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Cross-correlation detection and analysis for California's electricity market based on analogous multifractal analysis
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10.1063/1.4793355
/content/aip/journal/chaos/23/1/10.1063/1.4793355
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/1/10.1063/1.4793355

Figures

Image of FIG. 1.
FIG. 1.

PDF of critical points for the statistical test with 10 000 i.i.d. Gaussian series.

Image of FIG. 2.
FIG. 2.

3-D figures of real time price and load in California's 1999 and 2000 electricity markets.

Image of FIG. 3.
FIG. 3.

Statistical test vs. time delay L calculated for two kinds of electricity data between price series and load series in California's 1999 and 2000 power markets. Shown are also the critical values for the 95% confidence level under the assumption of no cross-correlation. The area below denotes insignificant cross-correlation.

Image of FIG. 4.
FIG. 4.

Multifractal nature in the power-law cross-correlations between the values of average daily prices and loads for California's 1999 electricity market. (a) Power-law scaling in MAMFA and MAMF-XA with respect to L for q = 2 and 5; (b) power-law exponents and for price series and load series with different the values of q.

Image of FIG. 5.
FIG. 5.

Distance errors of estimation with different q for the methods of AMF-XA and MF-DXA.

Image of FIG. 6.
FIG. 6.

Statistical test vs. time delay L calculated for the two electricity series between prices and loads in January, March, June, August, and December in California's 1999 and 2000 electricity markets. The black curve denotes the critical values for the 95% confidence level under assumption of no cross-correlations. For each time delay L, the area above means significant cross-correlations, and vice versa. (a) California's 1999 electricity market and (b) California's 2000 electricity market.

Image of FIG. 7.
FIG. 7.

Multifractal nature in the power-law cross-correlation of real time prices and loads series. The power-law scaling in MAMFA and MAMF-XA with respect to s for q = 2 and 5. (a) California's 1999 electricity market in June; (b) describes the same market in December, and (c) gives the power-law exponents and for prices series and loads series of June and December with different values of q.

Image of FIG. 8.
FIG. 8.

Statistical test vs. time delay L calculated for the two electricity series between prices and loads in the low price periods (four open symbols) and in the peak price periods (four closed symbols) in California's 1999 and 2000 electricity markets. The black curve shows the critical values for the 95% confidence level under the assumption of no cross-correlations. For each time delay L, the area below denotes insignificant cross-correlations. (a) describes California's 1999 electricity market and (b) describes California's 2000 electricity market. (c) shows time variations in 24 intervals of the cross-correlation exponents in California's 1999 electricity market.

Image of FIG. 9.
FIG. 9.

Statistical test vs. time delay L calculated for the two kinds of electricity series, respectively, between the California's 1999 and 2000 electricity markets for four seasons. The black curve shows also the critical values for the 95% confidence level under the assumption of no cross-correlations. For each time delay L, the area below denotes insignificant cross-correlations. (a) describes the price series and (b) describes the load series.

Image of FIG. 10.
FIG. 10.

Statistical test vs. time delay L between the consecutive seasons in the California's 2000 electricity market for the prices and loads, respectively.

Tables

Generic image for table
Table I.

Critical values for the AMF-XA cross-correlation coefficient when for a given couple of time series each series is Gaussian i.i.d. with zero mean and unit variance.

Generic image for table
Table II.

Relative speedup of the critical values calculated based on the methods of DXA and AMF-XA for different series lengths N and different time delays L.

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/content/aip/journal/chaos/23/1/10.1063/1.4793355
2013-02-26
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Cross-correlation detection and analysis for California's electricity market based on analogous multifractal analysis
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/1/10.1063/1.4793355
10.1063/1.4793355
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