Unit 1

Introduction – Fourier Vs Wavelets – Seasonality filtering – Signal denoising – Identification of structural breaks – Scaling – Aggregate heterogeneity and time scales – Multiscale Cross Correlation. Review of linear filters – The EWMA and volatility estimation – The Hodrick – Prescott filter – Baxter – King filter – Filters in technical analysis of financial markets. Optimum linear estimation – Weiner filer – Recursive filtering and Kalman filter – Prediction with Kalmanfilter – Vector Kalman filter estimation – Applications.

Unit 2

Discrete Wavelet transforms – properties – DWT filters – The maximal overlap DWT – Multi resolution analysis – ANOVA – practical issues – Filtering FX intraday seasonalities – Causality and co-integration in economics – Money growth and inflation – Long memory processes -Fractional difference processes (FDP) – The DWT of FDP – Simulation of FDP – OLS estimation of FDP – Approximate Maximum likelihood estimation of FDP – Application to stock prices – Generalization of DWT and MODWT – Applications to money supply – Wavelets and seasonal long memory – Applications to money supply – GNP – Seasonality and trends – Unemployment – Consumer price index – Tourism revenues.

Unit 3

1. Ramazan Gencay, FarukSelcuk& Brandon Whitdly “An Introduction to Wavelets and other filtering methods in Finance and Economics,” Academic Press 2002
2. John F Ehlers “Rocket Science for Traders: Digital Signal Processing Applications”, John Wiley 2001.