Transcript Analysis of Financial Data Spring 2012 Lecture: Introduction

Analysis of Financial Data
Spring 2012
Lecture 5: Time Series Models - 3
Priyantha Wijayatunga
Department of Statistics, Umeå University
[email protected]
Course homepage:
http://www8.stat.umu.se/kursweb/vt012/staa2st017mom2/
Some Demonstrations
ACF and PACF
ACF and PACF (that cuts-off at lag 1 ) look like if the AR(1)
model can fit the data
Best Fitting Model
Model Description
Model Type
Model ID
x
Model_1
ARIMA(1,0,0)
Model Statisticsa
Model Fit statistics
Model
Number of Predictors
x-Model_1
Ljung-Box Q(18)
Stationary R-squared
0
Statistics
,614
20,822
DF
Sig.
17
Number of Outliers
,234
0
a. Best-Fitting Models according to Stationary R-squared (larger values indicate better fit).
ARIMA Model Parametersa
Estimate
x-Model_1
x
No Transformation
Constant
AR
Lag 1
SE
t
Sig.
50,239
,203
247,646
,000
,783
,014
56,311
,000
a. Best-Fitting Models according to Stationary R-squared (larger values indicate better fit).
Stationary R-squared should be big!
Check the significance of the residual autocorrelation with the
Ljung–Box test
Another Time Series
ACF and PACF
ACF and PACF (that cuts-off at lag 2 ) show that if AR(2)
model can fit the data
Best Fitting Model
Model Description
Model Type
Model ID
x
Model_1
ARIMA(2,0,0)
Model Statistics
Model Fit statistics
Model
Number of
Stationary R-
Predictors
squared
x-Model_1
1
Ljung-Box Q(18)
Number of
RMSE
,818
Statistics
1,949
DF
19,147
Outliers
Sig.
16
,261
0
ARIMA Model Parameters
Estimate
x-Model_1
x
No Transformation
Constant
AR
DAY, not periodic
No Transformation
Numerator
SE
t
Sig.
48,829
,994
49,121
,000
Lag 1
,810
,022
36,359
,000
Lag 2
,104
,022
4,685
,000
Lag 0
,001
,001
1,319
,187
Stationary R-squared should be big!
Check the significance of the residual autocorrelation with the
Ljung–Box test
Residual ACF and PACF
Another Time Series
ACF of Time Series
Since ACF is
positive until large
lags, it is an
indication of
nonstationarity.
Differencing is
needed
ACF and PACF of 1-Differenced
Time Series
Model Description
Model Type
Model ID
x
Model_1
ARIMA(2,1,0)
Model Statistics
Model Fit statistics
Model
Number of Predictors Stationary R-squared
x-Model_1
0
Ljung-Box Q(18)
RMSE
,779
Statistics
1,980
DF
11,835
Sig.
16
Number of Outliers
,755
0
ARIMA Model Parameters
Estimate
x-Model_1
x
No Transformation
Constant
AR
Difference
SE
t
Sig.
,248
,418
,593
,553
Lag 1
,781
,022
35,119
,000
Lag 2
,114
,022
5,110
,000
1