Generate n = 100 observations from each of the three models.
- ARMA (1,1)
- ARMA...
Generate n = 100 observations from each of the three models.
- ARMA (1,1)
- ARMA (1,0)
-ARMA (0,1)
Compute the sample ACF for each model and compare it to the
theoretical values. Compute the sample PACF for each of the
generated series and compare the Sample ACFs and PACFs
Simulate 100 observations from an ARMA(1,1) model and
another 30 observations from an ARMA(1,1) model both with = 0.8 and
= 0.3.
please use Rstudio and provide the codes.
Using R:
1. Generate AR(1), AR(2), MA(1), MA(2), and ARMA(1,1) processes
with different parameter values, and draw ACF and PACF. Discuss the
characteristics of ACF snd PACF for these processes.
2. Generate AR(1) process {X_t}. Compute the first difference
Y_t = X_t - X_(t-1). Draw ACF and PACF of {Y_t}. What can you say
about this process? Is it again a AR(1) process? What can you say
in general?
3.For the AR(2) processes with the following parameters,
determine if AR(2)...
Generate 100 samples of size n=8 from an exponential
distribution with mean 3 . Each row of your data will denote an
observed random sample of size 8, from an exponential distribution
with mean 3. Obtain sample mean for each sample, store in another
column and make a histogram for sample means. Repeat for n=100.
Compare and interpret the histograms you obtained for n=8 and
n=100. Submit the histograms along with your one small paragraph
comparison.
Can you solve it...
Generate a simulated data set with 100 observations based on the
following model. Each data point is a vector Z= (X, Y) where X
describes the age of a machine New, FiveYearsOld, and TenYearsOld
and Y describes whether the quality of output from the machine
Normal or Abnormal. The probabilities of a machine being in the
three states are
P(X = New) = 1/4
P(X = FiveYearsOld) = 1/3
P(X = TenYearsOld) = 5/12
The probabilities of Normal output conditioned...
2. Use MINITAB to generate 10,000 observations from a binomial
distribution with n = 50 trials and probability of success p = 0.02
. Create a histogram of the 10,000 observations. Comment on the
shape of the distribution. Why does it makes sense for the
histogram to have this shape?
3. Use MINITAB to generate 10,000 observations from a binomial
distribution with n = 1000 trials and probability of success p =
0.02. Create a histogram of the 10,000 observations....
A random sample of n = 100 observations is drawn from a
population with mean 10 and variance 400.
(a) Describe the shape of the sampling distribution of ¯x. Does
your answer depend on the sample size? (
b) Give the mean and standard deviation of the sampling
distribution of ¯x.
(c) Find the probability that ¯x is less than 8.
(d) Find the probability that ¯x is greater than 9.5.
(e) Find the probability that ¯x is between 8...
Coding Language: R
Generate 100 observations from the normal distribution with mean
3 and variance 1.
Compute the sample average, the standard error for the sample
average, and the 95% confidence interval.
Repeat the above two steps 1000 times. Report (a) the mean of
the 1000 sample means, (b) the standard deviation of the 1000
sample means, (c) the mean of the 1000 standard errors, and (d) how
many times (out of 1000) the 95% confidence intervals include the
population...
For each of the following cases, assume a sample of n
observations is taken from a normally distributed population with
unknown mean μ and unknown variance σ2. Complete the following: i)
Give the form of the test statistic. ii) State and sketch the shape
of the prob. distribution of the test statistic when the null
hypothesis is true. iii) Give the range of values of the test
statistic which comprises the rejection region. iv) Sketch in the
area(s) associated with...
Write the R code
First, generate 1000 observations from a binomial distribution
with n=30 and p=0.2 Use the 1000 observations you generated:
a) Generate poisson, binomial, negative binomial Diagnostic
Distribution Plots using distplot.
b) Generate a histogram and overlay a kernel estimator of the
density
(You can use: binom <- rbinom(n=1000,size=30, prob=0.2))
Use Excel to generate 100 N (10,5) distributed random values
(that is 100 values of a Normally distributed random variable with
mean 10 and standard deviation 5). Plot histogram for your data.
See Appendix on how to generate these values.