Statistics — Page 30
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Nonlinear Fixed Effects Model
The nonlinear fixed effects model extends fixed effects panel estimation to outcomes governed by nonlinear response functions — such as binary, count, or censored outcomes — while absorbing unobserved individual heterogeneity through unit-s...
Nonlinear GARCH model
The Nonlinear GARCH model extends the standard GARCH framework to capture asymmetric and nonlinear responses of conditional volatility to past shocks. It allows negative returns (bad news) to amplify volatility more than positive returns of...
Nonlinear GLS
Nonlinear Generalized Least Squares extends the classical GLS framework to regression models where the mean function is nonlinear in the parameters. It accounts for non-spherical errors — heteroscedasticity or autocorrelation — by pre-weigh...
Nonlinear Granger Causality
Nonlinear Granger causality extends the classic linear Granger causality framework to detect predictive relationships that operate through nonlinear dynamics. Using nonparametric or semi-parametric statistics based on correlation integrals...
Nonlinear Hausman test
The Nonlinear Hausman test extends Hausman's (1978) endogeneity specification test to nonlinear models such as probit, logit, Tobit, and count-data regressions. It tests whether suspected regressors are endogenous — i.e., correlated with th...
Nonlinear Johansen Cointegration
Nonlinear Johansen cointegration extends the classical Johansen framework to detect long-run equilibrium relationships among integrated time series when the adjustment process is nonlinear. Using rank-based transformations, the approach tes...
Nonlinear KPSS Test
The nonlinear KPSS test extends the classic Kwiatkowski-Phillips-Schmidt-Shin stationarity test by modelling unknown smooth structural breaks in the deterministic trend using a Fourier approximation. Under the null hypothesis the series is...
Nonlinear MA model
The Nonlinear Moving Average (NMA) model extends the classical linear MA model by allowing the current observation to depend on past innovations through a nonlinear function rather than a simple weighted sum. It is used in time series analy...
Nonlinear NARDL
The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing an explanatory variable into its positive and negative partial sums, it tests whether...
Nonlinear OLS
Nonlinear Ordinary Least Squares (NLS) estimates regression models in which the conditional mean function is nonlinear in the parameters. Like standard OLS it minimises the sum of squared residuals, but because no closed-form solution exist...
Nonlinear PP unit root test
The Nonlinear Phillips-Perron unit root test extends the classic PP test by allowing the adjustment toward equilibrium to follow a nonlinear path — such as a smooth transition or threshold mechanism — rather than assuming a constant linear...
Nonlinear Panel Data Analysis
Nonlinear panel data analysis applies nonlinear models — such as probit, logit, Poisson, or Tobit — to repeated observations on the same units over time. It accounts for unit-specific unobserved heterogeneity while capturing non-linear rela...
Nonlinear Random Effects Model
The nonlinear random effects model extends classical random effects estimation to settings where the outcome variable is binary, count-based, censored, or otherwise non-continuously distributed across panel units. It accounts for unobserved...
Nonlinear SARIMA Model
The Nonlinear SARIMA model extends the classical Seasonal ARIMA framework by replacing the linear conditional mean function with a nonlinear specification — such as threshold switching or smooth transition — while retaining seasonal differe...
Nonlinear SVAR Model
The Nonlinear Structural VAR model extends the standard SVAR framework to allow structural relationships and dynamic responses to vary across economic regimes or states of the world. By imposing nonlinear transition mechanisms — such as thr...
Nonlinear System GMM
Nonlinear System GMM extends the Generalized Method of Moments framework to estimate a system of structural equations in which the parameter vector enters the moment conditions nonlinearly. It jointly exploits moment restrictions across mul...
Nonlinear TGARCH model
The Nonlinear TGARCH (Threshold GARCH) model extends the standard GARCH framework by allowing positive and negative shocks of equal magnitude to exert different effects on future volatility. It models conditional volatility in terms of the...
Nonlinear Toda-Yamamoto Causality
The Nonlinear Toda-Yamamoto causality test extends the classic Toda-Yamamoto (1995) modified Wald procedure to detect causal linkages that are hidden in the means of series but manifest through nonlinear dynamics such as asymmetries, thresh...
Nonlinear VAR Model
The Nonlinear VAR (NLVAR) model extends the standard vector autoregression by allowing the dynamic relationships among multiple time series to switch or change smoothly depending on an observed threshold variable, a latent regime state, or...
Nonlinear VECM
The Nonlinear VECM extends the standard linear VECM by allowing the speed of adjustment toward long-run equilibrium to differ depending on the sign, magnitude, or regime of deviations from that equilibrium. It captures asymmetric or thresho...
Nonlinear WLS
Nonlinear Weighted Least Squares combines the flexibility of nonlinear regression with the variance-stabilizing power of observation-level weights. It minimises a weighted sum of squared residuals around a user-specified nonlinear mean func...
Nonlinear Zivot-Andrews test
The Nonlinear Zivot-Andrews test extends the classical Zivot-Andrews structural-break unit root test by embedding smooth-transition nonlinear adjustment into the test regression. It jointly searches for an endogenous structural break and al...
Nonlinear difference GMM
Nonlinear Difference GMM extends the Arellano-Bond difference GMM estimator to models where the structural relationship between the outcome and its predictors is inherently nonlinear. By first-differencing to eliminate individual fixed effe...
Nonparametric Quantile Regression
Quantile regression, introduced by Koenker and Bassett in 1978, models a chosen conditional quantile (such as the median or the 25th and 75th percentiles) of a continuous outcome rather than its mean. Its nonparametric variants fit these qu...