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Lecture

Forecasting & Long Memory: Time Series

In course

MATH-342: Time series

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

Description

This lecture covers autoregressive and moving average processes for forecasting in time series analysis. It delves into the implications of MA processes, invertibility, and forecasting for ARMA processes. Additionally, it explores the properties of forecast errors, predictive intervals, and error metrics. The second part of the lecture discusses long memory in stationary processes, the decay of autocovariances, and the concept of long-memory processes with polynomial decay.

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)

Forecasting

Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results creating a variance actual analysis. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself.

Stationary process

In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time. If you draw a line through the middle of a stationary process then it should be flat; it may have 'seasonal' cycles around the trend line, but overall it does not trend up nor down.

Economic forecasting

Economic forecasting is the process of making predictions about the economy. Forecasts can be carried out at a high level of aggregation—for example for GDP, inflation, unemployment or the fiscal deficit—or at a more disaggregated level, for specific sectors of the economy or even specific firms. Economic forecasting is a measure to find out the future prosperity of a pattern of investment and is the key activity in economic analysis.

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).

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.

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