U mdWg@sbdZdddddgZdddd gd d d d gddddgddddgddddgddddgddd d!gd"d#d$d%gd&d'd(d)gd*d+d,d-gd.d/d0d1gd2d3d4d5gd6d7d8d9gd:d;dd?d@dAgdBdCdDdEgdFdGdHdIgdJdKdLdMgdNdOdPdQgdRdSdTdUgdVdWdXdYgdZd[d\d]gd^d_d`dagdbdcdddegdfdgdhdigdjdkdldmgdndodpdqgdrdsdtdugdvdwdxdygdzd{d|d}gd~dddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgdddd gd d d d gddddgddddgddddgddddgddd d!gd"d#d$d%gd&d'd(d)gd*d+d,d-gd.d/d0d1gd2d3d4d5gd6d7d8d9gd:d;d<d=gd>d?d@dAgdBdCdDdEgdFdGdHdIgdJdKdLdMgdNdOdPdQgdRdSdTdUgdVdWdXdYgdZd[d\d]gd^d_d`dagdbdcdddegdfdgdhdigdjdkdldEgdmdndodpgdqdrdsdtgdudvdwdxgdydzd{d|gd}d~ddgddddgddddgddddgddddgddddgddZdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdÐdĐdgdƐdǐdgdɐdʐdgd̐d͐dgdϐdАdgdҐdӐdgdՐd֐dgdؐdِdgdېdܐdgdސdߐdgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgddd gd d d gd ddgdddgdddgdddgdddgdddgdd d!gd"d#d$gd%d&d'gd(d)d*gd+d,d-gd.d/d0gd1d2d3gd4d5d6gd7d8d9gd:d;dd?gd@dAdBgdCdDdEgdFdGdHgdIdJdKgdLdMdNgdOdPdQgdRdSdTgdUdVdWgdXdYdZgd[d\d]gd^d_d`gdadbdcgdddedfgdgdhdigdjdkdlgdmdndogdpdqdrgdsdtdugdvdwdxgdydzd{gd|d}d~gdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgdddgddZdddÐdĐdŐdƐdǐdȐdɐdʐdːd̐d͐dΐdϐdАdѐdҐdӐdԐdՐd֐dאdؐdِdڐdېdܐdݐdސdߐdddddddddddddddddddddddddddddddddddddddddd d d d d ddddddddddddddddddd d!d"d#d$ddZd%Zd&d'd(d)gd*d+d,d-gd.d/d0d1gd2d3d4d5gd6d7d8d9gd:d;d<d=gd>d?d@dAgdBdCdDdEgdFdGdHdIgdJdKdLdMgdNdOdPdQgdRdSdTdUgdVdWdXdYgdZd[d\d]gd^d_d`dagdbdcdddegdfdgdhdigdjdkdldmgdndodpdqgdrdsdtdugdvdwdxdygdzd{d|d}gd~dddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddÐdĐdgdƐdǐdȐdgdʐdːd̐dgdΐdϐdАdgdҐdӐdԐdgd֐dאdؐdgdڐdېdܐdgdސdߐddgddddgddddgddddgddddgddddgddddgddddgddddgddddgdddd gd d d d gddddgddddgddddgddddgddd d!gd"d#d$d%gd&d'd(d)gd*d+d,d-gd.d/d0d1gd2d3d4d5gd6d7d8d9gd:d;d<d=gd>d?d@dAgdBdCdDdEgdFdGdHdIgdJdKdLdMgdNdOdPdQgdRdSdTdUgdVdWdXdYgdZd[d\d]gd^d_d`dagdbdcdddegdfdgdhdigdjdkdldmgdndodpdqgdrdsdtdugdvdwdxdygdzd{d|d}gd~dddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddddgddZdS(a Critical value polynomials and related quantities for the bounds test of Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of applied econometrics, 16(3), 289-326. These were computed using 32,000,000 simulations for each key using the methodology of PSS, who only used 40,000. The asymptotic P-value response functions were computed based on the simulated value. Critical values are the point estimates for the respective quantiles. The simulation code is contained in pss.py. The output files from this function are then transformed using pss-process.py. The format of the keys are (k, case, I1) where * k is is the number of x variables included in the model (0 is an ADF) * case is 1, 2, 3, 4 or 5 and corresponds to the PSS paper * I1 is True if X contains I1 variables and False if X is stationary The parameters are for polynomials of order 3 (large) or 2 (small). stat_star is the value where the switch between large and small occurs. Stat values less then stat_star use large_p, while values above use small_p. In all cases the stat is logged prior to computing the p-value so that the p-value is 1 - Phi(c[0] + c[1] * x + c[2] * x**2 + c[3] * x**3) where x = np.log(stat) and Phi() is the normal cdf. 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