Trend extraction methods for time series analysis

The need to extract the trend from a given time series is a common problem in a wide variety of fields, such as signal processing or econometrics. Ordinary least squares regression (OLS), locally weighted polynomial regression (LWP), moving average, wavelet decomposition and empirical mode decomposition (EMD) are examples of methods which are used for trend extraction. In the present work, the aforementioned methods are first presented and then showcased on a simulated time series. Some of the properties of the methods are discussed afterwards