Consciousness-Based Education - Maharishi University of ...

consciousness-based education and GovernmentN tis a stochastic noise component, to be empirically determined,which may take the form of any stationary and invertible autoregressivemoving average (ARMA) process.The linear transfer function (LTF) method was used to empiricallyidentify the transfer function model (Liu, 1985, 1986; Liu and Hudak,1986; Pankratz, 1991). The LTF procedure is a refinement of the “leastsquares”approach to the identification of transfer function models, whichhas been shown to outperform the standard “pre-whitening” identificationprocedure based on cross correlations (Liu and Hanssens, 1982). Amajor advantage of the LTF procedure is that, unlike the prewhiteningprocedure, it is readily generalized to multiple input series (Pankratz,1991). It can also be applied to the identification of transfer functions forbinary intervention variables. A further advantage of the LTF method isthat simulation studies have shown it to be very effective in detecting thelack of relation ships between variables which are, in fact, unrelated, thusreducing the probability of spurious findings (Liu, 1985).Using the LTF approach, initial estimates of the impulse responseweights for each input variable were based on maximum likelihoodestimates of the TF equation after approximating each transfer functionby a linear polynomial of impulse response weights V i(B) (Liu,1985). The impulse response weights were given by the estimated coefficientsof the following polynomialsV i(B) = v i0+ v i1B + v i2B 2 + … + v imB m , i = 1, 2with the maximum lag m set to four months. For the endogenous inputvariable US t, the lag-zero (contemporaneous) impulse response weightv i0was set equal to zero in order to avoid possible simultaneous equationbias (Liu and Hudak, 1985). 1The noise component was initially specified as a first-order autoregressiveprocess since there was no suggestion of annual seasonality inthe estimated autocorrelations for the dependent variable USSR t. Thetentative, initial assumption of an AR(1) noise process—which may bemodified at a later stage, if appropriate—allows a check for the possiblenecessity of differencing and will generally improve the efficiency of theinitial estimates of the impulse response weights (Liu, 1985). 2 A formaltest for mean nonstationarity was also applied to both the dependentvariable USSR tand the independent variable US t. The Phillips-Perronunit root test (Phillips and Perron, 1988) was used for this purpose.464