Time Series Analysis Periodic Events Hormone Levels

1
Time Series Analysis(Periodic Events - Hormone
Levels)

2
Time Series Analysis(Trend - Growth of
Paramecium Aurelium)
3
Time Series Analysis

• Time plot - sequence chart - seasonal
  differences
• Spectral Analysis
• Auto-correlation
• Cross-correlation
• Curve Fitting
• Time series modelling
• AR autoregressive models
• ARIMA autoregressive integrated moving average

4
Time plot - sequence charts(Trend - Growth of
Paramecium Aurelium)
5
Time plot - seasonal difference(Trend - Growth
of Paramecium Aurelium)
6
Curve fit.(Growth of Paramecium Aurelium)
7
Moving Average (MA)
Time Series Raw Data Centre MA 2.00
. 17.00 16.00 29.00
28.33 39.00 43.67 63.00 95.67
185.00 168.67 258.00 236.67 267.00
305.67 392.00 389.67 510.00 490.67
570.00 576.67 650.00 593.33 560.00
595.00 575.00 628.33 750.00 778.33
1010.00 1086.67 1500.00 1603.33 2300.00
2266.67 3000.00 .
8
Time Series Analysis(Periodic Events - Hormone
Levels)

9
Spectral Density
10
Autocorrelation
Time Periods
Lag 0
Time Periods
Lag 1
Time Periods
Lag 2
11
Autocorrelation

12
Sequence Plot
13
Cross-correlation
14
Autoregressive Models

• x(t) ß0 ß1x(t-1) ß2x(t-2) ß3x(t-3) ...
  ßnx(t-n) error
• x - value
• t - time
• ß0 - constant
• ß1-n - model coefficients

Notes- Time series must be stationary, i.e.-
constant mean, constant variance and constant
autocorrelation through time.- Common to
transform data to achieve stationarity (e.g.
square-root, log).
15
ARIMA (Box-Jenkins) Models(AutoRegressive
Integrated Moving Average)

• Three components
• Autoregressive component - a value related to
  previous values.
• Integrated or difference component -
  differences between values important rather than
  absolute values.
• Moving average component - values averaged
  (smoothed) .
• Note ARIMA Models specified as ARIMA(p,d,q).
• Each component can have non-seasonal
  and seasonal components.

16
Survival Analysis(e.g. Cox regression)

• Models survival in relation to number of
  variables. For example-
• Continuing participation in new treatment in
  relation to age, gender, hospital attended etc.
• Customer variables associated with changing
  service supplier.
• Model provides evidence of which variables are
  associated with survival/failure and beta
  coefficients associated with these variables.

17
SPSS Commands/Procedures

• Sequence Charts.
• Create time series.
• Spectral analysis.
• Autocorrelation and cross-correlation.
• Curve estimation.
• ARIMA models
• Survival analysis