STAT 231 Time series

Time Series

multiple observations of same variable over time, usually for regularly spaced intervals

time series graph

x-axis values = points in time

data points usually connected by line

main reasons to study:

1) determine patterns in a variable over time

2) predict future value of particular variable (forecasting)

3) investigate causes of variable and impacts of interventions

need to have many observation points to be useful

if too short, cannot identify key components

key components:

trend

cycles

random fluctuations

Determining patterns in a variable over time

trend

global warming

economic time series - adjust for inflation

cycles

irregular

regular

seasonal patterns & adjustments

compare same seasons/ periods across years rather than adjacent seasons/ periods within years

random fluctuations

erratic ups and downs not corresponding to trend or cycles

natural variability due to unknown factors - unreliability of measurement, other unidentified causal variables

Forecasting

extrapolation with time series - predicting the future value of a variable based on pattern of past observations

e.g., projecting revenues for the federal government

e.g., world records in running events

use extreme caution with extrapolation

Explaining patterns and evaluating interventions

explaining patterns - identifying independent variables that could account for changes over time in dependent variable

plot time series for independent and dependent variables together, observe degree of similarity

also, regression and correlation between two time series variables

e.g., global warming and solar irradiance

embed interpretations of recent changes in longer time series

evaluating programs, policy changes, other types of interventions

time series "quasi-experiment"

Campbell and Stanley

problem for causal interpretation - another event at similar time as intervention that could have caused shift?

e.g., ethanol in gasoline and air pollution (CO) violations

e.g., gun ownership as deterrent to crime

multiple time series - one time series does not include an intervention or experiences the intervention at a different time (time series for two different but related areas or units)

helps control against events coincident to intervention as explanation for changes corresponding to intervention

multiple baseline/reversal design - alternating intervention and non-intervention periods

strength - less likely that multiple intervention periods could correspond to other events; each intervention period serves as a replicate

e.g., intensified motorized patrol as intervention against burglary

e.g., single subject, single-blind, placebo-controlled experiments in clinical contexts