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Trends do not have to be linear or log-linear. For example, a variable could have a quadratic trend: = + + +. This can be regressed linearly in the coefficients using t and t 2 as regressors; again, if the residuals are shown to be stationary then they are the detrended values of .
Curve fitting[ 1][ 2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [ 3] possibly subject to constraints. [ 4][ 5] Curve fitting can involve either interpolation, [ 6][ 7] where an exact fit to the data is required, or smoothing, [ 8][ 9] in which a "smooth" function is ...
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an n th degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E ( y | x ).
In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. [ 1] Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each .
Quadratic programming. Quadratic programming ( QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming .
Quadratically constrained quadratic program. In mathematical optimization, a quadratically constrained quadratic program ( QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions. It has the form. where P0, ..., Pm are n -by- n matrices and x ∈ Rn is the optimization variable.
Extrapolation. In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk ...
The red line represents the local polynomial being used to fit a sub-set of the data. The smoothed values are shown as circles. A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting the signal ...