Sovita ARMA(p,q) malli SP500 tuottoihin.
file<-"http://cc.oulu.fi/~jklemela/timeseries/sp500.csv"
data<-read.csv(file=file)
sp500<-data[,7] # otetaan kunkin paivan lopetuskurssi
sp500<-sp500[length(sp500):1] # aloitetaan aikasarja vanhimmasta havainnosta
# piiretaan aikasarja
plot(sp500,type="l")
# tulostetaan tuotot
y<-sp500[2:length(sp500)]-sp500[1:(length(sp500)-1)]
r<-y/sp500[1:(length(sp500)-1)]
plot(r,type="l")
acf(r)
pacf(r)
library(tseries)
# estimoidaan ARMA(1,1)-malli ######################
order<-c(1,1)
ar<-arma(r,order=order)
ar
Call:
arma(x = r, order = order)
Coefficient(s):
ar1 ma1 intercept
-0.4651911 0.5037691 0.0004926
# summary
summary(ar)
Call:
arma(x = r, order = order)
Model:
ARMA(1,1)
Residuals:
Min 1Q Median 3Q Max
-0.2030770 -0.0044682 0.0001331 0.0046357 0.1143614
Coefficient(s):
Estimate Std. Error t value Pr(>|t|)
ar1 -0.4651911 0.0825093 -5.638 1.72e-08 ***
ma1 0.5037691 0.0805997 6.250 4.10e-10 ***
intercept 0.0004926 0.0001187 4.148 3.35e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Fit:
sigma^2 estimated as 9.45e-05, Conditional Sum-of-Squares = 1.52, AIC = -103161.1
###### kokeillaan arima0-funktiota #############################
order<-c(1,0,1)
ari<-arima0(r,order=order)
ari
Call:
arima0(x = r, order = order)
Coefficients:
ar1 ma1 intercept
-0.4892 0.5273 3e-04
s.e. 0.0072 0.1103 1e-04
sigma^2 estimated as 9.449e-05: log likelihood = 51584.44, aic = -103160.9
#### estimoidaan AR(p)-malli tuottojen nelioille ##################
order<-c(10,0)
ar<-arma(r^2,order=order)
ar
summary(ar)
Call:
arma(x = r^2, order = order)
Model:
ARMA(10,0)
Residuals:
Min 1Q Median 3Q Max
-2.754e-03 -6.229e-05 -4.120e-05 1.113e-07 4.143e-02
Coefficient(s):
Estimate Std. Error t value Pr(>|t|)
ar1 9.103e-02 7.894e-03 11.532 < 2e-16 ***
ar2 1.973e-01 7.911e-03 24.943 < 2e-16 ***
ar3 2.068e-02 8.058e-03 2.567 0.0103 *
ar4 5.542e-03 8.059e-03 0.688 0.4917
ar5 1.480e-01 8.055e-03 18.370 < 2e-16 ***
ar6 3.558e-02 8.055e-03 4.417 1.00e-05 ***
ar7 -3.907e-03 8.059e-03 -0.485 0.6278
ar8 3.567e-02 8.058e-03 4.427 9.55e-06 ***
ar9 6.257e-02 7.911e-03 7.910 2.66e-15 ***
ar10 1.216e-02 7.894e-03 1.541 0.1233
intercept 3.752e-05 3.655e-06 10.264 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Fit:
sigma^2 estimated as 1.829e-07, Conditional Sum-of-Squares = 0, AIC = -203400.5
#################
order<-c(5,0,0)
ari<-arima0(r^2,order=order)
ari
Call:
arima0(x = r^2, order = order)
Coefficients:
ar1 ar2 ar3 ar4 ar5 intercept
0.1034 0.2036 0.0314 0.0263 0.1596 1e-04
s.e. 0.0078 0.0078 0.0080 0.0078 0.0078 0e+00
sigma^2 estimated as 1.843e-07: log likelihood = 101647.5, aic = -203281
ari$aic
[1] -203281
#######################################
order<-c(5,0,0)
arima0(abs(r),order=order)
p<-30
aics<-matrix(0,p,1)
for (i in 1:p){
order<-c(i,0,0)
aics[i]<-arima0(abs(r),order=order)$aic
}
plot(aics[1:29])
[,1]
[1,] -113887.8
[2,] -114749.5
[3,] -115170.9
[4,] -115444.7
[5,] -115876.5
[6,] -116013.9
[7,] -116117.5
[8,] -116188.3
[9,] -116253.2
[10,] -116295.5
[11,] -116371.9
[12,] -116398.2
[13,] -116409.6
[14,] -116411.0
[15,] -116424.4
[16,] -116436.7
[17,] -116445.6
[18,] -116469.6
[19,] -116472.4
[20,] -116478.0
[21,] -116482.8
[22,] -116481.0
[23,] -116488.0
[24,] -116494.3
[25,] -116494.0
[26,] -116492.2
[27,] -116522.7
[28,] -116523.7
[29,] -116532.8
[30,] 0.0
>