# Appendix - Introduction (in R/Python)

Copyright 2011 - 2020 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: https://www.gnu.org/licenses/.

##### Listing R.1: Entering and Printing Data in R Last updated June 2018

x = 10   # assign x the value 10
print(x) # print x

##### Listing P.1: Entering and Printing Data in Python Last updated June 2018

x = 10   # assign x the value 10
print(x) # print the value of x


##### Listing R.2: Vectors, Matrices and Sequences in R Last updated June 2018

y = c(1,3,5,7,9)     # create vector using c()
print(y)
print(y[3])          # calling 3rd element (R indices start at 1)
print(dim(y))        # gives NULL since y is a vector, not a matrix
print(length(y))     # as expected, y has length 5
v = matrix(nrow=2,ncol=3)      # fill a 2 x 3 matrix with NaN values (default)
print(dim(v))        # as expected, v is size (2,3)
w = matrix(c(1,2,3),nrow=6,ncol=3) # repeats matrix twice by rows, thrice by columns
print(w)
s = 1:10   # s is a list of integers from 1 to 10 inclusive
print(s)

##### Listing P.2: Vectors, Matrices and Sequences in Python Last updated July 2020

y = [1,3,5,7,9]      # lists in square brackets are stored as arrays
print(y)
print(y[2])          # 3rd element (Python indices start at 0)
print(len(y))        # as expected, y has length 5
import numpy as np   # NumPy: Numeric Python package
v = np.full([2,3], np.nan)  # create a 2x3 matrix with NaN values
print(v)
print(v.shape)       # as expected, v is size (2,3)
w = np.tile([1,2,3], (3,2)) # repeats thrice by rows, twice by columns
print(w)
s = range(10)        # an iterator from 0 to 9
print([x for x in s])          # return  elements using list comprehension


##### Listing R.3: Basic Summary Statistics in R Last updated June 2018

y=matrix(c(3.1,4.15,9))
sum(y)    # sum of all elements of y
prod(y)   # product of all elements of y
max(y)    # maximum value of y
min(y)    # minimum value of y
range(y)  # min, max value of y
mean(y)   # arithmetic mean
median(y) # median
var(y)    # variance
cov(y)    # covar matrix = variance for single vector
cor(y)    # corr matrix = [1] for single vector
sort(y)   # sorting in ascending order
log(y)    # natural log

##### Listing P.3: Basic Summary Statistics in Python Last updated July 2020

import numpy as np
y = [3.14, 15, 9.26, 5]
print(sum(y))        # sum of all elements of y
print(max(y))        # maximum value of y
print(min(y))        # minimum value of y
print(np.mean(y))     # arithmetic mean
print(np.median(y))   # median
print(np.var(y))     # population variance
print(np.cov(y))     # covar matrix = sample variance for single vector
print(np.corrcoef(y)) # corr matrix = [1] for single vector
print(np.sort(y))     # sort in ascending order
print(np.log(y))     # natural log


##### Listing R.4: Calculating Moments in R Last updated June 2018

library(moments)
mean(y)     # mean
var(y)     # variance
sd(y)      # unbiased standard deviation, by default
skewness(y) # skewness
kurtosis(y) # kurtosis

##### Listing P.4: Calculating Moments in Python Last updated June 2018

from scipy import stats
print(np.mean(y))    # mean
print(np.var(y))     # variance
print(np.std(y, ddof = 1))     # ddof = 1 for unbiased standard deviation
print(stats.skew(y))           # skewness
print(stats.kurtosis(y, fisher = False)) # fisher = False gives Pearson definition


##### Listing R.5: Basic Matrix Operations in R Last updated June 2018

z = matrix(c(1,2,3,4),2,2) # z is a 2 x 2 matrix
x = matrix(c(1,2),1,2)     # x is a 1 x 2 matrix
## Note: z * x is undefined since the two matrices are not conformable
z %*% t(x)           # this evaluates to a 2 x 1 matrix
rbind(z,x)           # "stacking" z and x vertically
cbind(z,t(x))        # "stacking z and x' horizontally
## Note: dimensions must match along the combining axis

##### Listing P.5: Basic Matrix Operations in Python Last updated June 2018

z = np.matrix([[1, 2], [3, 4]])          # z is a 2 x 2 matrix
x = np.matrix([1, 2])          # x is a 1 x 2 matrix
## Note: z * x is undefined since the two matrices are not conformable
print(z * np.transpose(x))     # this evaluates to a 2 x 1 matrix
b = np.concatenate((z,x), axis = 0)      # "stacking" z and x vertically
print(b)
c = np.concatenate((z,np.transpose(x)), axis = 1) # "stacking" z and x horizontally
print(c)
## note: dimensions must match along the combining axis


##### Listing R.6: Statistical Distributions in R Last updated June 2018

q = seq(from = -3, to = 3, length = 7)    # specify a set of values
p = seq(from = 0.1, to = 0.9, length = 9) # specify a set of probabilities
qnorm(p, mean = 0, sd = 1)     # element-wise inverse Normal quantile
pt(q, df = 4)        # element-wise cdf under Student-t(4)
dchisq(q, df = 2)    # element-wise pdf under Chisq(2)
## Similar syntax for other distributions
## q for quantile, p for cdf, d for pdf
## followed by the abbreviation of the distribution
## One can also obtain pseudorandom samples from distributions
x = rt(100, df = 5)  # Sampling 100 times from TDist with 5 df
y = rnorm(50, mean = 0, sd = 1)          # Sampling 50 times from a standard normal
## Given data, we obtain MLE estimates of distribution parameters with package MASS:
library(MASS)
res = fitdistr(x, densfun = "normal")     # Fitting x to normal dist
print(res)

##### Listing P.6: Statistical Distributions in Python Last updated July 2020

q = np.arange(-3,4,1)          # specify a set of values, syntax arange(min, exclusive-max, step)
p = np.arange(0.1,1.0,0.1)     # specify a set of probabilities
print(stats.norm.ppf(p))       # element-wise inverse Normal quantile
print(stats.t.cdf(q,4))        # element-wise cdf under Student-t(4)
print(stats.chi2.pdf(q,2))     # element-wise pdf under Chisq(2)
## One can also obtain pseudorandom samples from distributions using numpy.random
x = np.random.standard_t(df=5, size=100) # Sampling 100 times from TDist with 5 df
y = np.random.normal(size=50)  # Sampling 50 times from a standard normal
## Given data, we obtain MLE estimates of parameters with stats:
res = stats.norm.fit(x)        # Fitting x to normal dist
print(res)           # First element is mean, second sd


##### Listing R.7: Statistical Tests in R Last updated June 2018

library(tseries)
x = rt(500, df = 5)  # Create hypothetical dataset x
jarque.bera.test(x)  # Jarque-Bera test for normality
Box.test(x, lag = 20, type = c("Ljung-Box")) # Ljung-Box test for serial correlation

##### Listing P.7: Statistical Tests in Python Last updated July 2020

from statsmodels.stats.diagnostic import acorr_ljungbox
x = np.random.standard_t(df=5, size=500) # Create dataset x
print(stats.jarque_bera(x))    # Jarque-Bera test - prints statistic and p-value
print(acorr_ljungbox(x, lags=20))        # Ljung-Box test - prints array of statistics and p-values


##### Listing R.8: Time Series in R Last updated June 2018

x = rt(60, df = 5) # Create hypothetical dataset x
par(mfrow=c(1,2), pty='s')
acf(x,20)  # autocorrelation for lags 1:20
pacf(x,20)           # partial autocorrelation for lags 1:20

##### Listing P.8: Time Series in Python Last updated June 2018

import statsmodels.api as sm
import matplotlib.pyplot as plt
y = np.random.standard_t(df = 5, size = 60) # Create hypothetical dataset y
q1 = sm.tsa.stattools.acf(y, nlags=20)   # autocorrelation for lags 1:20
plt.bar(x = np.arange(1,len(q1)), height = q1[1:])
plt.show()
plt.close()
q2 = sm.tsa.stattools.pacf(y, nlags=20)     # partial autocorr for lags 1:20
plt.bar(x = np.arange(1,len(q2)), height = q2[1:])
plt.show()
plt.close()


##### Listing R.9: Loops and Functions in R Last updated June 2018

## For loops
for (i in 3:7)       # iterates through [3,4,5,6,7]
print(i^2)
## If-else loops
X = 10
if (X %% 3 == 0) {
print("X is a multiple of 3")
} else {
print("X is not a multiple of 3")
}
## Functions (example: a simple excess kurtosis function)
excess_kurtosis = function(x, excess = 3){ # note: excess optional, default=3
m4 = mean((x-mean(x))^4)
excess_kurt = m4/(sd(x)^4) - excess
excess_kurt
}
x = rt(60, df = 5)   # Create hypothetical dataset x
excess_kurtosis(x)

##### Listing P.9: Loops and Functions in Python Last updated June 2018

## For loops
for i in range(3,8):           # NOTE: range(start, end), end excluded
print(i**2)      # range(3,8) iterates through [3,4,5,6,7)
## If-else loops
X = 10
if X % 3 == 0:
print("X is a multiple of 3")
else:
print("X is not a multiple of 3")
## Functions (example: a simple excess kurtosis function)
def excess_kurtosis(x, excess = 3):    # note: excess optional, default = 3
m4=np.mean((x-np.mean(x))**4)        # note: exponentiation in Python uses **
excess_kurt=m4/(np.std(x)**4)-excess
return excess_kurt
x = np.random.standard_t(df=5,size=60) # Create hypothetical dataset x
print(excess_kurtosis(x))


##### Listing R.10: Basic Graphs in R Last updated June 2018

y = rnorm(50, mean = 0, sd = 1)
par(mfrow=c(2,2)) # sets up space for subplots
barplot(y)           # bar plot
plot(y,type='l')  # line plot
hist(y)    # histogram
plot(y)    # scatter plot

##### Listing P.10: Basic Graphs in Python Last updated July 2020

y = np.random.normal(size = 50)
z = np.random.standard_t(df = 4, size = 50)
## using Matplotlib to plot bar, line, histogram and scatter plots
## subplot(a,b,c) creates a axb grid and plots the next plot in position c
plt.subplot(2,2,1)
plt.bar(range(len(y)), y);
plt.subplot(2,2,2)
plt.plot(y);
plt.subplot(2,2,3)
plt.hist(y);
plt.subplot(2,2,4)
plt.scatter(y,z);


##### Listing R.11: Miscellaneous Useful Functions in R Last updated June 2018

## Convert objects from one type to another with as.integer() etc
## To check type, use typeof(object)
x = 8.0
print(typeof(x))
x = as.integer(x)
print(typeof(x))

##### Listing P.11: Miscellaneous Useful Functions in Python Last updated June 2018

## Convert objects from one type to another with int(), float() etc
## To check type, use type(object)
x = 8.0
print(type(x))
x = int(x)
print(type(x))