In the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process. The trend does not have to be linear.
Conversely, if the process requires differencing to be made stationary, then it is called difference stationary and possesses one or more unit roots. Those two concepts may sometimes be confused, but while they share many properties, they are different in many aspects. It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent impact on the mean (i.e. no convergence over time).
A process {Y} is said to be trend-stationary if
where t is time, f is any function mapping from the reals to the reals, and {e} is a stationary process. The value is said to be the trend value of the process at time t.
Suppose the variable Y evolves according to
where t is time and et is the error term, which is hypothesized to be white noise or more generally to have been generated by any stationary process. Then one can use 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. The residuals from this regression are given by
If these estimated residuals can be statistically shown to be stationary (more precisely, if one can reject the hypothesis that the true underlying errors are non-stationary), then the residuals are referred to as the detrended data, and the original series {Yt} is said to be trend-stationary even though it is not stationary.
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart).
A first course in statistical time series analysis and applications.
Production management deals with producing goods sustainably at the right time, quantity, and quality with the minimum cost. This course equips students with practical skills and tools for effectively
The course covers basic econometric models and methods that are routinely applied to obtain inference results in economic and financial applications.
Elevated nitrate from human activity causes ecosystem and economic harm globally. The factors that control the spatiotemporal dynamics of riverine nitrate concentration remain difficult to describe and predict. We analyzed nitrate concentration from 4450 s ...
Severe thunderstorms can have devastating impacts. Concurrently high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are known to be conducive to severe weather, so high values of PROD - (CAPE)(1/2) x SRH have been ...
Functional time series analysis, whether based on time or frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless, as is often the c ...
INST MATHEMATICAL STATISTICS2020
Explores demand forecasting methods, time series analysis, trend forecasting, and the application of the Holt-Winter model.
Explores extremal limit theorems, point processes, and multivariate extremes in extreme value time series modelling, emphasizing the effect of local dependence on extreme values.
Covers demand management, forecasting methods, and trend analysis in production management.