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The procedure for the ADF test is the same as for the Dickey–Fuller test but it is applied to the model Δ y t = α + β t + γ y t − 1 + δ 1 Δ y t − 1 + ⋯ + δ p − 1 Δ y t − p + 1 + ε t , {\displaystyle \Delta y_{t}=\alpha +\beta t+\gamma y_{t-1}+\delta _{1}\Delta y_{t-1}+\cdots +\delta _{p-1}\Delta y_{t-p+1}+\varepsilon _{t},}
Pandas – High-performance computing (HPC) data structures and data analysis tools for Python in Python and Cython (statsmodels, scikit-learn) Perl Data Language – Scientific computing with Perl; Ploticus – software for generating a variety of graphs from raw data; PSPP – A free software alternative to IBM SPSS Statistics
In Python, the statsmodels [15] module includes functions for the covariance matrix using Newey–West. In Gretl, the option --robust to several estimation commands (such as ols) in the context of a time-series dataset produces Newey–West standard errors. [16]
Python has the statsmodelsS package which includes many models and functions for time series analysis, including ARMA. Formerly part of the scikit-learn library, it is now stand-alone and integrates well with Pandas. PyFlux has a Python-based implementation of ARIMAX models, including Bayesian ARIMAX models.
The general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of multiple linear regression to the case of more than one dependent variable.
The t-test p-value for the difference in means, and the regression p-value for the slope, are both 0.00805. The methods give identical results. This example shows that, for the special case of a simple linear regression where there is a single x-variable that has values 0 and 1, the t-test gives the same results as the linear regression. The ...
Python: a durbin_watson function is included in the statsmodels package (statsmodels.stats.stattools.durbin_watson), but statistical tables for critical values are not available there. SPSS: Included as an option in the Regression function. Julia: the DurbinWatsonTest function is available in the HypothesisTests package. [7]
MATLAB includes an implementation of the Jarque–Bera test, the function "jbtest". Python statsmodels includes an implementation of the Jarque–Bera test, "statsmodels.stats.stattools.py". R includes implementations of the Jarque–Bera test: jarque.bera.test in the package tseries, [3] for example, and jarque.test in the package moments. [4]