common case in practice. This drawback is not present for the other methods, which have similar properties. Theoretical results are provided to explain the drawbacks of Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218 method

Fractionally integrated processes and structural changes: theoretical analyses and bootstrap methods

The first chapter considers the asymptotic validity of bootstrap methods in a linear trend model with a change in slope at an unknown time. Perron and Zhu (2005) analyzed the consistency, rate of convergence, and limiting distributions of the parameter estimates in this model. I provide theoretical results for the asymptotic validity of bootstrap methods related to forming confidence intervals for the break date. I consider two bootstrap schemes, the residual (for white noise errors) and the sieve bootstrap (for correlated errors). Simulation experiments confirm that confidence intervals obtained using bootstrap methods perform well in terms of exact coverage rate. The second chapter extends Perron and Zhu's (2005) analysis to cover more general fractionally integrated errors with memory parameter d in the interval (-0.5,1.5). My theoretical results uncover some interesting features. For example, with a concurrent level shift allowed, the rate of convergence of the estimate of the break date is the same for all values of d in the interval (-0.5,0.5), a feature linked to the contamination induced by allowing a level shift. In all other cases, the rate of convergence is decreasing as d increases. I also provide results about the spurious break issue. The third chapter considers constructing confidence intervals for the break date in linear regressions. I compare the performance of various procedures in terms of the exact coverage rates and lengths: Bai's (1997) based on the asymptotic distribution with shrinking shifts, Elliott and Müller's (EM) (2007) based on inverting a test locally invariant to the magnitude of the change, Eo and Morley's (2013) based on inverting a likelihood ratio test, and various bootstrap procedures. In terms of coverage rates, EM's approach is the best but with a high cost in terms of length. With serially correlated errors and a change in intercept or in the coefficient of a regressor with a high signal-to-noise ratio, or when a lagged dependent variable is present, the length approaches the whole sample as the magnitude of the change increases. This drawback is not present for the other methods. Theoretical results are provided to explain the drawbacks of EM's method

The Effect Of Brand Experience Provider On Brand Experience: Focus On Korean Cosmetic Brand Shop

This present research distinguishes brand experience providers of cosmetic companies that include three elements: Brand identity elements of cosmetic brand shops (feminine and environmental-friendly brand identity); Marketing mix elements (level of iconic product, level of steady-seller product, reasonable pricing, convenience of location, quality of additional service); Cosmetic brand store elements (effective product assortment, atmosphere of a store, availability of testers, proficiency of consultants). This paper aims to explore these elements and the effect of brand experience provider on all brand experience dimensions; sensory, affective, intellectual, and behavioral experience. After the review of extant studies, we propose 11 hypotheses. Based on the collected 295 consumers of experienced cosmetic brand shop, the proposed model is testified with the SPSS 15.0 and AMOS 7.0 is supported. According to the result of empirical analysis, it turns out that, in terms of characteristics of brand experiential provider, 'feminine brand identity', 'iconic product', 'steady seller product', 'convenient location', 'additional service quality', 'assortment', 'atmosphere', 'self-tester', and 'consultant' affected the customers' holistic brand experience of cosmetic brand shop. However, 'environmental-friendly brand identity', 'reasonable price' results to have no influence on the holistic brand experience of brand of cosmetic brand shop. The study produced a theoretical implication on brand experience that it empirically approached to factors of brand experiential provider on holistic brand experience of store. The earlier studies were at best conceptual analysis or they mainly dealt with in-store factor, whereas this paper divides factors that affect the customer's overall experience into 'brand identity', 'marketing mix strategy', and 'physical environment of in-store'