Defining a trend for a time series is a fundamental task in time series analyses. It has very practical outcomes: determining a trend in a financial signal, the average behavior of a dynamic process, defining exceptional and likely behavior as evidenced by a time series.
On signals and time series that have an underlying stationary statistical distribution there are a variety of ways to estimate a trend, many of which come equipped with a very concrete notion of optimality. Signals that are not statistically stationary are commonly encountered in nature, business, and the social sciences and for these the challenge of defining a trend is two-fold: computing it, and figuring out what this trend means.
Adaptive filtering is frequently explored as a means to calculating/proposing a trend. The Empirical Mode Decomposition and the Intrinsic Time Decomposition are such schemes. I will describe a practical notion of trend based upon the ITD we call a "tendency." We will briefly describe how to compute the tendency and explain its meaning.