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Because many statistical procedures in time series analysis assume stationarity, non-stationary data are frequently transformed to achieve stationarity before analysis. A common cause of non-stationarity is a trend in the mean, which can be due to either a unit root or a deterministic trend.
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 ...
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 ...
Time series: random data plus trend, with best-fit line and different applied filters. 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.
In statistics, a unit root test tests whether a time series variable is non-stationary and possesses a unit root.The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either stationarity, trend stationarity or explosive root depending on the test used.
Specifically, for a wide-sense stationary time series, the mean and the variance/autocovariance are constant over time. Differencing in statistics is a transformation applied to a non-stationary time-series in order to make it stationary in the mean sense (that is, to remove the non-constant trend), but it does not affect the non-stationarity ...
Cointegration is a crucial concept in time series analysis, particularly when dealing with variables that exhibit trends, such as macroeconomic data. In an influential paper, [ 1 ] Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic ...
In statistics, the order of integration, denoted I(d), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series (i.e., a time series whose mean and autocovariance remain constant over time).