I now choose intrinsic persistence, [rho], and the relative volatility of the NKPC shock, [[sigma].sub.u]/[[sigma].sub.s], to match the sample first-order autocorrelation
coefficient of inflation, Corr ([^.[pi].sub.t], [^.[pi].sub.t-1]) = 0.88, and the contemporaneous correlation of inflation and marginal cost, Corr ([^.[pi].sub.t], [^.s.sub.t]) = 0.33.
For detection of the deterministic components masked in a random background the autocorrelation
function (ACF) may be used, because autocorrelation
functions of deterministic data persist over all time displacements, while autocorrelation
functions of stochastic processes tend to zero for large time displacement.
As discussed by various authors that various economic players at times do follow the same trends because of the presence of significant autocorrelation
. Moreover an economy also observes the possible co-movements and cross-correlations of two or more trends such as a fall in the aggregate demand would mean less consumption of goods and services leading to laying off workers.
(7) Another well-known measure of spatial autocorrelation
is Getis and Ord's G statistic [see Anselin (1995a), p.
For a real Gaussian process Van Vleck and Middleton  have shown that the autocorrelation
coefficient ([R.sub.t] with t = [t.sub.2] - [t.sub.1]) of the output from a hard limiter is related with the input autocorrelation
coefficient (here denoted r) by the well-known arcsine law:
The sample autocorrelation
functions are analyzed in order to examine the reasons for the lack of independence.
The relation between the oscillation frequency and autocorrelation
is defined by power spectrum.
Sarwate, "Bounds on crosscorrelation and autocorrelation
of sequences," IEEE Transactions on Information Theory, vol.
A zero mean, single mean, and trend ADF along with autocorrelation
, partial autocorrelation
and cross correlation diagnostics can be used.
In ARIMA modeling the order of AR(p) is identified by partial autocorrelation
function (PACF) while the order of MA(q) is identified by autocorrelation
function (ACF) (Tsay 2002).
For 30 and 60 minute price distributions we recognize that the volatility autocorrelation
is low and due to the significant departures in the price distribution we consider a non-clustering mechanism to be the key reason for the departures from normality.
Our method, which involves a two-tiered estimation of the autocorrelation
function to refine its estimate, decreases the root mean square error (RMSE) of the estimated effective sample size by as much as a factor of 3-4 compared to the original formula for AR1 time series with large persistence (i.e., large lag-1 autocorrelation