Library of Methods and Models

Linear regression:

• Linear regression calculation methods:

• • Least-squares method.

  • Instrumental variables estimation method.

• Linear regression with truncated and censored data.

Binary linear regression.

Multiple linear regression.

Binary regression.

Non-linear regression.

Autoregression.

Panel data regression.

Quantile regression.

Rolling regression.

Trend with functional dependency estimation.

Stationarity and characteristic roots.

ARIMA:

• Regression model with autoregression residuals and moving average.

• ARIMA model coefficient estimation:

• • Coefficients estimation using maximum likelihood method.

  • Quasi Newton method.

  • Levenberg-Marquardt method.

Distributed lag models:

• Polynomial distributed lag model. Almon's method.

• Geometrical distributed lag model. Koyck method.

Methods of smoothing and seasonality selection:

• Median smoothing.

• Moving average.

• GM(1,1) model (Grey forecast).

• Hodrick-Prescott filter.

• LRX filter.

• Baxter-King filter.

• Exponential smoothing:

• • Model with additive and multiplicative seasonal effects.

  • Growth models.

  • Best trial method.

• Census1.

• X11.

• X12-ARIMA.

• TRAMO/SEATS.

Cointegrated processes:

• Error correction model.

• Vector error correction model.

Spectrum analysis.

GARCH model.

Geometric extrapolation.

Aggregation (basic and extended).

Interpolation.

Missing data treatment.

Distributions:

• Binomial distribution.

• Exponential distribution.

• Lognormal distribution.

• Normal distribution.

• Uniform distribution.

• Student's distribution.

• Chi-squared distribution.

• Fisher distribution.

• Beta distribution.

• Gamma distribution.

• Weibull distribution.

• Logistic distribution.

• Cauchy distribution.

• Poisson distribution.

• Hypergeometric distribution.

• Multivariate normal distribution.

• Pareto distribution.

• Generalized Pareto distribution.

• Generalized distribution of extreme values.

Distribution parameters estimation:

• Maximum likelihood estimation.

• Linear combination of ratios of spaces.

Distribution functions:

Naive Bayes classifier.

Exception analysis.

Decision tree.

Logistic regression.

Back-propagation network.

Kohonen self-organizing maps.

K-modes clustering.

Discriminatory analysis.

Association analysis.

Input-output balance model.

Value-At-Risk:

• Delta normal calculation method.

• Historical method of calculation.

• Monte Carlo method.

• Back-testing: Traffic Lights principle.

Solution methods for system of non-linear equations.

Solution of linear equation system. Gauss method.

Multivariate statistical analysis:

• Principal components method.

• Singular spectrum analysis.

• Hierarchical cluster analysis.

• K-means clustering.

Constrained optimal control problem.

Quadratic programming problem.

Difference equation system.

Average.

Geometric mean.

Harmonic mean.

Variance.

Root-mean-square deviation.

Variation coefficient.

Mean deviation.

Index of skewness.

Index of kurtosis.

Median.

Mode.

Quantile.

Range.

Sum of squares.

Dickey-Fuller test.

Granger test.

Autocorrelation analysis.

Correlation coefficient.

t-statistics.

Johansen test.

Kolmogorov-Smirnov test.

Analysis of variance.

Fisher criterion.

Chi test.

Performance criteria:

• Fisher statistics.

• Determination coefficient.

• Adjusted determination coefficient.

• Performance criteria of binary choice model.

• Information criteria.

• Likelihood function.

• Standard error.

• Pearson fitting criterion.

• J statistic.

Tests for unit roots:

• Augmented Dickey-Fuller Test.

Diagnostic criteria:

• Durbin-Watson test.

Residual analysis:

• Standard deviation.

• Jarque–Bera statistic.