Statistics — Page 16
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
FMOLS Estimator
Fully Modified OLS, introduced by Phillips and Hansen (1990), estimates the long-run coefficients of a cointegrating relationship among I(1) variables. It applies a semi-parametric correction to ordinary least squares to remove the bias tha...
Factor Risk Model
A factor risk model is a multi-factor framework that links asset returns to systematic risk factors such as the market, value, size, and momentum. The Fama-French three- and five-factor models (1993) and Ross's Arbitrage Pricing Theory (197...
Fama-MacBeth Regression
The Fama-MacBeth procedure is a two-step regression methodology for analyzing cross-sectional relationships while controlling for time-series structure. Introduced by Fama and MacBeth (1973), it first estimates time-series parameters for ea...
Fine-Gray Competing Risks Model
The Fine-Gray model is a semiparametric regression method for survival data in which two or more mutually exclusive event types compete to occur first. Proposed by Fine and Gray in 1999, it models the subdistribution hazard of each event ty...
Firm Survival and Exit Analysis
Firm survival and exit analysis applies hazard and duration models to the question of why some firms survive and others fail, treating the age at which a firm exits the market as a time-to-event outcome. Audretsch and Mahmood's 1995 study o...
First-Difference Estimator
The First-Difference (FD) estimator is a panel data method that eliminates unobserved, time-invariant individual heterogeneity by subtracting each unit's observation in period t-1 from its observation in period t. By operating on changes ra...
Fisher Panel Unit-Root Test
The Fisher-type (Maddala-Wu) panel unit-root test, introduced in 1999, combines individual-level ADF unit-root p-values using Fisher's chi-squared meta-analytic framework to produce a single panel-level test statistic. Unlike the Levin-Lin-...
Fisher's exact test
Fisher's exact test is a nonparametric exact-probability test of independence for small-sample contingency tables, introduced by R. A. Fisher in 1922. Rather than relying on a large-sample approximation, it computes the exact probability of...
Fixed Effects Model
The fixed effects (FE) model is the workhorse estimator for panel data when unobserved unit-specific characteristics are suspected to correlate with the regressors. By absorbing each entity's time-invariant heterogeneity into a separate int...
Fixed Effects Panel Model
The fixed effects panel model estimates relationships in panel data (many units observed over time) by exploiting only the within-unit variation, so that unobserved time-invariant heterogeneity is controlled away. It is the central within e...
Fleiss' Kappa
Fleiss' Kappa is a non-parametric statistic for measuring the degree of agreement among three or more raters who classify items into mutually exclusive nominal categories. Introduced by Joseph L. Fleiss in 1971 as a generalization of Cohen'...
Fligner-Killeen Test
The Fligner-Killeen test is a rank-based test that checks whether several independent groups share the same variance (scale). Introduced by Fligner and Killeen in 1976, it does not require the data to be normally distributed, making it a ro...
Forensic Likelihood Ratio
The Forensic Likelihood Ratio (LR) is a Bayesian framework for quantifying the weight of forensic evidence relative to two competing propositions — typically the prosecution and defence hypotheses. Formally developed and systematised by Col...
Fourier ADF unit root test
The Fourier ADF unit root test extends the standard Augmented Dickey-Fuller framework by incorporating low-frequency Fourier terms into the deterministic component. This allows the test to approximate smooth, gradual structural breaks in th...
Fourier AR Model
The Fourier AR model extends the standard autoregressive specification by adding trigonometric (sine and cosine) terms to the deterministic component. This allows the model to capture smooth, gradual shifts in the mean or trend of a time se...
Fourier ARCH Model
The Fourier ARCH model extends the classical ARCH framework by incorporating trigonometric (Fourier) terms into the conditional variance equation. This allows the model to capture smooth, gradual shifts in volatility dynamics over time with...
Fourier ARDL Bounds Test
The Fourier ARDL bounds test augments the Pesaran-Shin-Smith cointegration framework with trigonometric (Fourier) terms that capture gradual, smooth structural breaks in the data-generating process. It tests for a long-run level relationshi...
Fourier ARIMA model
The Fourier ARIMA model augments a standard ARIMA specification with trigonometric sine and cosine terms, allowing it to capture smooth, gradual structural change and flexible nonlinear seasonality without specifying the exact timing or num...
Fourier ARMA model
The Fourier ARMA model augments the classical Autoregressive Moving Average framework with low-frequency Fourier (sine and cosine) terms to capture smooth, gradual shifts in the mean or trend of a time series. Unlike dummy-variable approach...
Fourier Arellano-Bond GMM
Fourier Arellano-Bond GMM is a dynamic panel estimator that augments the classic Arellano-Bond first-differenced GMM framework with Fourier trigonometric terms to capture smooth, gradual structural breaks in the time dimension. It handles e...
Fourier DCC-GARCH
The Fourier DCC-GARCH model extends Engle's Dynamic Conditional Correlation GARCH framework by embedding Fourier trigonometric terms in the conditional mean or variance equations. This allows the model to approximate smooth, gradual structu...
Fourier Dynamic Panel Data Model
The Fourier dynamic panel data model extends standard dynamic panel specifications by incorporating low-frequency trigonometric (Fourier) terms to flexibly capture smooth, gradual structural breaks or time-varying patterns in the data, with...
Fourier EGARCH
Fourier EGARCH extends Nelson's (1991) Exponential GARCH model by embedding Fourier trigonometric terms in the conditional variance equation to capture smooth, gradual shifts in the unconditional variance level over time. This allows the mo...
Fourier Engle-Granger cointegration
The Fourier Engle-Granger cointegration test extends the classic two-step Engle-Granger procedure by embedding low-frequency trigonometric (Fourier) terms in the cointegrating regression. This accommodates an unknown number of smooth struct...