FinMath.Statistics.HypothesisTesting Namespace

Allows to perform the augmented Dickey-Fuller test for an unit root.

References:

1. Dickey, D. A., and W. A. Fuller. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root." Econometrica. Vol. 49, 1981, pp. 1057-1072.2.Dickey, D. A., and W. A. Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association. Vol. 74, 1979, pp. 427-431.3.Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.

One-sample χ²-test of the null hypothesis that the data in the sample comes from a normal distribution with specified supposed variance, against the alternative that data comes from a normal distribution with a different variance. http://en.wikipedia.org/wiki/Chi-squared_test#Chi-squared_test_for_variance_in_a_normal_population Default supposed variance is 1.

One-sample entropy-based runs test of the null hypothesis that data in the sample are independent and identically distributed.

Note. Decision based on P-value and significance level comparison is more exact.

Two-sample F-test of the null hypothesis that data in the samples are random samples from independent normal distributions with equal variances, against the alternative that the variances are different.

http://en.wikipedia.org/wiki/F-test_of_equality_of_variances

By default variances are supposed to be equal.

Represents base statistical hypothesis test. http://en.wikipedia.org/wiki/Statistical_hypothesis_testing

One sample Kolmogorov-Smirnov test of the null hypothesis that data in the sample is a random sample from specified distribution, against the alternative that the distribution is different. http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test#Kolmogorov.E2.80.93Smirnov_test Default supposed distribution is standard normal distribution.

Two sample Kolmogorov-Smirnov test of the null hypothesis that data in the samples are random samples from equal distributions, against the alternative that the distributions are different. http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test#Two-sample_Kolmogorov.E2.80.93Smirnov_test Default supposed distribution is standard normal distribution.

Allows to perform KPSS test for stationarity.

The test of Kwiatkowski, Phillips, Schmidt and Shin (KPSS) assesses the null hypothesis that a univariate time series is trend stationary against the alternative that it is a nonstationary unit-root process.

References: 1.Kwiatkowski, D., P. C. B. Phillips, P. Schmidt and Y. Shin. "Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root." Journal of Econometrics. Vol. 54, 1992, pp. 159-178.2.Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.

Represents base one-sample statistical hypothesis test. http://en.wikipedia.org/wiki/Statistical_hypothesis_testing

One sample Pearson’s χ² test of the null hypothesis that frequency distribution of events in the sample is consistent with provided theoretical distribution, against the alternative that the mean is different. http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test Default supposed distribution is standard normal distribution. Default number of bins is 10. Default number of estimated parameters is 0.

One-sample t-test of the null hypothesis that data in the sample are a random sample from a normal distribution with specified supposed mean and unknown variance, against the alternative that the mean is different. http://en.wikipedia.org/wiki/Student's_t-test#One-sample_t-test Default supposed mean value is 0.

Two-sample t-test of the null hypothesis that data in the samples are random samples from independent normal distributions with equal means, against the alternative that the means are different.

http://en.wikipedia.org/wiki/Student's_t-test#Independent_two-sample_t-test

By defaul means are supposed to be equal.

Note. Welch-Satterthwaite equation is used for approximation of degrees of freedom for unequal variances case.

Represents base two-sample statistical hypothesis test. http://en.wikipedia.org/wiki/Statistical_hypothesis_testing

One-sample Wald-Wolfowitz runs test of the null hypothesis that data in the sample are independent and identically distributed concerning being above/below specified value. http://en.wikipedia.org/wiki/Wald%E2%80%93Wolfowitz_runs_test The boundary values are compared to is sample mean if no other value is provided.

Note. Decision based on P-value and significance level comparison is more exact.

Two sample Wicoxon rank sum test of the null hypothesis that the distributions of both samples are equal, so that the probability of a sample of the first distribution exceeding a sample of the second distribution equals the probability of a sample from the second distribution exceeding a sample of the first distribution, that is, there is a symmetry between distributions with respect to probability of random drawing of a larger sample.

Note. Decision based on P-value and significance level comparison is more exact.

One sample Wicoxon signed rank test of the null hypothesis that the distribution is symmetric with respect to the supposed median, i.e. there are equal probabilities to get sample greater than m+x and less than m-x, where m is supposed median.

Note. Decision based on P-value and significance level comparison is more exact.

One sample z-test of the null hypothesis that data in the sample are a random sample from a normal distribution with specified supposed mean and standard deviation, against the alternative that the mean is different. http://en.wikipedia.org/wiki/Z-test Default supposed values of mean and variance are 0 and 1 correspondingly.

Type of time series model to use while performing test.

Enum used to indicate whether decision should be made comparing P-value with significance level or test statistics with critical value.

Marks whether we need to make one- or two-taled test and which tale we need for one-tailed test. http://en.wikipedia.org/wiki/One-_and_two-tailed_tests