Showing posts with label How to generate the two time series. Show all posts
Showing posts with label How to generate the two time series. Show all posts

Wednesday, July 31, 2019

How to generate the two time series

Generate the two time series length 999

Fixed random seeds
set.seed(20140625) 
Define length of simulation
> N <- 999
Simulate normal random walk
> x <- cumsum(rnorm(N)) 
Set an initial parameter
> gamma <- 0.7 
Get cointegrating series
> y <- gamma * x + rnorm(N)
plot the two series
> plot(x, type='l') 
> lines(y,col="green")
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summary(ur.df(x,type="none"))

###############################################

# Augmented Dickey-Fuller Test Unit Root Test # 

###############################################

Test regression none


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
    Min      1Q  Median      3Q     Max
-2.9293 -0.6857 -0.0430  0.6568  3.0650

Coefficients:
            Estimate Std. Error t value
z.lag.1    -0.002151   0.002995  -0.718
z.diff.lag  0.015978   0.031770   0.503
           Pr(>|t|)
z.lag.1       0.473
z.diff.lag    0.615

Residual standard error: 0.9896 on 995 degrees of freedom
Multiple R-squared:  0.0007246, Adjusted R-squared:  -0.001284
F-statistic: 0.3608 on 2 and 995 DF,  p-value: 0.6972


Value of test-statistic is: -0.7182

Critical values for test statistics:
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62

 summary(ur.df(y,type="none"))


###############################################
# Augmented Dickey-Fuller Test Unit Root Test #
###############################################

Test regression none


Call:
lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)

Residuals:
    Min      1Q  Median      3Q     Max
-4.9951 -1.0130  0.0000  0.9533  4.2422

Coefficients:
            Estimate Std. Error t value
z.lag.1    -0.010684   0.006218  -1.718
z.diff.lag -0.391398   0.029214 -13.398
           Pr(>|t|) 
z.lag.1      0.0861 .
z.diff.lag   <2e-16 ***
---
Signif. codes:
  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’
  0.1 ‘ ’ 1

Residual standard error: 1.448 on 995 degrees of freedom
Multiple R-squared:  0.1606, Adjusted R-squared:  0.1589
F-statistic: 95.18 on 2 and 995 DF,  p-value: < 2.2e-16


Value of test-statistic is: -1.7182

Critical values for test statistics:
      1pct  5pct 10pct
tau1 -2.58 -1.95 -1.62
The test statistics is larger than the critical value at the significance level.so
we can't reject the null hypothesis.

Now take a linear combination of two series

> z = y - gamma*x
> plot(z,type='l')
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