### Table A-1: LR Tests for Lag Length in the 5-Variable VAR with Long-Term U.S.-U.K. Data

1999

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### Table 2: EXPERIMENT 2 | Long time lags. Success percentage and learning time until success. With 100 time step delays, only CH and LSTM are successful. Method Delay p Learning rate # weights % Successful trials Success after

"... In PAGE 6: ... Experimental details can be found in [8]. Table2 gives the results. Gradient based methods (RTRL, BPTT) get into trouble when the minimal time lag exceeds 10 steps.... ..."

### Table 1. Powers of the long-memory coe cients with 150 truncated lags. d ?(d) E( t) A1 A2 A3 A4 B4

"... In PAGE 6: ...Table1 indicates the powers of the long-memory coe cient of t according to di erent values of d and m=150. Some results for d that were found by Ding and Granger were around 0.... ..."

### Table 7 - Determinants of TFP log differences 1998-2000: specification with lagged ICT intensity (LONG sample; 1119 observations) 1 2 3 4 Constant -0.083* -0.081* -0.081* -0.070

"... In PAGE 20: ...20 sample (reported in Table7 ) show that the (gross) rate of return of the lagged ICT investment is significant and higher than that of R amp;D investment (79% versus 53%). The latter results suggest that those of the previous regressions are probably influenced by the fact that ICT outlays are not necessarily persistent and, often, are undertaken in a modular way.... ..."

### Table 1: Leading Indicator Lags for GDP

"... In PAGE 10: ...Table1... In PAGE 13: ... s is the standard error of the regression. bi represents the coefficient on the i -th regressor (not the coefficient on the i -th lag, see Table1 for the appropriate lags). Standard errors are given inside parentheses.... In PAGE 14: ...210 .558 Notes : b1 i and b0 i correspond to regime 1 and regime 0 respectively, with i =0 giving the constant transition probability while i =1 is the lagged leading indicator coefficient (see Table1 for appropriate lags). Standard errors are given inside parentheses.... In PAGE 15: ...194 .547 Notes : b1 i and b0 i correspond to regime 1 and regime 0 respectively, with i =0 giving the constant transition probability while i =1 is the lagged leading indicator coefficient (see Table1 for appropriate lags). Standard errors are given inside parentheses.... ..."

### Table 9: Box-Ljung statistic using 1500 lags using the randomised residuals from the fit of the GLARMA model. If the model is correctly fitting the statistics should be around 1500 with a standard error of 55.

"... In PAGE 18: ... Work on this topic continues. In Table9 we also give the Box-Ljung statistics for the fitted model using the ran- domisation procedure, (1), discussed in the previous subsection. The statistic is computed using 1, 500 lags and is designed to pick up correlations at long lags.... ..."

### Table 3: Task 2c: LSTM with very long minimal time lags q + 1 and a lot of noise. p is the number of available distractor symbols (p + 4 is the number of input units). q p is the expected number of occurrences of a given distractor symbol in a sequence. The rightmost column lists the number of training sequences required by LSTM (BPTT, RTRL and the other competitors have no chance of solving this task). If we let the number of distractor symbols (and weights) increase in proportion to the time lag, learning time increases very slowly. The lower block illustrates the expected slow-down due to increased frequency of distractor symbols.

"... In PAGE 15: ... 20 trials were made for all tested pairs (p; q). Table3 lists the mean of the number of training sequences required by LSTM to achieve success (BPTT and RTRL have no chance of solving non-trivial tasks with minimal time lags of 1000 steps). Scaling.... In PAGE 15: ... Scaling. Table3 shows that if we let the number of input symbols (and weights) increase in proportion to the time lag, learning time increases very slowly. This is a another remarkable property of LSTM not shared by any other method we are aware of.... In PAGE 15: ... Distractor in uence. In Table3 , the column headed by q p gives the expected frequency of distractor symbols. Increasing this frequency decreases learning speed, an e ect due to weight oscillations caused by frequently observed input symbols.... ..."

### Table 5 Results of Unemployment Lags Specification Search Assuming twelve inflation lags

1999

"... In PAGE 20: ...mplied weight of lagged unemployment in the temporary NAIRU of between 0.25 and 0.4. Table5 shows results when we use a relatively short lag on past changes in inflation, of just twelve quarters. Looking first at the top panel, the results for the CPI and the nonfarm business sector deflator are now qualitatively different from those in the top panel of table 4: The preferred lag length on past unemployment is now very long, five years for the CPI and six for the NFB deflator.... ..."

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### Table 4: Long run estimates (ARDL)

"... In PAGE 21: ... Based on the choice of these lags, the asymptotic long run coefficients and their standard errors can be estimated. Table4 shows the results for some of the models discussed so far. (These use the Schwarz-Bayesian criteria, which Pesaran and Shin found the most reliable).... ..."

### Table 1 Mean and standard error (in smooth parentheses) of median RTs (ms) for consistent responses to Controls and Repeats, and their difference (priming), for each lag, collapsed across participant group (N = 27) Long Short Delayed Immediate

"... In PAGE 6: ...ag [F(2.63,65.8) = 2.04, P = 0.12]. If Delayed and Immediate Controls were restricted to those trials in which the same response was given as the previous trial (as was necessarily the case for Delayed and Immediate Repeats; see Materials and methods), the mean Control RTs decreased, but only slightly (see Table1 ). The ANOVA for Delayed and Immediate lags still showed a main effect of priming, [ F(1,25) = 115, P lt; 0.... ..."