{"title":"通过典型相关分析估计大T和N因子模型中共同趋势的数量","authors":"Massimo Franchi, Iliyan Georgiev, Paolo Paruolo","doi":"10.1016/j.ecosta.2023.10.001","DOIUrl":null,"url":null,"abstract":"Asymptotic results for canonical correlations are derived when the analysis is performed between levels and cumulated levels of N time series of length T, generated by a factor model with s common stochastic trends. For T→∞ and fixed N and s, the largest s squared canonical correlations are shown to converge to a non-degenerate limit distribution while the remaining N−s converge in probability to 0. Furthermore, if s grows at most linearly in N, the largest s squared canonical correlations are shown to converge in probability to 1 as (T,N)seq→∞. This feature allows one to estimate the number of common trends as the integer with largest decrease in adjacent squared canonical correlations. The maximal gap equals 1 in the limit and this criterion is shown to be consistent. A Monte Carlo simulation study illustrates the findings.","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"113 1","pages":"0"},"PeriodicalIF":2.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Estimating the number of common trends in large T and N factor models via canonical correlations analysis\",\"authors\":\"Massimo Franchi, Iliyan Georgiev, Paolo Paruolo\",\"doi\":\"10.1016/j.ecosta.2023.10.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Asymptotic results for canonical correlations are derived when the analysis is performed between levels and cumulated levels of N time series of length T, generated by a factor model with s common stochastic trends. For T→∞ and fixed N and s, the largest s squared canonical correlations are shown to converge to a non-degenerate limit distribution while the remaining N−s converge in probability to 0. Furthermore, if s grows at most linearly in N, the largest s squared canonical correlations are shown to converge in probability to 1 as (T,N)seq→∞. This feature allows one to estimate the number of common trends as the integer with largest decrease in adjacent squared canonical correlations. The maximal gap equals 1 in the limit and this criterion is shown to be consistent. A Monte Carlo simulation study illustrates the findings.\",\"PeriodicalId\":54125,\"journal\":{\"name\":\"Econometrics and Statistics\",\"volume\":\"113 1\",\"pages\":\"0\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Econometrics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1016/j.ecosta.2023.10.001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1016/j.ecosta.2023.10.001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
Estimating the number of common trends in large T and N factor models via canonical correlations analysis
Asymptotic results for canonical correlations are derived when the analysis is performed between levels and cumulated levels of N time series of length T, generated by a factor model with s common stochastic trends. For T→∞ and fixed N and s, the largest s squared canonical correlations are shown to converge to a non-degenerate limit distribution while the remaining N−s converge in probability to 0. Furthermore, if s grows at most linearly in N, the largest s squared canonical correlations are shown to converge in probability to 1 as (T,N)seq→∞. This feature allows one to estimate the number of common trends as the integer with largest decrease in adjacent squared canonical correlations. The maximal gap equals 1 in the limit and this criterion is shown to be consistent. A Monte Carlo simulation study illustrates the findings.
期刊介绍:
Econometrics and Statistics is the official journal of the networks Computational and Financial Econometrics and Computational and Methodological Statistics. It publishes research papers in all aspects of econometrics and statistics and comprises of the two sections Part A: Econometrics and Part B: Statistics.