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Table 4 The results of the binomial distribution test under different manufactured thresholds, Δ

From: Detecting the lead–lag effect in stock markets: definition, patterns, and investment strategies

Δ

CSI 300

S&P 500

\(\hat{\beta }\) of K–S

p value

\(\hat{\beta }\) of Kuiper

p value

\(\hat{\beta }\) of A–D

p value

\(\hat{\beta }\) of K–S

p value

\(\hat{\beta }\) of Kuiper

p value

\(\hat{\beta }\) of A–D

p value

0.10

0.409

0.000

0.420

0.003

0.392

0.000

0.343

0.000

0.347

0.000

0.352

0.000

0.15

0.536

0.000

0.553

0.180

0.510

0.000

0.710

0.001

0.695

0.178

0.714

0.000

0.20

0.660

0.000

0.641

0.049

0.660

0.000

0.759

0.000

0.782

0.046

0.752

0.000

0.25

0.723

0.000

0.739

0.047

0.765

0.000

0.777

0.000

0.773

0.013

0.782

0.000

0.30

0.819

0.000

0.835

0.006

0.803

0.000

0.792

0.000

0.793

0.007

0.766

0.000

  1. The statistical significance level is set to 0.05. Here, \(\hat{\beta }\) is the estimated value of parameter β contained in the probability function of the binomial distribution (i.e., \(P(X = k) = \left( {\begin{array}{*{20}c} n \\ k \\ \end{array} } \right)\beta^{k} (1 - \beta )^{n - k}\))