HW1
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Stevens Institute Of Technology *
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Course
513
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
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Uploaded by LieutenantLobster1814
HW1
# PartI
# 1.1 Vector
# 1. Create 2 vector, each containing 10 random numbers.
# First vector
vector1 <- sample(1:10, 10, replace = F)
# Second vector
vector2 <- sample(11:20, 10, replace = F)
# Printing the vectors
print(vector1)
## [1] 4 5 2 8 6 1 3 10 9 7
print(vector2)
## [1] 14 16 20 17 12 15 13 11 19 18
# 2. Append the second vector to the first one.
vector_12 <- c(vector1, vector2)
print(vector_12)
## [1] 4 5 2 8 6 1 3 10 9 7 14 16 20 17 12 15 13 11 19 18
# 3. Calculate the mean of the new combined vector.
vector_mean <- mean(vector_12)
print(vector_mean)
## [1] 10.5
# 4. For each number in the new combined vector, if it is lager than the mean then print out a ’True’, otherwise print out a ’False’.
result <- logical(length(vector_12))
for
(i in
1:length(vector_12)) {
if
(vector_12[i] > vector_mean) {
print('True')
} else
{
print('False')
}
}
## [1] "False"
## [1] "False"
## [1] "False"
## [1] "False"
## [1] "False"
## [1] "False"
## [1] "False"
## [1] "False"
## [1] "False"
## [1] "False"
## [1] "True"
## [1] "True"
## [1] "True"
## [1] "True"
## [1] "True"
## [1] "True"
## [1] "True"
## [1] "True"
## [1] "True"
## [1] "True"
# 1.2 Matrix
# 1. Create a vector with 100 random numbers.
vector_100 <- sample(1:100, 100, replace = F)
vector_100
## [1] 79 60 43 83 77 93 65 72 33 58 95 90 7 10 86 22 40 69
## [19] 4 100 56 35 30 67 66 91 14 52 8 32 94 15 20 28 84 18
## [37] 11 89 70 3 34 6 85 23 31 61 63 62 96 19 81 2 82 36
## [55] 24 38 97 88 44 47 39 46 12 17 54 57 76 1 49 98 71 75
## [73] 53 29 73 87 48 13 55 9 74 27 16 37 92 45 5 21 80 99
## [91] 68 41 64 25 51 42 50 26 78 59
# 2. Transfer the above vector into a 10 by 10 matrix M.
matrix_10 <- matrix(vector_100, nrow = 10, ncol = 10)
matrix_10
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 79 95 56 94 34 81 39 71 74 68
## [2,] 60 90 35 15 6 2 46 75 27 41
## [3,] 43 7 30 20 85 82 12 53 16 64
## [4,] 83 10 67 28 23 36 17 29 37 25
## [5,] 77 86 66 84 31 24 54 73 92 51
## [6,] 93 22 91 18 61 38 57 87 45 42
## [7,] 65 40 14 11 63 97 76 48 5 50
## [8,] 72 69 52 89 62 88 1 13 21 26
## [9,] 33 4 8 70 96 44 49 55 80 78
## [10,] 58 100 32 3 19 47 98 9 99 59
# 3. Find the transposed matrix M^T . Print the value of element who is in the second ro
w and the first column of M^T .
matrix_transpose <- t(matrix_10)
matrix_transpose
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 79 60 43 83 77 93 65 72 33 58
## [2,] 95 90 7 10 86 22 40 69 4 100
## [3,] 56 35 30 67 66 91 14 52 8 32
## [4,] 94 15 20 28 84 18 11 89 70 3
## [5,] 34 6 85 23 31 61 63 62 96 19
## [6,] 81 2 82 36 24 38 97 88 44 47
## [7,] 39 46 12 17 54 57 76 1 49 98
## [8,] 71 75 53 29 73 87 48 13 55 9
## [9,] 74 27 16 37 92 45 5 21 80 99
## [10,] 68 41 64 25 51 42 50 26 78 59
print(matrix_transpose[2,1])
## [1] 95
# 4.Write a nested loop to calculate the inner product between M^T and M. The result is also a matrix N = ⟨
M^T , M ⟩
.
inner_product = function
(a1,a2){
dim_matrix = matrix(nrow = dim(a1)[1], ncol = dim(a2)[2]) for
(i in
1:dim(a1)[1]){
for
(j in
1:dim(a2)[2]){ dim_matrix[i,j] = sum(a1[i,]*a2[,j])
} }
return
(dim_matrix)
}
matrix_inner1 <- inner_product(matrix_transpose,matrix_10)
matrix_inner1
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## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 47019 36204 33694 29259 29499 35234 29540 34900 32713 31610
## [2,] 36204 41531 24408 25481 17685 26537 27102 26285 30713 26164
## [3,] 33694 24408 26375 20885 19284 22310 18688 24945 23185 20590
## [4,] 29259 25481 20885 30576 22320 25112 15283 22931 25076 22528
## [5,] 29499 17685 19284 22320 31018 30310 19580 24887 21664 26087
## [6,] 35234 26537 22310 25112 30310 37903 22531 24992 23116 27901
## [7,] 29540 27102 18688 15283 19580 22531 28017 23487 26505 24309
## [8,] 34900 26285 24945 22931 24887 24992 23487 32793 25635 26956
## [9,] 32713 30713 23185 25076 21664 23116 26505 25635 34986 27547
## [10,] 31610 26164 20590 22528 26087 27901 24309 26956 27547 28132
# 5. Calculate the same inner product using operator %∗%. And compare two results.
matrix_inner2 <- matrix_transpose %*% matrix_10
matrix_inner2
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 47019 36204 33694 29259 29499 35234 29540 34900 32713 31610
## [2,] 36204 41531 24408 25481 17685 26537 27102 26285 30713 26164
## [3,] 33694 24408 26375 20885 19284 22310 18688 24945 23185 20590
## [4,] 29259 25481 20885 30576 22320 25112 15283 22931 25076 22528
## [5,] 29499 17685 19284 22320 31018 30310 19580 24887 21664 26087
## [6,] 35234 26537 22310 25112 30310 37903 22531 24992 23116 27901
## [7,] 29540 27102 18688 15283 19580 22531 28017 23487 26505 24309
## [8,] 34900 26285 24945 22931 24887 24992 23487 32793 25635 26956
## [9,] 32713 30713 23185 25076 21664 23116 26505 25635 34986 27547
## [10,] 31610 26164 20590 22528 26087 27901 24309 26956 27547 28132
equal_matrix <- all.equal(matrix_inner1,matrix_inner2)
equal_matrix
## [1] TRUE
# 1.3 Function
# 1. Load the given CSV file in R
df <- read.csv("/Users/incharanagaraju/Desktop/513/stock_data-1.csv", header = TRUE)
#df
# 2. Delete the columns containing NA(empty values).
new_df <- df[ , colSums(is.na(df))==0]
#new_df
# 3. Calculate daily log return for each stock. (Hint. log return is defined as rt = ln Pt = ln(Pt)−ln(Pt−1), where Pt is the stock price at time t.)
n_col <- ncol(new_df)
date <- as.Date(new_df[,1], format = "%Y-%m-%d")
daily_logreturns <- sapply(new_df[2:n_col], function
(new_df) diff(log(new_df))) daily_logreturns <- data.frame(daily_logreturns)
daily_logreturns <- rbind(NA,daily_logreturns)
daily_logreturns <- cbind(date,daily_logreturns)
#daily_logreturns
# 4. Calculate the mean and standard deviation of log return for each stock. Transfer t
he result into a 2 by N data frame (N is the number of stocks).
mean <- apply(daily_logreturns[2:n_col],2,mean, na.rm = TRUE)
mean
## AAPL AMGN AXP BA CAT CSCO ## 0.0009168344 0.0004641248 0.0003855638 0.0003478159 0.0003798480 0.0004002217 ## CVX DIS HD IBM INTC JNJ ## 0.0002502413 0.0003264233 0.0005012099 0.0002923392 0.0003470648 0.0003197527 ## JPM KO MCD MMM MRK MSFT ## 0.0003240281 0.0001789796 0.0003573148 0.0002726557 0.0001724428 0.0005522446 ## NKE PG TRV UNH VZ WBA ## 0.0005167696 0.0002963599 0.0002607877 0.0005950182 0.0001155210 0.0003405546 ## WMT ## 0.0003856492
standard_deviation <- apply(daily_logreturns[2:n_col],2, sd, na.rm = TRUE)
standard_deviation
## AAPL AMGN AXP BA CAT CSCO CVX ## 0.02840478 0.02085579 0.02197895 0.01937864 0.02049348 0.02476240 0.01596826 ## DIS HD IBM INTC JNJ JPM KO ## 0.01884281 0.01956586 0.01737205 0.02370960 0.01291141 0.02385872 0.01383933 ## MCD MMM MRK MSFT NKE PG TRV ## 0.01493950 0.01493651 0.01733853 0.01954384 0.01995818 0.01423707 0.01779765 ## UNH VZ WBA WMT ## 0.02196304 0.01596795 0.01810263 0.01608582
df1 <- data.frame(mean,standard_deviation)
df1
mean
<dbl>
standard_deviation
<dbl>
AAPL
0.0009168344
0.02840478
AMGN
0.0004641248
0.02085579
Next
1
2
3
Previous
mean
<dbl>
standard_deviation
<dbl>
AXP
0.0003855638
0.02197895
BA
0.0003478159
0.01937864
CAT
0.0003798480
0.02049348
CSCO
0.0004002217
0.02476240
CVX
0.0002502413
0.01596826
DIS
0.0003264233
0.01884281
HD
0.0005012099
0.01956586
IBM
0.0002923392
0.01737205
1-10 of 25 rows
data <- as.data.frame(t(df1))
data
AAPL
<dbl>
AMGN
<dbl>
AXP
<dbl>
BA
<dbl>
CAT
<dbl>
mean
0.0009168344
0.0004641248
0.0003855638
0.0003478159
0.000379848
standard_deviation
0.0284047796
0.0208557858
0.0219789482
0.0193786437
0.020493476
2 rows | 1-7 of 26 columns
# 5. Build a graph with two sub-plots. In the first sub-plot, plot the first three stock
s’ daily prices. The y axis is stock price and x axis is date. In the second sub-plot, b
uild a scatter plot of the statistical result you calculated above. In other words, the x-axis is the stocks’ names and the y-axis is the statistical values. (Notes. Please inc
lude legend, tile, and axis labels for each sub-plots.)
rows <- rownames(df1)
library
(patchwork)
library
(ggplot2)
par(mfrow = c(1,2))
colors <- c("AAPL" ="lightblue", "AMGN" = "pink", "AXP" = "maroon")
plot_1 <- ggplot(new_df, aes(x= X))+
geom_line(aes(y = AAPL, color = "AAPL", group = 1), size = 0.5)+
geom_line(aes(y = AMGN, color = "AMGN", group = 1), size = 0.5) +
geom_line(aes(y = AXP, color = "AXP", group = 1), size = 0.5) +
labs(x = "Date",
y = "Stock Prices",
color = "Stocks") + scale_color_manual(values = colors)
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ
Please use `linewidth` instead.
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plot_2 <- ggplot(df1, aes(x=rows))+
geom_point(aes(y = mean, group = 1), size = 0.5)+
geom_point(aes(y=standard_deviation, group = 1), size = 0.5)+
labs(x = 'Stock',
y = 'statistical Values')
plot_1 / plot_2
# Part II
# 1. Download Amazon daily stock price data from 2021-01-01 to 2021-12-31. And save the data to a csv file.
# install.packages("quantmod",repos = "http://cran.us.r-project.org")
library
(quantmod)
## Loading required package: xts
## Loading required package: zoo
## ## Attaching package: 'zoo'
Next
1
2
3
4
5
6
...
26
Previous
## The following objects are masked from 'package:base':
## ## as.Date, as.Date.numeric
## Loading required package: TTR
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
# Downloading Amazon's stock price data
AMZN_df <- getSymbols("AMZN", from = '2021-01-01',
to = "2021-12-31")
# Saving the data to a CSV file
# Convert the stock price data to a data frame
amzn_df <- as.data.frame(AMZN)
# Save the data frame to a CSV file
write.csv(amzn_df, "/Users/incharanagaraju/Desktop/513/amzn_df.csv", row.names = TRUE)
AMZN_df <- read.csv("/Users/incharanagaraju/Desktop/513/amzn_df.csv")
AMZN_df
X
<chr>
AMZN.Op…
<dbl>
AMZN.High
<dbl>
AMZN.L…
<dbl>
AMZN.Close
<dbl>
AMZN.Volume
<int>
AMZN.Adjusted
<dbl>
2021-01-04
163.5000
163.6000
157.2010
159.3315
88228000
159.3315
2021-01-05
158.3005
161.1690
158.2530
160.9255
53110000
160.9255
2021-01-06
157.3240
159.8755
156.5580
156.9190
87896000
156.9190
2021-01-07
157.8500
160.4270
157.7500
158.1080
70290000
158.1080
2021-01-08
159.0000
159.5320
157.1100
159.1350
70754000
159.1350
2021-01-11
157.4005
157.8190
155.5000
155.7105
73668000
155.7105
2021-01-12
156.0000
157.1070
154.3000
156.0415
70292000
156.0415
2021-01-13
156.4220
159.4975
156.1040
158.2945
66424000
158.2945
2021-01-14
158.3760
158.9000
156.0295
156.3735
61418000
156.3735
2021-01-15
156.1510
157.1275
154.7585
155.2125
84880000
155.2125
1-10 of 251 rows
# 2. Calculate weekly log returns based on adjusted close price.
weekly_logreturns <- diff(log(AMZN_df$AMZN.Adjusted),lag = 7)
weekly_logreturns
## [1] -6.529728e-03 -2.869416e-02 -1.093468e-02 -1.317883e-02 2.503364e-02
## [6] 6.006295e-02 5.346610e-02 3.966843e-02 6.158508e-02 4.050847e-02
## [11] 3.676195e-02 -1.767708e-02 1.079426e-02 2.631059e-02 5.609604e-03
## [16] 1.463093e-03 3.632135e-02 2.601148e-02 3.035005e-02 -1.698521e-02
## [21] -3.549532e-02 -1.056722e-02 -1.880378e-02 -1.306465e-02 1.590674e-03
## [26] -1.681228e-02 -3.273359e-02 -2.094977e-02 -3.672171e-02 -6.698241e-02
## [31] -6.741841e-02 -5.626428e-02 -4.898815e-02 -5.683632e-02 -7.032313e-02
## [36] -5.165771e-02 -3.502040e-02 -9.772994e-03 -2.853295e-02 6.140384e-03
## [41] 2.772848e-02 3.436741e-02 3.000729e-02 6.039600e-02 -1.144680e-02
## [46] 5.648497e-03 -8.739779e-04 1.542026e-02 1.747518e-03 -1.485823e-02
## [51] -2.705505e-02 1.564319e-02 -6.417411e-03 -5.411873e-03 7.462148e-03
## [56] 4.424683e-02 5.665232e-02 7.185047e-02 7.016804e-02 9.869087e-02
## [61] 8.820463e-02 7.288698e-02 3.240351e-02 4.703948e-02 3.595329e-02
## [66] 2.179867e-02 -1.118565e-02 -5.153236e-03 -2.711734e-02 2.361518e-03
## [71] 8.812545e-03 5.278130e-03 2.532602e-02 4.015238e-02 3.086884e-02
## [76] 2.313585e-02 -8.721260e-03 -4.146391e-02 -3.303795e-02 -4.945815e-02
## [81] -8.435753e-02 -7.281593e-02 -7.177581e-02 -4.647590e-02 -1.467347e-02
## [86] -1.094164e-02 -1.818908e-02 1.286469e-02 7.346030e-03 1.609475e-02
## [91] 2.607512e-02 1.115414e-02 -1.600508e-03 -6.716092e-04 -2.704893e-03
## [96] -8.978928e-03 9.603735e-03 -1.802911e-02 -1.634303e-02 -2.078002e-02
## [101] 1.047102e-02 1.785960e-02 3.989386e-02 3.429705e-02 5.993687e-02
## [106] 5.370858e-02 6.572196e-02 6.669681e-02 6.081915e-02 3.066554e-02
## [111] 4.630239e-02 3.483376e-02 1.930622e-02 -4.045940e-03 -1.308231e-02
## [116] -1.117815e-02 -4.003429e-03 -2.089029e-02 2.041410e-03 6.364699e-02
## [121] 8.320330e-02 8.018449e-02 7.571126e-02 7.781588e-02 6.876931e-02
## [126] 4.747399e-02 -1.219133e-02 -3.382614e-02 -4.995401e-02 -4.008745e-02
## [131] -3.651960e-02 -1.075273e-02 -6.824471e-03 1.872099e-02 1.465578e-02
## [136] 2.248869e-02 7.452880e-03 -7.456591e-02 -8.802567e-02 -8.274833e-02
## [141] -9.791589e-02 -7.154907e-02 -8.187211e-02 -7.438107e-02 -2.078761e-03
## [146] -1.188799e-02 -1.881384e-02 -1.827473e-02 -2.307230e-02 -3.127059e-02
## [151] -4.299855e-02 -4.085424e-02 -2.839352e-02 -1.145632e-02 3.578921e-03
## [156] 5.763416e-05 2.258113e-02 4.531791e-02 7.078423e-02 8.124709e-02
## [161] 6.321867e-02 4.649749e-02 5.279782e-02 5.665444e-02 5.117231e-02
## [166] 1.812740e-02 -4.726323e-04 -6.294515e-03 -3.795720e-03 -6.499488e-04
## [171] -6.016370e-03 -1.802555e-02 -3.755762e-02 -3.685257e-02 -2.255985e-02
## [176] -9.903938e-03 -1.456853e-02 -2.391751e-02 -4.324949e-02 -1.640752e-02
## [181] -1.767824e-02 -2.905372e-02 -6.851836e-02 -6.156140e-02 -4.313629e-02
## [186] -4.088601e-03 -3.793781e-03 -1.186292e-02 -1.100367e-02 2.919554e-02
## [191] 2.418813e-02 4.408135e-02 4.277029e-02 4.620914e-02 5.067920e-02
## [196] 5.618673e-02 1.549008e-02 6.196167e-03 -9.712590e-03 -1.586475e-02
## [201] 7.024056e-04 -1.256151e-02 -3.462450e-02 -6.858917e-03 1.898224e-02
## [206] 2.945759e-02 3.660984e-02 1.222989e-02 5.867555e-02 4.822580e-02
## [211] 4.709615e-02 4.086460e-02 1.956006e-02 6.150493e-03 1.705640e-02
## [216] 3.295822e-02 5.435912e-02 2.841040e-02 1.545094e-02 9.747336e-03
## [221] -1.025951e-02 3.535636e-03 -5.248642e-02 -6.542797e-02 -3.858148e-02
## [226] -5.460598e-02 -4.368408e-02 5.330280e-03 -1.084315e-02 -6.766333e-03
## [231] 1.509939e-04 -1.347561e-02 -2.350960e-03 1.129455e-02 -4.228312e-02
## [236] -3.547996e-02 -4.157088e-02 -1.047790e-02 8.628818e-03 1.162401e-02
## [241] -2.125836e-02 1.054398e-02 -4.814004e-03 9.326230e-03
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# 3. Calculate median, mean, standard deviation of log returns.
# Calculate median log return
median_log_return <- median(weekly_logreturns)
median_log_return
## [1] -0.000660779
# Calculate mean log return
mean_log_return <- mean(weekly_logreturns)
mean_log_return
## [1] 0.002113911
# Calculate standard deviation of log returns
sd_log_return <- sd(weekly_logreturns)
sd_log_return
## [1] 0.03867562
# 4. Plot the distribution of stock daily log returns
daily_log_returns <- diff(log(AMZN_df$AMZN.Adjusted), lag = 1)
daily_log_returns
## [1] 9.954650e-03 -2.521178e-02 7.548570e-03 6.474511e-03 -2.175439e-02
## [6] 2.123541e-03 1.433517e-02 -1.220978e-02 -7.452301e-03 5.304422e-03
## [11] 4.468698e-02 1.327492e-02 -4.473306e-03 5.374911e-04 9.706870e-03
## [16] -2.852892e-02 1.557906e-03 -9.752051e-03 4.174627e-02 1.104302e-02
## [21] -2.016349e-02 5.560360e-03 6.329342e-03 -8.751968e-03 -5.413478e-03
## [26] -5.588993e-03 -7.467087e-03 4.764603e-03 -2.676194e-03 1.206847e-02
## [31] 5.903354e-03 -2.381643e-02 -2.151030e-02 4.316726e-03 -1.100733e-02
## [36] -3.293690e-02 1.163247e-02 1.705749e-02 -1.654031e-02 -2.935848e-02
## [41] -9.170077e-03 7.658086e-03 -1.629958e-02 3.687987e-02 -1.702465e-03
## [46] 1.813302e-02 -7.770379e-03 -2.531145e-03 3.297962e-03 1.408913e-02
## [51] -3.496292e-02 1.539283e-02 1.161055e-02 8.523855e-03 -1.620388e-02
## [56] -1.330779e-02 1.892315e-03 7.735315e-03 -6.667777e-03 1.261609e-02
## [61] 2.139788e-02 2.058080e-02 -9.022983e-04 1.709046e-02 6.052883e-03
## [66] 2.185506e-02 2.129852e-03 6.080224e-03 -1.990267e-02 1.373367e-02
## [71] 6.004282e-03 -8.101742e-03 -1.112927e-02 8.162268e-03 -1.588388e-02
## [76] 9.576188e-03 2.018469e-02 2.469866e-03 1.194614e-02 3.697092e-03
## [81] -1.121266e-03 -2.361687e-02 -2.228092e-02 -1.255795e-02 1.089583e-02
## [86] -4.474056e-03 -3.120229e-02 1.042034e-02 -2.257675e-02 3.018986e-03
## [91] 1.924448e-02 1.462765e-02 -1.172149e-02 -1.485254e-04 4.901681e-03
## [96] -1.382802e-02 1.299935e-02 4.323492e-03 1.873006e-03 -1.079259e-02
## [101] -2.181809e-03 -1.372354e-03 4.754640e-03 -1.463349e-02 6.009569e-03
## [106] -2.563982e-03 2.045845e-02 5.206772e-03 2.066191e-02 -8.421798e-04
## [111] 1.100634e-02 -2.187262e-04 9.449398e-03 2.143330e-02 -6.708868e-04
## [116] -9.491708e-03 1.479468e-02 -4.622970e-04 -1.574627e-02 -1.390276e-02
## [121] 1.239693e-02 1.233274e-03 -2.316985e-03 -2.092189e-03 2.246941e-02
## [126] 4.585931e-02 5.653552e-03 9.378116e-03 -3.239951e-03 -2.123721e-04
## [131] -1.113875e-02 1.174088e-03 -1.380601e-02 -1.598126e-02 -6.749759e-03
## [136] 6.626611e-03 3.355478e-03 1.462812e-02 5.102345e-03 1.173946e-02
## [141] -2.004647e-02 1.083147e-03 -8.409198e-03 -7.866331e-02 1.168355e-03
## [146] 1.037969e-02 -3.428109e-03 6.320353e-03 -9.239894e-03 -9.181539e-04
## [151] -6.361003e-03 -8.640873e-03 3.453840e-03 -2.888994e-03 1.522782e-03
## [156] -1.743819e-02 -1.264611e-02 -4.216698e-03 3.819852e-03 2.039104e-02
## [161] 1.214625e-02 -1.998505e-03 5.085303e-03 1.009067e-02 2.124962e-02
## [166] 1.428272e-02 2.362616e-03 -4.574927e-03 4.301817e-03 8.941929e-03
## [171] 4.608538e-03 -1.179529e-02 -4.317312e-03 -3.459266e-03 -2.076133e-03
## [176] 7.447589e-03 3.575508e-03 -7.400640e-03 -3.132736e-02 -3.612265e-03
## [181] 1.083345e-02 1.057978e-02 2.782997e-03 -5.773471e-03 -2.673262e-02
## [186] -4.485394e-03 -4.882982e-03 -5.420276e-04 -2.888486e-02 9.739953e-03
## [191] 1.265164e-02 1.231506e-02 -4.190574e-03 -1.295213e-02 3.172278e-04
## [196] 1.131435e-02 4.732539e-03 3.254486e-02 1.100401e-02 -7.517287e-04
## [201] -8.482065e-03 5.824763e-03 -2.938230e-02 -4.561373e-03 1.663611e-02
## [206] 4.851848e-03 1.581543e-02 -2.174598e-02 -1.623823e-02 -1.616714e-03
## [211] 2.127978e-02 2.711146e-02 1.200409e-02 -8.564518e-03 2.469968e-02
## [216] -2.668797e-02 -2.746365e-03 1.504823e-02 5.806916e-03 -1.405474e-03
## [221] 2.341386e-03 4.060150e-02 -5.287070e-03 -2.869509e-02 2.088777e-03
## [226] 1.033119e-04 -2.141232e-02 1.613653e-02 -1.542056e-02 -1.822862e-02
## [231] -1.848600e-03 -1.393573e-02 1.102522e-02 2.760204e-02 -3.689801e-05
## [236] -1.134374e-02 -1.131129e-02 -1.547520e-02 -2.811077e-03 2.467073e-02
## [241] -2.597564e-02 6.766263e-03 -1.743466e-02 1.978169e-02 3.631509e-03
## [246] 1.841186e-04 -8.211646e-03 5.826706e-03 -8.591722e-03 -3.294426e-03
par(mar = c(1, 1, 1, 1))
hist(daily_log_returns,breaks = 10,
xlab = "daily log returns",
main = "Histogram of Amazon daily log returns",
col = "blue")
# 5. Count how many observation in this series whose log return is between 0.01 and 0.01
5.
length(which(daily_log_returns > 0.01 & daily_log_returns < 0.015))
## [1] 31
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