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If the trend can be assumed to be linear, trend analysis can be undertaken within a formal regression analysis, as described in Trend estimation. If the trends have other shapes than linear, trend testing can be done by non-parametric methods, e.g. Mann-Kendall test, which is a version of Kendall rank correlation coefficient.
If the estimated trend, ^, is larger than the critical value for a certain significance level, then the estimated trend is deemed significantly different from zero at that significance level, and the null hypothesis of a zero underlying trend is rejected. The use of a linear trend line has been the subject of criticism, leading to a search for ...
Because of the stochastic nature of the trend it is not possible to break up integrated series into a deterministic (predictable) trend and a stationary series containing deviations from trend. Even in deterministically detrended random walks spurious correlations will eventually emerge. Thus detrending does not solve the estimation problem.
Parameter estimation using computation algorithms to arrive at coefficients that best fit the selected ARIMA model. The most common methods use maximum likelihood estimation or non-linear least-squares estimation. Statistical model checking by testing whether the estimated model conforms to the specifications of a stationary univariate process ...
Then one can use [5] [6] [7] linear regression to obtain an estimate ^ of the true underlying trend slope and an estimate ^ of the underlying intercept term b; if the estimate ^ is significantly different from zero, this is sufficient to show with high confidence that the variable Y is non-stationary.
Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median (or other quantiles) of the response variable.
The trend test exploits the suspected effect direction to increase power, but this does not affect the sampling distribution of the test statistic under the null hypothesis. Thus, the suspected trend in effects is not an assumption that must hold in order for the test results to be meaningful.
The aim of the PRISMA statement is to help authors improve the reporting of systematic reviews and meta-analyses. [3] PRISMA has mainly focused on systematic reviews and meta-analysis of randomized trials, but it can also be used as a basis for reporting reviews of other types of research (e.g., diagnostic studies, observational studies).