2

LINEAR FILTERS

2.1 INTRODUCTION

The inherent interaction of a particular variable with the underlying environment may produce complicated features. Filtering methods deal with the identification and extraction of certain features (e.g., trends, seasonalities) from a time series, which are important in terms of modeling and inference. Filtering is a universal research field used in scientific areas such as astronomy, biology, engineering, and physics, as well as in economics and finance. Traditionally, filters in economics and finance are used to extract components of a time series such as trends, seasonalities, business cycles, and noise.1Our aim is to provide a unified framework for filters that will show their applicability in economics ...

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