Time domain

Abstract: Any series of observations ordered along a single dimension, such as time, may be thought of as a time series. The emphasis in time series analysis is on studying the dependence among observations at different points in time. What distinguishes time series analysis from general multivariate analysis is precisely the temporal order imposed on the observations. Many economic variables, such as GNP and its components, price indices, sales, and stock returns are observed over time. In addition to being interested in the contemporaneous relationships among such variables, we are often concerned with relationships between their current and past values, that is, relationships over time.

Abstract: Preface. Preface to Volume 2. Contents of Volume 2. List of Main Notation. Basic Concepts. Elements of Probability Theory. Stationary Random Processes. Spectral Analysis. Estimation in the Time Domain. Estimation in the Frequency Domain. Spectral Analysis in Practice. Analysis of Processes with Mixed Spectra.

Abstract: This paper gives an exposition of linear prediction in the analysis of discrete signals The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum The major part of the paper is devoted to all-pole models The model parameters are obtained by a least squares analysis in the time domain Two methods result, depending on whether the signal is assumed to be stationary or nonstationary The same results are then derived in the frequency domain The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra This also leads to a discussion of the advantages and disadvantages of the least squares error criterion A spectral interpretation is given to the normalized minimum prediction error Applications of the normalized error are given, including the determination of an "optimal" number of poles The use of linear prediction in data compression is reviewed For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients Finally, a brief introduction to pole-zero modeling is given

Abstract: Simple descriptive techniques probability models for time series estimation in the time domain forecasting stationary processes in the frequency domain spectral analysis bivariate processes linear systems state-space models and the Kalman filter non-linear models multivariate time series modelling some other topics.

Abstract: Conventionally, time series have been studied either in the time domain or the frequency domain. The representation of a signal in the time domain is localized in time, i.e. the value of the signal at each instant in time is well defined. However, the time representation of a signal is poorly localized in frequency, i.e. little information about the frequency content of the signal at a certain frequency can be known by looking at the signal in the time domain. On the other hand, the representation of a signal in the frequency domain is well localized in frequency, but is poorly localized in time, and as a consequence it is impossible to tell when certain events occurred in time.