energy

get started

load libraries

options(digits = 4, width = 70)
library(boot)
library(tseries)
library(zoo)
library(PerformanceAnalytics)
library(multicore)

load data

returns.df = read.csv(file = "~/Documents/annual/returnsCME.csv", sep = ";", 
    header = TRUE, stringsAsFactors = FALSE)
returns.df[is.na(returns.df)] = 0
returns.z = zooreg(data = returns.df[, -1], start = c(1992, 41), end = c(2011, 
    12), frequency = 52)
energy.z = returns.z[, c("crude", "gasoline", "heating", "natural", "electricity")]

load functions

wget.and.source <- function(url) {
    fname <- tempfile()
    download.file(url, fname, method = "wget")
    source(fname)
    unlink(fname)
}
wget.and.source("https://gist.github.com/bautheac/b2e8269868a881b66a69/raw/")

energy distributions:

rolling estimates

rollMomentsenergy.ls = rollingMoments.fun(energy.z, startYear = 1992, startWeek = 41, 
    width = 52)

crude

summary

plot of chunk crude distribution summary

moments

mean (\( \widehat{\mu} \)) and 95% confidence interval:

mu95CI(energy.z, "crude")

##         muhat standard error lower bound upper bound
## [1,] 0.001722       0.001495   -0.001268    0.004712

standard deviation (\( \widehat{\sigma} \)) and 95% confidence interval:

sd95CI(energy.z, "crude")

##        sdhat standard error lower bound upper bound
## [1,] 0.04642       0.001528     0.04336     0.04947

coeffciient of skweness (\( \widehat{\gamma}_{1} \)) and 95% confidence interval:

skew95CI(returns.df, "crude")

##      skewhat standard error lower bound upper bound
## [1,] -0.5614         0.2088     -0.9791     -0.1438

coefficient of kurtosis (\( \widehat{\beta}_{2} \)) and 95% confidence interval:

kurt95CI(returns.df, "crude")

##      kurthat standard error lower bound upper bound
## [1,]   2.285         0.7825      0.7201        3.85

rolling moments

rolling \( \widehat{\mu} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["crude"]][["mu"]])

##          muhat.lower muhat muhat.upper
## 1993(41)     -0.2959 -0.24     -0.1841
## 1993(42)     -0.3155 -0.26     -0.2045
## 1993(43)     -0.3357 -0.28     -0.2243
## 1993(44)     -0.3044 -0.25     -0.1956
## 1993(45)     -0.3469 -0.29     -0.2331
## 1993(46)     -0.3271 -0.27     -0.2129
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "crude", statistic = "mu")

plot of chunk crude rolling mu plot

rolling \( \widehat{\sigma} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["crude"]][["sd"]])

##          sdhat.lower  sdhat sdhat.upper
## 1993(41)      0.1962 0.2017      0.2072
## 1993(42)      0.1947 0.2002      0.2057
## 1993(43)      0.1949 0.2007      0.2065
## 1993(44)      0.1904 0.1961      0.2017
## 1993(45)      0.1992 0.2052      0.2111
## 1993(46)      0.1997 0.2057      0.2117
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "crude", statistic = "sd")

plot of chunk crude rolling sd plot

rolling \( \widehat{\gamma}_{1} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["crude"]][["skew"]])

##          skewhat.lower skewhat skewhat.upper
## 1993(41)       -0.3063  0.2330        0.7723
## 1993(42)       -0.2952  0.2666        0.8284
## 1993(43)       -0.2258  0.3033        0.8324
## 1993(44)       -0.2420  0.3453        0.9326
## 1993(45)       -0.4542  0.1588        0.7718
## 1993(46)       -0.4666  0.1200        0.7066
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "crude", statistic = "skew")

plot of chunk crude rolling skew plot

rolling \( \widehat{\beta}_{2} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["crude"]][["kurt"]])

##          kurthat.lower    kurthat kurthat.upper
## 1993(41)       -1.0570 -1.086e-05         1.057
## 1993(42)       -1.0025  9.250e-02         1.187
## 1993(43)       -0.9689  7.988e-02         1.129
## 1993(44)       -0.8974  2.044e-01         1.306
## 1993(45)       -0.7573  2.238e-01         1.205
## 1993(46)       -0.8462  1.845e-01         1.215
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "crude", statistic = "kurt")

plot of chunk crude rolling kurt plot

gasoline

summary

plot of chunk gasoline distribution summary

moments

mean (\( \widehat{\mu} \)) and 95% confidence interval:

mu95CI(energy.z, "gasoline")

##          muhat standard error lower bound upper bound
## [1,] 0.0003008       0.000935   -0.001569    0.002171

standard deviation (\( \widehat{\sigma} \)) and 95% confidence interval:

sd95CI(energy.z, "gasoline")

##        sdhat standard error lower bound upper bound
## [1,] 0.02903        0.00215     0.02473     0.03333

coeffciient of skweness (\( \widehat{\gamma}_{1} \)) and 95% confidence interval:

skew95CI(returns.df, "gasoline")

##      skewhat standard error lower bound upper bound
## [1,]  -1.174         0.9267      -3.027      0.6795

coefficient of kurtosis (\( \widehat{\beta}_{2} \)) and 95% confidence interval:

kurt95CI(returns.df, "gasoline")

##      kurthat standard error lower bound upper bound
## [1,]   19.63          4.447       10.74       28.53

rolling moments

rolling \( \widehat{\mu} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["gasoline"]][["mu"]])

##          muhat.lower muhat muhat.upper
## 1993(41)           0     0           0
## 1993(42)           0     0           0
## 1993(43)           0     0           0
## 1993(44)           0     0           0
## 1993(45)           0     0           0
## 1993(46)           0     0           0
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "gasoline", statistic = "mu")

plot of chunk gasoline rolling mu plot

rolling \( \widehat{\sigma} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["gasoline"]][["sd"]])

##          sdhat.lower sdhat sdhat.upper
## 1993(41)           0     0           0
## 1993(42)           0     0           0
## 1993(43)           0     0           0
## 1993(44)           0     0           0
## 1993(45)           0     0           0
## 1993(46)           0     0           0
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "gasoline", statistic = "sd")

plot of chunk gasoline rolling sd plot

rolling \( \widehat{\gamma}_{1} \) and 95% confidence interval:

time series overview
tail(rollMomentsenergy.ls[["gasoline"]][["skew"]])

##          skewhat.lower skewhat skewhat.upper
## 2011(12)        -1.733 -0.9065     -0.079810
## 2011(13)        -1.588 -0.8008     -0.013348
## 2011(14)        -1.611 -0.8008      0.009806
## 2011(15)        -1.574 -0.7839      0.006485
## 2011(16)        -1.583 -0.7673      0.048287
## 2011(17)        -1.618 -0.8318     -0.045333
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "gasoline", statistic = "skew")

plot of chunk gasoline rolling skew plot

rolling \( \widehat{\beta}_{2} \) and 95% confidence interval:

time series overview
tail(rollMomentsenergy.ls[["gasoline"]][["kurt"]])

##          kurthat.lower kurthat kurthat.upper
## 2011(12)       -0.3900   1.837         4.063
## 2011(13)       -0.4243   1.601         3.627
## 2011(14)       -0.2780   1.601         3.481
## 2011(15)       -0.3358   1.542         3.419
## 2011(16)       -0.3483   1.504         3.356
## 2011(17)       -0.3976   1.588         3.573
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "gasoline", statistic = "kurt")

plot of chunk gasoline rolling kurt plot

heating

summary

plot of chunk heating distribution summary

moments

mean (\( \widehat{\mu} \)) and 95% confidence interval:

mu95CI(energy.z, "heating")

##         muhat standard error lower bound upper bound
## [1,] 0.001566       0.001433     -0.0013    0.004433

standard deviation (\( \widehat{\sigma} \)) and 95% confidence interval:

sd95CI(energy.z, "heating")

##       sdhat standard error lower bound upper bound
## [1,] 0.0445       0.001297     0.04191     0.04709

coeffciient of skweness (\( \widehat{\gamma}_{1} \)) and 95% confidence interval:

skew95CI(returns.df, "heating")

##      skewhat standard error lower bound upper bound
## [1,] -0.3483          0.169     -0.6863     -0.0104

coefficient of kurtosis (\( \widehat{\beta}_{2} \)) and 95% confidence interval

kurt95CI(returns.df, "heating")

##      kurthat standard error lower bound upper bound
## [1,]   1.559         0.5963      0.3664       2.752

rolling moments

rolling \( \widehat{\mu} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["heating"]][["mu"]])

##          muhat.lower muhat muhat.upper
## 1993(41)     -0.2590 -0.20     -0.1410
## 1993(42)     -0.2983 -0.24     -0.1817
## 1993(43)     -0.3187 -0.26     -0.2013
## 1993(44)     -0.2875 -0.23     -0.1725
## 1993(45)     -0.2980 -0.24     -0.1820
## 1993(46)     -0.2571 -0.20     -0.1429
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "heating", statistic = "mu")

plot of chunk heating rolling mu plot

rolling \( \widehat{\sigma} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["heating"]][["sd"]])

##          sdhat.lower  sdhat sdhat.upper
## 1993(41)      0.2058 0.2128      0.2198
## 1993(42)      0.2032 0.2101      0.2170
## 1993(43)      0.2047 0.2116      0.2184
## 1993(44)      0.2004 0.2071      0.2139
## 1993(45)      0.2020 0.2091      0.2163
## 1993(46)      0.1991 0.2060      0.2129
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "heating", statistic = "sd")

plot of chunk heating rolling sd plot

rolling \( \widehat{\gamma}_{1} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["heating"]][["skew"]])

##          skewhat.lower skewhat skewhat.upper
## 1993(41)      -0.11553  0.5525         1.221
## 1993(42)      -0.14099  0.6233         1.388
## 1993(43)      -0.04607  0.6374         1.321
## 1993(44)      -0.06649  0.6916         1.450
## 1993(45)      -0.09261  0.6519         1.396
## 1993(46)      -0.07471  0.6378         1.350
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "heating", statistic = "skew")

plot of chunk heating rolling skew plot

rolling \( \widehat{\beta}_{2} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["heating"]][["kurt"]])

##          kurthat.lower kurthat kurthat.upper
## 1993(41)       -0.6487  0.7416         2.132
## 1993(42)       -0.5331  0.9669         2.467
## 1993(43)       -0.6207  0.9017         2.424
## 1993(44)       -0.5510  1.0684         2.688
## 1993(45)       -0.6173  1.0102         2.638
## 1993(46)       -0.4145  1.1361         2.687
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "heating", statistic = "kurt")

plot of chunk heating rolling kurt plot

natural

summary

plot of chunk natural distribution summary

moments

mean (\( \widehat{\mu} \)) and 95% confidence interval:

mu95CI(energy.z, "natural")

##          muhat standard error lower bound upper bound
## [1,] -0.003102       0.002094   -0.007289    0.001085

standard deviation (\( \widehat{\sigma} \)) and 95% confidence interval:

sd95CI(energy.z, "natural")

##      sdhat standard error lower bound upper bound
## [1,] 0.065       0.001774     0.06145     0.06855

coeffciient of skweness (\( \widehat{\gamma}_{1} \)) and 95% confidence interval:

skew95CI(returns.df, "natural")

##       skewhat standard error lower bound upper bound
## [1,] -0.07297         0.1311     -0.3352      0.1893

coefficient of kurtosis (\( \widehat{\beta}_{2} \)) and 95% confidence interval:

kurt95CI(returns.df, "natural")

##      kurthat standard error lower bound upper bound
## [1,]  0.9401         0.2883      0.3634       1.517

rolling moments

rolling \( \widehat{\mu} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["natural"]][["mu"]])

##          muhat.lower muhat muhat.upper
## 1993(41)      0.1219  0.21      0.2981
## 1993(42)      0.1219  0.21      0.2981
## 1993(43)      0.1020  0.19      0.2780
## 1993(44)      0.1222  0.21      0.2978
## 1993(45)      0.1624  0.25      0.3376
## 1993(46)      0.1723  0.26      0.3477
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "natural", statistic = "mu")

plot of chunk natural rolling mu plot

rolling \( \widehat{\sigma} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["natural"]][["sd"]])

##          sdhat.lower  sdhat sdhat.upper
## 1993(41)      0.3105 0.3178      0.3251
## 1993(42)      0.3105 0.3178      0.3251
## 1993(43)      0.3097 0.3174      0.3251
## 1993(44)      0.3092 0.3165      0.3238
## 1993(45)      0.3085 0.3159      0.3233
## 1993(46)      0.3087 0.3163      0.3239
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "natural", statistic = "sd")

plot of chunk natural rolling sd plot

rolling \( \widehat{\gamma}_{1} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["natural"]][["skew"]])

##          skewhat.lower  skewhat skewhat.upper
## 1993(41)       -0.5181 -0.03897        0.4402
## 1993(42)       -0.5037 -0.03897        0.4258
## 1993(43)       -0.4789 -0.01361        0.4517
## 1993(44)       -0.5208 -0.03718        0.4465
## 1993(45)       -0.5537 -0.08634        0.3810
## 1993(46)       -0.5686 -0.09857        0.3715
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "natural", statistic = "skew")

plot of chunk natural rolling skew plot

rolling \( \widehat{\beta}_{2} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["natural"]][["kurt"]])

##          kurthat.lower kurthat kurthat.upper
## 1993(41)        -1.271 -0.5628        0.1452
## 1993(42)        -1.304 -0.5628        0.1788
## 1993(43)        -1.254 -0.5519        0.1506
## 1993(44)        -1.301 -0.5251        0.2505
## 1993(45)        -1.249 -0.5044        0.2400
## 1993(46)        -1.266 -0.5128        0.2410
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "natural", statistic = "kurt")

plot of chunk natural rolling kurt plot

electricity

summary

plot of chunk electricity distribution summary

moments

mean (\( \widehat{\mu} \)) and 95% confidence interval:

mu95CI(energy.z, "electricity")

##          muhat standard error lower bound upper bound
## [1,] -0.001929       0.001232   -0.004393    0.000534

standard deviation (\( \widehat{\sigma} \)) and 95% confidence interval:

sd95CI(energy.z, "electricity")

##        sdhat standard error lower bound upper bound
## [1,] 0.03824       0.001817     0.03461     0.04188

coeffciient of skweness (\( \widehat{\gamma}_{1} \)) and 95% confidence interval:

skew95CI(returns.df, "electricity")

##      skewhat standard error lower bound upper bound
## [1,] -0.2474         0.3272     -0.9018      0.4069

coefficient of kurtosis (\( \widehat{\beta}_{2} \)) and 95% confidence interval:

kurt95CI(returns.df, "electricity")

##      kurthat standard error lower bound upper bound
## [1,]   6.691           0.85       4.991       8.391

rolling moments

rolling \( \widehat{\mu} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["electricity"]][["mu"]])

##          muhat.lower muhat muhat.upper
## 1993(41)           0     0           0
## 1993(42)           0     0           0
## 1993(43)           0     0           0
## 1993(44)           0     0           0
## 1993(45)           0     0           0
## 1993(46)           0     0           0
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "electricity", 
    statistic = "mu")

plot of chunk electricity rolling mu plot

rolling \( \widehat{\sigma} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["electricity"]][["sd"]])

##          sdhat.lower sdhat sdhat.upper
## 1993(41)           0     0           0
## 1993(42)           0     0           0
## 1993(43)           0     0           0
## 1993(44)           0     0           0
## 1993(45)           0     0           0
## 1993(46)           0     0           0
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "electricity", 
    statistic = "sd")

plot of chunk electricity rolling sd plot

rolling \( \widehat{\gamma}_{1} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["electricity"]][["skew"]])

##          skewhat.lower skewhat skewhat.upper
## 1993(41)           NaN     NaN           NaN
## 1993(42)           NaN     NaN           NaN
## 1993(43)           NaN     NaN           NaN
## 1993(44)           NaN     NaN           NaN
## 1993(45)           NaN     NaN           NaN
## 1993(46)           NaN     NaN           NaN
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "electricity", 
    statistic = "skew")

plot of chunk electricity rolling skew plot

rolling \( \widehat{\beta}_{2} \) and 95% confidence interval:

time series overview
head(rollMomentsenergy.ls[["electricity"]][["kurt"]])

##          kurthat.lower kurthat kurthat.upper
## 1993(41)           NaN     NaN           NaN
## 1993(42)           NaN     NaN           NaN
## 1993(43)           NaN     NaN           NaN
## 1993(44)           NaN     NaN           NaN
## 1993(45)           NaN     NaN           NaN
## 1993(46)           NaN     NaN           NaN
plot
plotRollingMoments(data = rollMomentsenergy.ls, commo = "electricity", 
    statistic = "kurt")

plot of chunk electricity rolling kurt plot