Introduction
In this fourth post, I am going to analyse the Dow Jones Industrial Average (DJIA) trade volume log ratio.
Packages
The packages being used in this post series are herein listed.
suppressPackageStartupMessages(library(lubridate))
suppressPackageStartupMessages(library(fBasics))
suppressPackageStartupMessages(library(lmtest))
suppressPackageStartupMessages(library(urca))
suppressPackageStartupMessages(library(ggplot2))
suppressPackageStartupMessages(library(quantmod))
suppressPackageStartupMessages(library(PerformanceAnalytics))
suppressPackageStartupMessages(library(rugarch))
suppressPackageStartupMessages(library(FinTS))
suppressPackageStartupMessages(library(forecast))
suppressPackageStartupMessages(library(strucchange))
suppressPackageStartupMessages(library(TSA))Getting Data
We upload the environment status as saved at the end of part 1.
load(file='DowEnvironment.RData')From saved environment, we can find back our DJI object. We plot the daily volume.
dj_vol <- DJI[,"DJI.Volume"]
plot(dj_vol)
Daily volume log-ratio Exploratory Analysis
Simlarly to log-returns, we can define the trade volume log ratio as.
\[ v_{t}\ := ln \frac{V_{t}}{V_{t-1}} \] We can compute it by CalculateReturns within the PerformanceAnalytics package.
dj_vol_log_ratio <- CalculateReturns(dj_vol, "log")
dj_vol_log_ratio <- na.omit(dj_vol_log_ratio)
plot(dj_vol_log_ratio)
Mapping the trade volume log-ratio time series data and timeline index into a dataframe.
dj_vol_df <- xts_to_dataframe(dj_vol_log_ratio)
head(dj_vol_df)## year value
## 1 2007 -0.233511910
## 2 2007 -0.096538449
## 3 2007 -0.051109832
## 4 2007 0.007533076
## 5 2007 0.006109458
## 6 2007 0.144221282tail(dj_vol_df)## year value
## 3014 2018 0.44563907
## 3015 2018 -1.07149878
## 3016 2018 0.33945998
## 3017 2018 -0.05980236
## 3018 2018 -0.19249224
## 3019 2018 -0.15278959Basic statistics summary
(dj_stats <- dataframe_basicstats(dj_vol_df))## 2007 2008 2009 2010 2011
## nobs 250.000000 253.000000 252.000000 252.000000 252.000000
## NAs 0.000000 0.000000 0.000000 0.000000 0.000000
## Minimum -1.606192 -1.122526 -1.071225 -1.050181 -2.301514
## Maximum 0.775961 0.724762 0.881352 1.041216 2.441882
## 1. Quartile -0.123124 -0.128815 -0.162191 -0.170486 -0.157758
## 3. Quartile 0.130056 0.145512 0.169233 0.179903 0.137108
## Mean -0.002685 0.001203 -0.001973 -0.001550 0.000140
## Median -0.010972 0.002222 -0.031748 -0.004217 -0.012839
## Sum -0.671142 0.304462 -0.497073 -0.390677 0.035162
## SE Mean 0.016984 0.016196 0.017618 0.019318 0.026038
## LCL Mean -0.036135 -0.030693 -0.036670 -0.039596 -0.051141
## UCL Mean 0.030766 0.033100 0.032725 0.036495 0.051420
## Variance 0.072112 0.066364 0.078219 0.094041 0.170850
## Stdev 0.268536 0.257612 0.279677 0.306661 0.413341
## Skewness -0.802037 -0.632586 0.066535 -0.150523 0.407226
## Kurtosis 5.345212 2.616615 1.500979 1.353797 14.554642
## 2012 2013 2014 2015 2016
## nobs 250.000000 252.000000 252.000000 252.000000 252.000000
## NAs 0.000000 0.000000 0.000000 0.000000 0.000000
## Minimum -2.158960 -1.386215 -2.110572 -1.326016 -1.336471
## Maximum 1.292956 1.245202 2.008667 1.130289 1.319713
## 1. Quartile -0.152899 -0.145444 -0.144280 -0.143969 -0.134011
## 3. Quartile 0.144257 0.149787 0.134198 0.150003 0.141287
## Mean 0.001642 -0.002442 0.000200 0.000488 0.004228
## Median -0.000010 -0.004922 0.013460 0.004112 -0.002044
## Sum 0.410521 -0.615419 0.050506 0.123080 1.065480
## SE Mean 0.021293 0.019799 0.023514 0.019010 0.019089
## LCL Mean -0.040295 -0.041435 -0.046110 -0.036952 -0.033367
## UCL Mean 0.043579 0.036551 0.046510 0.037929 0.041823
## Variance 0.113345 0.098784 0.139334 0.091071 0.091826
## Stdev 0.336667 0.314299 0.373274 0.301780 0.303028
## Skewness -0.878227 -0.297951 -0.209417 -0.285918 0.083826
## Kurtosis 8.115847 4.681120 9.850061 4.754926 4.647785
## 2017 2018
## nobs 251.000000 251.000000
## NAs 0.000000 0.000000
## Minimum -0.817978 -1.071499
## Maximum 0.915599 0.926101
## 1. Quartile -0.112190 -0.119086
## 3. Quartile 0.110989 0.112424
## Mean -0.000017 0.000257
## Median -0.006322 0.003987
## Sum -0.004238 0.064605
## SE Mean 0.013446 0.014180
## LCL Mean -0.026500 -0.027671
## UCL Mean 0.026466 0.028185
## Variance 0.045383 0.050471
## Stdev 0.213032 0.224658
## Skewness 0.088511 -0.281007
## Kurtosis 3.411036 4.335748In the following, we make specific comments to some relevant aboveshown metrics.
Mean
Years when Dow Jones daily trade volume log-ratio has positive mean are:
filter_dj_stats(dj_stats, "Mean", 0)## [1] "2008" "2011" "2012" "2014" "2015" "2016" "2018"All Dow Jones daily trade volume log-ratio mean values in ascending order.
dj_stats["Mean",order(dj_stats["Mean",,])]## 2007 2013 2009 2010 2017 2011 2014
## Mean -0.002685 -0.002442 -0.001973 -0.00155 -1.7e-05 0.00014 2e-04
## 2018 2015 2008 2012 2016
## Mean 0.000257 0.000488 0.001203 0.001642 0.004228Median
Years when Dow Jones daily volume log-ratio has positive median are:
filter_dj_stats(dj_stats, "Median", 0)## [1] "2008" "2014" "2015" "2018"All Dow Jones daily trade volume log-ratio median values in ascending order.
dj_stats["Median",order(dj_stats["Median",,])]## 2009 2011 2007 2017 2013 2010
## Median -0.031748 -0.012839 -0.010972 -0.006322 -0.004922 -0.004217
## 2016 2012 2008 2018 2015 2014
## Median -0.002044 -1e-05 0.002222 0.003987 0.004112 0.01346Skewness
Years when Dow Jones daily volume log-ratio has positive skewness are:
filter_dj_stats(dj_stats, "Skewness", 0)## [1] "2009" "2011" "2016" "2017"All Dow Jones daily trade volume log-ratio mean values in ascending order.
dj_stats["Skewness",order(dj_stats["Skewness",,])]## 2012 2007 2008 2013 2015 2018
## Skewness -0.878227 -0.802037 -0.632586 -0.297951 -0.285918 -0.281007
## 2014 2010 2009 2016 2017 2011
## Skewness -0.209417 -0.150523 0.066535 0.083826 0.088511 0.407226Excess Kurtosis
Years when Dow Jones daily log-returns has positive excess kurtosis are:
filter_dj_stats(dj_stats, "Kurtosis", 0)## [1] "2007" "2008" "2009" "2010" "2011" "2012" "2013" "2014" "2015" "2016"
## [11] "2017" "2018"All Dow Jones daily trade volume log-ratio excess kurtosis values in ascending order.
dj_stats["Kurtosis",order(dj_stats["Kurtosis",,])]## 2010 2009 2008 2017 2018 2016 2013
## Kurtosis 1.353797 1.500979 2.616615 3.411036 4.335748 4.647785 4.68112
## 2015 2007 2012 2014 2011
## Kurtosis 4.754926 5.345212 8.115847 9.850061 14.55464Boxplots
dataframe_boxplot(dj_vol_df, "DJIA daily volume box plots 2007-2018")
The most positive extreme values can be spotted on years 2011, 2014 and 2016. The most negative extreme values, on years 2007, 2011, 2012, 2014.
Density plots
dataframe_densityplot(dj_vol_df, "DJIA daily volume density plots 2007-2018")
Shapiro Tests
dataframe_shapirotest(dj_vol_df)## result
## 2007 3.695053e-09
## 2008 6.160136e-07
## 2009 2.083475e-04
## 2010 1.500060e-03
## 2011 3.434415e-18
## 2012 8.417627e-12
## 2013 1.165184e-10
## 2014 1.954662e-16
## 2015 5.261037e-11
## 2016 7.144940e-11
## 2017 1.551041e-08
## 2018 3.069196e-09Based on reported p-values, for all we can reject the null hypothesis of normal distribution.
QQ plots
dataframe_qqplot(dj_vol_df, "DJIA daily volume QQ plots 2007-2018")
Departure from normality can be spotted for all reported years.
Saving the current enviroment for further analysis.
save.image(file='DowEnvironment.RData')References
[1] Dow Jones Industrial Average [https://en.wikipedia.org/wiki/Dow_Jones_Industrial_Average]
[2] Skewness [https://en.wikipedia.org/wiki/Skewness]
[3] Kurtosis [https://en.wikipedia.org/wiki/Kurtosis]
[4] An introduction to analysis of financial data with R, Wiley, Ruey S. Tsay [https://www.wiley.com/en-us/An+Introduction+to+Analysis+of+Financial+Data+with+R-p-9780470890813]
[5] Time series analysis and its applications, Springer ed., R.H. Shumway, D.S. Stoffer [https://www.springer.com/gp/book/9783319524511]
[6] Applied Econometric Time Series, Wiley, W. Enders, 4th ed. [https://www.wiley.com/en-us/Applied+Econometric+Time+Series%2C+4th+Edition-p-9781118808566]
[7] Forecasting - Principle and Practice, Texts, R.J. Hyndman [https://otexts.org/fpp2/]
[8] Options, Futures and other Derivatives, Pearson ed., J.C. Hull[https://www.pearson.com/us/higher-education/product/Hull-Options-Futures-and-Other-Derivatives-9th-Edition/9780133456318.html]
[9] An introduction to rugarch package [https://cran.r-project.org/web/packages/rugarch/vignettes/Introduction_to_the_rugarch_package.pdf]
Disclaimer
Any securities or databases referred in this post are solely for illustration purposes, and under no regard should the findings presented here be interpreted as investment advice or a promotion of any particular security or source.
