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

1

Time Series AnalysisPros & cons

Jonas Mellin

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

2

Overview

• Linear state space model• Trends & seasons• Basic structural time series– Combining parameters

• Types of models• Usefulness• Parameter estimation• Pros & cons• R packages

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

3

Basic: Linear State Space

• State equation (first order AR eq.),

• Observation equation,

• Machine learning -> constants• Extensible to multiple states, observations, lags

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

4

Trends

,

,

,

+,

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

5

Seasons

+,

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

6

Basic structural time series

• Any combination of – error, trend, and season

• For example

– , – ,

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

7

,

,

, ,

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

8

Season (s=4)

• ,

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

9

Basic: Linear State Space: Recap

• State equation (first order AR eq.),

• Observation equation,

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

10

Types of model

• Local model/structural time series• Linear/(non-linear) state space• Gaussian/(non-Gaussian)• Univariate/multivariate• Can model ARMA(p,q) and ARIMA(p,q)– Box-Jenkins

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

11

Usefulness

• Filtering• Smoothing• Estimating missing observations• Forecasting• Simulations• Compare and contrast models• Dynamic factor analysis

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

12

Parameter estimation

• Maximum likelihood estimation– Loglikelihood• )

– Maximize this• and converge, given or P1, where P1 is the initial

variance of y1

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

13

Advantages & disadvantages

• Advantages– Mature– Generic– Models can be analyzed (why-perspective)– Multivariate analysis possible

• Disadvantages– Cannot find optimal model itself,

• search-based optimization required

– More complex than ARMA, ARIMA– Can be hard to specify relations

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

14

Examples of existing packages

• R language– MARSS• Multi-variate analysis• Flexible

– KFAS• Univariate analysis• Less flexible

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

15

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