### Selected R commands and output used in Chapter 1
> require(fNonlinear)
> set.seed(1)
> x <- rnorm(300)
> bdsTest(x)
Title: BDS Test

Test Results:
  PARAMETER:
    Max Embedding Dimension: 3
    eps[1]: 0.482; eps[2]: 0.964
    eps[3]: 1.446; eps[4]: 1.927
  STATISTIC:
    eps[1] m=2: -1.1256;    eps[1] m=3: -1.4948
    eps[2] m=2: -0.7145;    eps[2] m=3: -1.1214
    eps[3] m=2: -0.6313;    eps[3] m=3: -0.8081
    eps[4] m=2: -0.7923;    eps[4] m=3: -1.2099
  P VALUE:
    eps[1] m=2: 0.2604;    eps[1] m=3: 0.135
    eps[2] m=2: 0.4749;    eps[2] m=3: 0.2621
    eps[3] m=2: 0.5278;    eps[3] m=3: 0.419
    eps[4] m=2: 0.4282;    eps[4] m=3: 0.2263
    
> require("quantmod")
> getSymbols("IBM",from="2010-01-02",to="2015-09-30")
> head(IBM)
           IBM.Open IBM.High IBM.Low IBM.Close IBM.Volume IBM.Adjusted
2010-01-04   131.18   132.97  130.85    132.45    6155300     117.6580
2010-01-05   131.68   131.85  130.10    130.85    6841400     116.2367
> rtn <- diff(log(as.numeric(IBM[,6])))
> ts.plot(rtn) # not shown
> Box.test(rtn,type="Ljung",lag=10)
        Box-Ljung test
data:  rtn
X-squared = 15.685, df = 10, p-value = 0.109 # No serial correlations
> bdsTest(rtn)
Title: BDS Test

Test Results:
  PARAMETER:
    Max Embedding Dimension: 3
    eps[1]: 0.006;    eps[2]: 0.012
    eps[3]: 0.018;    eps[4]: 0.024
  STATISTIC:
    eps[1] m=2: 4.4058;    eps[1] m=3: 5.3905
    eps[2] m=2: 4.2309;    eps[2] m=3: 5.429
    eps[3] m=2: 3.9341;    eps[3] m=3: 5.4255
    eps[4] m=2: 3.7848;    eps[4] m=3: 5.3304
  P VALUE:
    eps[1] m=2: 1.054e-05;    eps[1] m=3: 7.026e-08
    eps[2] m=2: 2.327e-05;    eps[2] m=3: 5.666e-08
    eps[3] m=2: 8.349e-05;    eps[3] m=3: 5.78e-08
    eps[4] m=2: 0.0001538;    eps[4] m=3: 9.802e-08

####
> set.seed(15)
> xt <- rnorm(300)
> Box.test(xt,lag=10,type='Ljung')
        Box-Ljung test
data:  xt
X-squared = 11.095, df = 10, p-value = 0.3502 # No serial correlations
> Box.test(xt^2,lag=10,type='Ljung')
        Box-Ljung test
data:  xt^2
X-squared = 8.4539, df = 10, p-value = 0.5846 # Q-star test

> require(quantmod)
> getSymbols("MSFT",from="2009-01-02",to="2015-10-15",src=''google'')
> msft <- diff(log(as.numeric(MSFT$MSFT.Close)))  #log returns
> Box.test(msft,lag=10,type='Ljung')
        Box-Ljung test
data:  msft
X-squared = 17.122, df = 10, p-value = 0.0717 # No serial correlations
> Box.test(msft^2,lag=10,type='Ljung')
        Box-Ljung test
data:  msft^2
X-squared = 70.54, df = 10, p-value = 3.487e-11 ## Nonlinearity
### Engle's test with m = 10.
> nT <- length(msft)
> y <- msft[11:nT]^2
> X <- NULL
> for (i in 1:10){
+ X <- cbind(X,msft[(11-i):(nT-i)]^2)
+ }
> m2 <- lm(y~X)  ## Linear regression
> anova(m2)
Analysis of Variance Table
Response: y
            Df     Sum Sq    Mean Sq F value    Pr(>F)
X           10 0.00003036 3.0358e-06    4.65 1.447e-06 ***
Residuals 1687 0.00110138 6.5286e-07
> qstar = 4.64*10
> pv = 1 -pchisq(qstar,10)
> print(c(qstar,pv))
[1] 4.65e+01 1.162495e-06  ### ARCH effect exists

####
> require(quantmod)
> getSymbols("MSFT",from="2009-01-02",to="2015-10-15",src=''google'')
> msft <- diff(log(as.numeric(MSFT$MSFT.Close)))  # log returns
> log(length(msft))
[1] 7.443078
> PRnd(msft,m=8)
ND-stat & p-value  0.1828238 0.8549363
> PRnd(abs(msft),m=8)
ND-stat & p-value  2.302991 0.02127936

####
> require(TSA)
> da=read.table(``q-unrate.txt'',header=T)
> rate <- da$rate
> Keenan.test(unrate)
$test.stat
[1] 7.428776
$p.value
[1] 0.006858382
$order
[1] 5
> Tsay.test(unrate)
$test.stat
[1] 2.626
$p.value
[1] 0.00108
$order
[1] 5

####
> require(TSA)
> data(lynx)
> y <- log10(lynx)
> Keenan.test(y)
$test.stat
[1] 11.66997
$p.value
[1] 0.0009550016
$order
[1] 11
> Tsay.test(y)
$test.stat
[1] 1.316
$p.value
[1] 0.2256
$order
[1] 11
> require(NTS)
> F.test(y,thres=1.645)
$test.stat
[1] 1.971
$p.value
[1] 0.02858
$order
[1] 11

######
> da <- read.table(``q-unrate.txt'',header=T)
> unrate <- da$rate
> require(NTS)
> require(TSA)
> thr.test(unrate,p=5,d=5)
SETAR model is entertained
Threshold nonlinearity test for (p,d):  5 5
F-ratio and p-value:  2.849921 0.01081263
> tlrt(unrate,p=5,d=5)
$percentiles
[1] 24.9 75.1
$test.statistic
    33.028
$p.value
    0.0003066953