# Chap6.R # Exhibit 6.5 data(ma1.1.s) win.graph(width=4.875, height=3,pointsize=8) acf(ma1.1.s,xaxp=c(0,20,10)) # if the arument xaxp is omitted, the # tick marks will be generated according to the default convention. # Run the command ?par to learn more the xaxp argment. acf(ma1.1.s) # see the new tickmarks # So how was xaxp determined? First run the command without xaxp to find out # how many lags are on the x-axis. Suppose there are 20 lags. Then we specify # xaxp=c(0,20,10), i.e. the two extreme tickmarks are 0 and 20, and we want # 10 tickmarks in between. How to set the xaxp argument if we want 1 tickmark for # each lag? # Exhibit 6.6 acf(ma1.1.s,ci.type='ma',xaxp=c(0,20,10)) # Exhibit 6.7 data(ma1.2.s) acf(ma1.2.s,xaxp=c(0,20,10)) # Exhibit 6.8 data(ma2.s) acf(ma2.s,xaxp=c(0,20,10)) # Exhibit 6.9 acf(ma2.s,ci.type='ma',xaxp=c(0,20,10)) # Exhibit 6.10 data(ar1.s) acf(ar1.s,xaxp=c(0,20,10)) # Exhibit 6.11 pacf(ar1.s,xaxp=c(0,20,10)) # Exhibit 6.12 data(ar2.s) acf(ar2.s,xaxp=c(0,20,10)) # Exhibit 6.13 pacf(ar2.s,xaxp=c(0,20,10)) # Exhibit 6.14 data(arma11.s) plot(arma11.s, type='b',ylab=expression(y[t])) # Exhibit 6.15 acf(arma11.s,xaxp=c(0,20,10)) # Exhibit 6.16 pacf(arma11.s,xaxp=c(0,20,10)) # Exhibit 6.17 eacf(arma11.s) # If desirable, a title can be added to the EACF table by the # following command. cat('Exhibit 6.17\n');eacf(arma11.s) # Exhibit 6.18 data(oil.price) acf(as.vector(oil.price),main='Sample ACF of the Oil Price Time Series',xaxp=c(0,24,12)) # The as.vector function strips the ts attaribute of oil.price in order to # prevent the plotting convention for seasonal time series. # The main argument supplies the main heading of the figure. # Try the following command to appreciate the effects of applying the as.vector # function. acf(oil.price,main='Sample ACF of the Oil Price Time Series') # The tickmark 1 on the x-axis now refers to a lag of # 1 period with each period containing 12 months, so it is lag 12! # Exhibit 6.19 acf(diff(as.vector(log(oil.price))),main='Sample ACF of the Difference of the Oil Price Time Series',xaxp=c(0,24,12)) # Exhibit 6.20 data(rwalk) acf(diff(rwalk,difference=2),ci.type='ma',xaxp=c(0,18,9)) # Exhibit 6.21 acf(diff(rwalk),ci.type='ma',xaxp=c(0,18,9)) library(uroot) # Carry out the Dickey-Fuller unit root tests # Find out the AR order for the differenced series ar(diff(rwalk)) # order 8 is indicated by AIC library(uroot) ADF.test(rwalk,selectlags=list(mode=c(1,2,3,4,5,6,7,8),Pmax=8),itsd=c(1,0,0)) # which is equivalent to # ADF.test(rwalk,selectlags=list(mode=c(1,2,3,4,5,6,7,8)),itsd=c(1,0,0)) # # The argument mode can be either a numerical vector, # or "aic","bic" and "signf". # If it is a numerical vector, the test assumes the vector corresponds to the # lags of the response that must be included in the test, and the Pmax # option is ignored. # However, if mode is specified as "aic", the function uses the AIC to # select lags up to and including Pmax to be included in the test. # Specifying mode to "bic" or "signf" changes the selection criterion # to BIC or significance criterion. Note "signf" not "signif" is the valid # option. # In comparison, setting the true order to be zero for the first difference ADF.test(rwalk,selectlags=list(Pmax=0),itsd=c(1,0,0)) # Repeat the test with the alternative have an intercept term and a linear trend # Run ?uroot to learn more about the selectlags option and the itsd option. ADF.test(rwalk,selectlags=list(mode=c(1,2,3,4,5,6,7,8),Pmax=8),itsd=c(1,1,0)) # # Similarly, a simplified command is # ADF.test(rwalk,selectlags=list(mode=c(1,2,3,4,5,6,7,8)),itsd=c(1,1,0)) # Repeat the preceding test but now setting the true order of the first difference # as zero. ADF.test(rwalk,selectlags=list(Pmax=0),itsd=c(1,1,0)) # Exhibit 6.22 set.seed(92397) test=arima.sim(model=list(ar=c(rep(0,11),.8),ma=c(rep(0,11),0.7)),n=120) res=armasubsets(y=test,nar=14,nma=14,y.name='test',ar.method='ols') plot(res) # A title may be added to the plot, by adding the main="..." option # in the above plot function. However, the title may crash with other # labels. A better approach is to add a title by the # following command. title(main="Exhibit 6.22", line=6) # The option line=6 means put the title 6 lines from the edge of the # plot region. You can experiment with this option to fine tune the # placement of the label. # Exhibit 6.23 data(larain) win.graph(width=3, height=3,pointsize=8) qqnorm(log(larain)) qqline(log(larain)) # Exhibit 6.24 win.graph(width=4.875, height=3,pointsize=8) acf(log(larain),xaxp=c(0,20,10)) # note the main heading now includes the data name. # Exhibit 6.25 data(color) acf(color,ci.type='ma') # Exhibit 6.26 pacf(color) # Exhibit 6.27 win.graph(width=4, height=4,pointsize=8) data(hare) bxh=BoxCox.ar(hare) bxh\$mle # the mle of the power parameter bxh\$ci # corresponding 95% C.I. # Exhibit 6.28 acf(hare^.5) # Exhibit 6.29 pacf(hare^.5) # Exhibit 6.30 eacf(diff(log(oil.price))) # Exhibit 6.31 res=armasubsets(y=diff(log(oil.price)),nar=7,nma=7, y.name='test', ar.method='ols') plot(res) # Exhibit 6.32 acf(as.vector(diff(log(oil.price))),xaxp=c(0,22,11)) # Exhibit 6.33 pacf(as.vector(diff(log(oil.price))),xaxp=c(0,22,11))