This paper argues that a linear statistical model with homoskedastic
errors cannot capture the nineteenth-century notion of a recurring cyclical pattern in key economic aggregates.
Under the null hypothesis of normality, the conditional mean and variance are expected to be zero and unity, respectively, and the variance is to be serially uncorrelated and homoskedastic
The model does not pass the diagnostic tests for serially independent and homoskedastic
residuals in the case of the United States, implying that estimated standard errors of the coefficients are inefficient.
A Lagrange multiplier test rejects the null of homoskedastic
errors in favor of error components.
i] represents the normally and homoskedastic
distributed error term.
36) (In the case where residuals are homoskedastic
within periods but heteroskedastic across time, adjusted values such as those produced by the nonparametric method proposed by Duan will give estimates that are numerically identical to unadjusted values produced by other methods.
For this reason, our traditional methodology for the CFNAI can be considered a special case of the dynamic factor model with a zero transition matrix and a homoskedastic
idiosyncratic error structure (that is, the assumption of equal variances across unobserved idiosyncratic drivers of the underlying data series).
idiosyncratic component, same variance for the common and idiosyncratic component: [e.
t] is specified as a homoskedastic
random walk with drift, that is, [mu](r) = r + [gamma], [sigma](r) = [sigma].
Smearing" estimators such as the Duan smearing estimator have been developed to account for this bias, but these are generally only appropriate when error terms are homoskedastic
(Duan 1983; Duan et al.
Because geometric Brownian motion produces homoskedastic
log-returns, an alternative model has been proposed by Cox and Ross (1976) to capture this heteroskedasticy feature.
1) Diagnostic test results reported in table 3 show that the VAR is not serially correlated and is homoskedastic