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Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor.
The adjustment of the sensitivity of the trend to short-term fluctuations is achieved by modifying a multiplier . The filter was popularized in the field of economics in the 1990s by economists Robert J. Hodrick and Nobel Memorial Prize winner Edward C. Prescott , [ 1 ] though it was first proposed much earlier by E. T. Whittaker in 1923. [ 2 ]
Prediction outside this range of the data is known as extrapolation. Performing extrapolation relies strongly on the regression assumptions. The further the extrapolation goes outside the data, the more room there is for the model to fail due to differences between the assumptions and the sample data or the true values.
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 of producing ...
The following statistical tests are used to determine the type of trend: significance of the breakpoint (BP) by expressing BP as a function of regression coefficients A 1 and A 2 and the means Y 1 and Y 2 of the y -data and the means X 1 and X 2 of the x data (left and right of BP), using the laws of propagation of errors in additions and ...
Romberg's method — Richardson extrapolation applied to trapezium rule; Gaussian quadrature — highest possible degree with given number of points Chebyshev–Gauss quadrature — extension of Gaussian quadrature for integrals with weight (1 − x 2) ±1/2 on [−1, 1]
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function.Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time.
Trend analysis is the widespread practice of collecting information and attempting to spot a pattern. In some fields of study, the term has more formally defined meanings. In some fields of study, the term has more formally defined meanings.