and other applications of multivariate time series analysis, a variance decomposition or forecast error variance decomposition (FEVD) is used to aid in...

analysis Variance Variance decomposition of forecast errors Variance gamma process Variance inflation factor Variance-gamma distribution Variance reduction...

estimate of the variance of the unobserved errors, and is called the mean squared error. Another method to calculate the mean square of error when analyzing...

ARIMA models and regression with ARIMA errors NCSS: includes several procedures for ARIMA fitting and forecasting. Python: the "statsmodels" package includes...

proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (invented in the last quarter of the 19th century)...

Wold decomposition. Kendall shows an example of a decomposition into smooth, seasonal and irregular factors for a set of data containing values of the...

Analysis of variance Blinder–Oaxaca decomposition Censored regression model Cross-sectional regression Curve fitting Empirical Bayes method Errors and residuals...

'observation error covariance matrix' is constructed to represent the magnitude of combined observational errors (on the diagonal) and the correlated errors between...

series Chirp Decomposition of time series Detrended fluctuation analysis Digital signal processing Distributed lag Estimation theory Forecasting Frequency...

that the square root of the sample variance is an underestimate. The use of n − 1 instead of n in the formula for the sample variance is known as Bessel's...

independent variables are not error-free, this is an errors-in-variables model, also outside this scope. Other examples of nonlinear functions include exponential...

the error term ε t {\displaystyle \varepsilon _{t}} equal to zero (because we forecast Xt to equal its expected value, and the expected value of the unobserved...

{C}}=(X_{1}-\mu ,\ldots ,X_{n}-\mu )} can be decomposed into the "mean part" and "variance part" by projecting to the direction of u → = ( 1 , … , 1 ) {\displaystyle...

the variance of e i {\displaystyle e_{i}} to change across values of X i {\displaystyle X_{i}} . Correlated errors that exist within subsets of the data...

with known mean 0 but unknown variance σ 2 {\displaystyle \sigma ^{2}} , the sample variance s 2 {\displaystyle s^{2}} of the observations X 1 , … , X...

autocorrelation of the errors, which themselves are unobserved, can generally be detected because it produces autocorrelation in the observable residuals. (Errors are...

distributions, and decompose the output variance into parts attributable to input variables and combinations of variables. The sensitivity of the output to...

forms of error are recognized: Type I errors (null hypothesis is rejected when it is in fact true, giving a "false positive") and Type II errors (null...

smoothing method can be estimated by minimizing the sum of squared errors (SSE). The errors are specified as e t = y t − y ^ t ∣ t − 1 {\textstyle e_{t}=y_{t}-{\hat...

\sigma ^{2}} is the variance of the white noise, θ {\displaystyle \theta } is the characteristic polynomial of the moving average part of the ARMA model,...

square root of the variance, and hence another measure of dispersion. Symmetry: a property of some distributions in which the portion of the distribution...

change over time in the parameters of regression models, which can lead to huge forecasting errors and unreliability of the model in general. This issue...

{\displaystyle e} 's are randomly distributed errors. If one can reject the null hypothesis that the errors are non-stationary, then the non-stationary...

vector autoregression, an extension of VAR models to panel data Variance decomposition For multivariate tests for autocorrelation in the VAR models, see...

information criterion Bias-variance tradeoff Mean squared error Errors and residuals in statistics Law of total variance Mallows's Cp Model selection...

outcome and error values exhibit high variance. Fundamentally, an ensemble learning model trains at least two high-bias (weak) and high-variance (diverse)...

R {\displaystyle R} describes the estimate of the error of the data; if the random errors in the entries of the data vector d {\displaystyle \mathbf {d}...

distributed, the mean squared error, root mean squared error or median absolute deviation could be used to summarize the errors. When users apply cross-validation...

Electricity price forecasting (EPF) is a branch of energy forecasting which focuses on using mathematical, statistical and machine learning models to...

transpose of row i of the matrix X . {\displaystyle \mathbf {X} .} It is also efficient under the assumption that the errors have finite variance and are...