Time Series Analysis and Signal Modeling

This is an early version of a set of notes for the course on Time Series Analysis offered at Lund University. Any and all comments and suggestions are most welcome and appreciated. Glossary and Abbreviations 1-D, 2-D, etc. One-dimensional, two-dimensional, etc. ACF Auto-covariance function AR Autoregressive ARIMA Integrated ARMA ARMA Autoregressive moving average ARMAX ARMA with exogenous input ARX AR with exogenous input BLUE Best linear unbiased estimate CRLB Cramér-Rao lower bound dB Decibel DFT Discrete Fourier transform FIM Fisher information matrix FFT Fast Fourier transform LS Least-squares MA Moving average MIMO Multiple-input multiple-output MISO Multiple-input single-output ML Maximum likelihood MSE Mean squared error NLS Non-linear least-squares PACF Partial auto-correlation function PDF Probability density function PSD Power spectral density SARIMA Seasonal ARIMA SARIMAX SARIMA with exogenous input SARMA Seasonal ARMA SARMAX SARMA with exogenous input SISO Single-input single-output SNR Signal-to-noise ratio SVD Singular value decomposition VARMA Vector ARMA 1 2 CONTENTS