Automatic Estimation of Monotonic Trends

Abstract

In this chapter we design an automatic algorithm to estimate monotonic trends over which an arbitrary stationary noise is superposed. It approximates the trend by a piecewise linear curve obtained by dividing into subintervals the time series values, instead of the time domain. The slope of each linear segment of the estimated trend is proportional to the average one-step displacement of the time series values included into the corresponding subinterval, therefore the method is referred to as average conditional displacement (ACD). Using Monte Carlo experiments we show that for AR(1) noises the accuracy of the ACD algorithm is comparable with that of the polynomial fitting and moving average but it has the advantage to be automatic. For time series with nonmonotonic trends the ACD algorithm determines one of the possible monotonic components which can be associated to the trend. As an illustration we apply the ACD algorithm to a paleoclimatic time series to determine the periods with a significant monotonic temperature variation.