Consciousness-Based Education - Maharishi University of ...

consciousness-based education and GovernmentMaximum likelihood estimates for the model are shown in Table2. 14 Under the assumption of normally distributed disturbances, themaximum likelihood (ML) estimates of Box-Jenkins models and timeseries regressions are consistent and asymptotically normally distributed(Harvey, 1990; Brockwell and Davis, 1987). The same propertiesof the ML estimates have been shown to hold, under very mild conditions,in the case of non-normal residual errors (Harvey, 1990; Li andMcCleod, 1988; Brockwell and Davis, 1987). Since the sample size forthis study is n = 93, the p-values for all reported asymptotic t-statisticsare based on the standard normal approximation. 15For the estimated AR noise model, the roots of the AR polynomial layoutside the unit circle, consistent with invertibility of the noise model andmean stationarity for the dependent variable. 16 The quality of estimateswas high, with uniformly low correlation among estimated parameters. 17ParameterTable 2: Transfer Function Model Parameter EstimatesEstimation Model:USSR t= c + (ω 11B)US t+ (ω 20+ ω 22B 2 + ω 24B 4 )I t+ N tVariableN t= 1/(φ 1B + φ 5B 5 + φ 6B 6 + φ 11B 11 ) a tParameterTypeLagParameterEstimateStd.Errort Valuep Value*1 ω 11US Num. 1 0.214 0.071 3.02 0.00262 ω 20I Num. 0 27.830 10.251 2.71 0.00343 ω 22I Num. 2 23.770 10.620 2.24 0.01254 ω 24I Num. 4 39.794 10.087 3.94 0.00005 c USSR Const. 0 –19.129 10.501 –1.82 0.06886 φ 1USSR AR 1 0.558 0.089 6.29 0.00007 φ 5USSR AR 5 0.417 0.097 4.30 0.00008 φ 6USSR AR 6 –0.383 0.099 –3.86 0.00019 φ 11USSR AR 11 0.148 0.077 1.94 0.0524* In the case of all intervention parameters for the variable It, reported p-values are for aone-tailed test of the directional hypothesis of a positive impact on the dependent variableUSSR t. All other reported p-values are for a two-tailed test.Residual Variance Estimate 718.445 Effective Number of Observations 93Residual Standard Error 26.804 Ljung-Box Q for Lags 1-12 (8 d.f.) 4.7R-Square 0.547 AIC 629.669470