In Figure 3, we display the autocorrelations
and cross-correlations of inflation and marginal cost for the four periods we have just mentioned: the 1960s, 1970s, 1980s, and the period beginning in 1992.
are uncorrelated with variances:
The findings of this paper as shown in table 1 reveal that all of the major economical players of Pakistan which include GDP deflator CPI Net export Remittances and Money supply (M2) have significant autocorrelations
for all first 10 lags (periods) which implies that all of the stated players do follow the certain upward trend with consistency for the period of before natural disasters.
ESDA describes and visualises spatial distributions, "identifies spatial outliers, detects agglomerations and local spatial autocorrelations
, and highlights the types of spatial heterogeneities" [van Oort (2004); Haining (1990); Bailey and Gatrell (1995); Anselin (1988); Le Gallo and Ertur (2003)].
Averaging different autocorrelations
we have computed the mean normalized autocorrelation
and its standard deviation (Figure 2 for BT = 10000).
This inconsistency can be explained by the fact that a linear AR(1) transformation can eliminate the long autocorrelations
in the absolute and squared return series.
Their 2D autocorrelations
are presented in Figures 7(c) and 7(d), respectively.
In addition, the autocorrelations
and power spectra  are presented to see whether the oscillations are periodic or not.
Correspondingly, we are interested in the maximum peak absolute values of cross-correlations and the minimum peak absolute values of autocorrelations
Changes in level or autocorrelations
that decline slowly at longer lags require first-order differencing, whereas slope changes require second-order differencing.
Distribution of residual autocorrelations
in autoregressive- integrated moving average time-series models.
The departures in the price distributions (Figs 2b and 4b) are probably caused by certain clustering mechanisms (autocorrelations
: 0.201, 0.22, 0.183) but we are not able to make any conclusion on non-clustering mechanism based on the measurement of volatility data series in this case.