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Lecture

Vector Autoregression (VAR): Sampling Properties and Examples

In course

MATH-342: Time series

A first course in statistical time series analysis and applications. ...

Description

This lecture covers the concept of Vector Autoregression (VAR) in time series analysis. It explains the generating mechanism of VAR, sampling properties, and provides examples of VAR processes. The lecture also discusses the stability of VAR models and the Yule-Walker equations for VAR(p) models.

Instructor

Sofia Charlotta Olhede

Sofia Olhede is a professor of Statistics at EPFL in Switzerland. She joined UCL prior to this in 2007, before which she was a senior lecturer of statistics (associate professor) at Imperial College London (2006-2007), a lecturer of statistics (assistant professor) (2002-2006), where she also completed her PhD in 2003 and MSci in 2000. She has held three research fellowships while at UCL: UK Engineering and Physical Sciences Springboard fellowship as well as a five-year Leadership fellowship, and now holds a European Research Council Consolidator fellowship. Sofia has contributed to the study of stochastic processes; time series, random fields and networks. Sofia was part of the multi-institutional team that set up the UK national data science institute, the Alan Turing Institute. She organised and served as chair of the science committee that developed the initial 500 000 pounds scientific programme of the institute; peer-reviewing over 100 workshop proposals and hosting over 30. She also chaired the first recruitment wave of the institute hiring 13 data scientists as a multi-university recruitment drive. Sofia was a member of the Royal Society and British Academy Data Governance Working Group, and the Royal Society working group on machine learning. Most recently she was one of 3 commissioners on a law society commission on the usage of algorithms in the justice system.

Official source

Ontological neighbourhood

Statistics

Data analysis: Time series

Related concepts (32)

Autoregressive model

In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation).

Vector autoregression

Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregressive model by allowing for multivariate time series. VAR models are often used in economics and the natural sciences. Like the autoregressive model, each variable has an equation modelling its evolution over time.

Autoregressive–moving-average model

In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA). The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins.

Time series

In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart).

Autocorrelation

Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.

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