Consciousness-Based Education - Maharishi University of ...

U.S.-Soviet Relations and the Maharishi EffectThe next step in the LTF method was tentative identification ofthe form of the noise model based on the autocorrelation (ACF), partialautocorrelation (PACF), and extended autocorrelation functions(EACF) of the noise process for the initially estimated model (Liu andHudak, 1986). The choice between alternative estimated noise modelssuggested by the ACF, PACF, and EACF was based on the minimizationof an objective criterion of model selection, the Akaike informationcriterion (AIC) described below.After tentative identification of the noise model, the LTF equationwas then re-estimated in order to obtain more efficient estimates of theimpulse response weights. Once satisfactory estimates of the impulseresponse weights were obtained, the pattern of the impulse responseweights was examined to identify the form of the transfer function foreach input variable. All estimated impulse response functions for themodels discussed in this paper displayed a “cutoff” pattern, suggestingthat each transfer function was linear, consisting only of numeratorparameters (Liu, 1985; Vandaele, 1983). 3 This finding was alsoconfirmed by the non-significance of estimated first and second orderdenominator parameters included in the TF model as a diagnostic“overfitting” exercise.Using the tentatively identified transfer functions and noise model, theTF equation was then estimated by maximum likelihood, and diagnosticchecks were used to suggest possible alterations in the model. Non-significantTF coefficients were deleted from the model, with higher-ordercoefficients generally being deleted first (Vandaele, 1983: 314).An objective criterion of model selection, minimization of the AIC,was employed to choose between alternative estimated noise models inthe LTF identification process. 4 Alternative models, often non-nested,frequently present tradeoffs between residual variance (goodness of fit)and number of model parameters (parsimony). The AIC criterion seeksto provide an optimal balance between the competing goals of parsimonyand precision of model fit (Akaike, 1974; Larimore and Mehra,1985). Larimore (1983) has demonstrated the optimality of the AIC forchoosing the model order and structure most likely to describe anothersample of the same process (“predictive inference”). In this context, theoptimality of the AIC was shown to be based on the fundamental sta-465