Time Series Analysis Pros & cons

Time Series AnalysisPros & cons Jonas Mellin HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Overview • Linearstate space model • Trends & seasons • Basic structuraltime series • Combining parameters • Typesofmodels • Usefulness • Parameter estimation • Pros & cons • R packages HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Basic: Linear State Space • State equation(first order AR eq.) , • Observation equation , • Machinelearning -> constants • Extensibletomultiplestates, observations, lags HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Trends , , , +, HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Seasons + , HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Basic structuraltime series • Any combination of • error, trend, and season • For example • , • , HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

, , , , HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Season (s=4) • , HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Basic: Linear State Space: Recap • State equation(first order AR eq.) , • Observation equation , HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Typesofmodel • Localmodel/structuraltime series • Linear/(non-linear) state space • Gaussian/(non-Gaussian) • Univariate/multivariate • Canmodel ARMA(p,q) and ARIMA(p,q) • Box-Jenkins HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Usefulness • Filtering • Smoothing • Estimating missing observations • Forecasting • Simulations • Compare and contrastmodels • Dynamicfactoranalysis HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Parameter estimation • Maximum likelihoodestimation • Loglikelihood • ) • Maximizethis • and converge, given or P1, where P1 is the initial variance of y1 HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Advantages & disadvantages • Advantages • Mature • Generic • Modelscan be analyzed (why-perspective) • Multivariate analysispossible • Disadvantages • Cannotfind optimal modelitself, • search-basedoptimizationrequired • Morecomplexthan ARMA, ARIMA • Can be hard tospecify relations HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Examples of existing packages • R language • MARSS • Multi-variateanalysis • Flexible • KFAS • Univariate analysis • Less flexible HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

References • Durbin, J 2012, Time series analysis by state space methods, 2nd ed., Oxford University Press, Oxford. • Holmes, E, Ward, E & Wills, K 2013, MARSS: Multivariate Autoregressive State-Space Modeling, viewed <http://cran.r-project.org/web/packages/MARSS/>. • Holmes, EE, Ward, EJ & Wills, K 2012, ‘MARSS: Multivariate autoregressive state-space models for analyzing time-series data’, The R Journal, vol. 4, no. 1, p. 30. • http://cran.r-project.org/web/views/TimeSeries.html • http://www.abs.gov.au/websitedbs/D3310114.nsf/home/Time+Series+Analysis:+The+Basics HELICOPTER – Initial presentation of HS/IF Jonas Mellin, 2013

Time Series Analysis Pros & cons