Simplified Spectral Analysis and Linear Filters for Analysis of Economic Time Series

We develop and simplify spectral analysis of time series. The main focus is on the spectral representation theorem, Bochner's theorem, and some key results concerning time-invariant linear filters. We then show how to apply these key results to shed some light on various applications including Yule-Slutsky effects, seasonal adjustment and trend estimation. We also show how spectral analysis can indicate appropriateness of certain statistical models when applied with some economic time series.