modeled as with Ut being hypothesized to be a stationary error process. To estimate the parameters and B, one first takes the natural logarithm (ln) of both sides of this equation: This log-linear equation is in the same form as the previous linear trend equation and can be detrended in the same way, giving the estimated as the detrended value of , and hence the implied as the detrended value of , assuming one can reject the hypothesis that is non-stationary. Quadratic trend 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 t2 as regressors; again, if the residuals are shown to be stationary then they are the detrended values of . See also Trend estimation Decomposition of time series KPSS test Notes Time series