flashier_stocks
Matthew Stephens
2021-05-22
Last updated: 2021-05-22
Checks: 7 0
Knit directory: misc/analysis/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 083b740 | Matthew Stephens | 2021-05-22 | ../data/prices.csv |
Introduction
In preparing homework for my class I ran flashier on some stock data. (Note that flash errored out here, and in any case flashier was quite a bit faster…) It got me thinking about appropriate application of flash/flashier for time series, so I’m reporting the results here.
The data were downloaded as in https://stephens999.github.io/stat34800/stocks.html We probably could do with looking at a bigger dataset if we want to take this seriously, but I do that for now.
# AAPL: Apple
# NFLX: Netflix
# AMZN: Amazon
# MMM: 3M
# K: Kellogs
# O: Realty Income Corp
# NSRGY: Nestle
# LDSVF: Lindt
# JPM: JP Morgan Chase
# JNJ: Johnson and Johnson
# TSLA: Tesla
# V: Visa
# PFE: Pfizerprices = read.csv("../data/prices.csv")
log_prices = log(prices)
log_returns = apply(log_prices,2, diff)You can see some structure in the correlation matrix: the tech companys are correlated, as are the PFE/JNJ and the financial companies (V,JPM).
S = cor(log_returns)
heatmap(S, xlab = names(prices), symm=TRUE)
Flashier on the raw data
Note I use column-specific variances. I found backfitting really increases the sparsity in this case (particularly in the time dimension).
#library("flashr")
library("ebnm")
library("flashier")
#fit.f = flashr::flash(as.matrix(log_prices),ebnm_fn = "ebnm_pl") ## errors out
fit.f = flashier::flash(as.matrix(log_prices),prior.family = prior.point.laplace(), var.type = 2, backfit = TRUE)Adding factor 1 to flash object...
Adding factor 2 to flash object...
Adding factor 3 to flash object...
Adding factor 4 to flash object...
Adding factor 5 to flash object...
Adding factor 6 to flash object...
Adding factor 7 to flash object...
Adding factor 8 to flash object...
Adding factor 9 to flash object...
Factor doesn't significantly increase objective and won't be added.
Wrapping up...
Done.
Backfitting 8 factors (tolerance: 5.17e-04)...
Difference between iterations is within 1.0e+03...
Difference between iterations is within 1.0e+02...
Difference between iterations is within 1.0e+01...
Difference between iterations is within 1.0e+00...
Difference between iterations is within 1.0e-01...
Difference between iterations is within 1.0e-02...
Difference between iterations is within 1.0e-03...
Wrapping up...
Done.
Nullchecking 8 factors...
Done.Plot the factors. Note that factor 1 is just a trend and factor 2 looks kind of like a sine wave…. is this just an artifact of looking at time series data? This result does maybe suggest that the data are auto-correlated along the time series.
for(i in 1:8){
barplot(fit.f$loadings.pm[[2]][,i], names.arg=names(prices), horiz=TRUE,las=2, main=paste0("Factor ",i))
}
for(i in 1:8){
plot(fit.f$loadings.pm[[1]][,i], main=paste0("Factor ",i))
}
JNJ issue, and residual variance
I was curious when I noticed that JNJ does not seem to belong to any factors except the first! In fact the first factor seems to be exactly JNJs log returns. It is overfitting and giving a very small residual variance for that stock…
fit.f$residuals.sd AAPL NFLX AMZN MMM K O
0.0884707914 0.1118814445 0.1212804169 0.0192397656 0.0567952716 0.0754391674
NSRGY LDSVF JPM JNJ TSLA V
0.0465249352 0.0689714652 0.0878101048 0.0004986196 0.0949300537 0.0393732055
PFE
0.0577105742 plot(fit.f$loadings.pm[[1]][,1],log_prices[,10], main="factor 1 vs JNJ log-returns")
Here I try using no column-specific variance to avoid that overfitting. I think this is a better idea. Now the first 3 factors kind of all look like the fourier components….
fit.f2 = flashier::flash(as.matrix(log_prices),prior.family = prior.point.laplace(), var.type = 0, backfit = TRUE)Adding factor 1 to flash object...
Adding factor 2 to flash object...
Adding factor 3 to flash object...
Adding factor 4 to flash object...
Adding factor 5 to flash object...
Adding factor 6 to flash object...
Factor doesn't significantly increase objective and won't be added.
Wrapping up...
Done.
Backfitting 5 factors (tolerance: 5.17e-04)...
Difference between iterations is within 1.0e+03...
Difference between iterations is within 1.0e+02...
Difference between iterations is within 1.0e+01...
Difference between iterations is within 1.0e+00...
Difference between iterations is within 1.0e-01...
Difference between iterations is within 1.0e-02...
Difference between iterations is within 1.0e-03...
Wrapping up...
Done.
Nullchecking 5 factors...
Done.fit.f2$residuals.sd[1] 0.08518904for(i in 1:5){
barplot(fit.f2$loadings.pm[[2]][,i], names.arg=names(prices), horiz=TRUE,las=2, main=paste0("Factor ",i))
}
for(i in 1:5){
plot(fit.f2$loadings.pm[[1]][,i], main=paste0("Factor ",i))
}
Flashier on the correlation matrix
Try factor analysis on the correlation matrix. I found it interesting that in the raw data analysis LDSVF was loaded on the first factor, but not in the correlation analysis, which I guess is because the correlation removes some of the overall mean effect and LDSVF is almost independent of others after that is removed?
Also, I feel like the raw correlation matrix shows some additional structure that is likely to be real – eg PFE and JNJ correlation – that is not picked out here….but maybe that is naive on my part.
Smiss = S
diag(Smiss) <- NA
S.f = flashier::flash(Smiss,prior.family = prior.point.laplace(), var.type = 0)Adding factor 1 to flash object...
Adding factor 2 to flash object...
Adding factor 3 to flash object...
Factor doesn't significantly increase objective and won't be added.
Wrapping up...
Done.
Nullchecking 2 factors...
Done.for(i in 1:2){
barplot(S.f$loadings.pm[[2]][,i], names.arg=names(prices), horiz=TRUE,las=2, main=paste0("Factor ",i))
}
Flashier on the standardized raw data
I was kind of surprised no factor picked out the JNJ/PFE correlation, so I tried rerunning on the standardized raw data. It still did not pick that out as a separate factor, but maybe it is naive to think things would be as simple as that.
fit.f3 = flashier::flash(scale(log_prices),prior.family = prior.point.laplace(), var.type = 0, backfit = TRUE)Adding factor 1 to flash object...
Adding factor 2 to flash object...
Adding factor 3 to flash object...
Adding factor 4 to flash object...
Adding factor 5 to flash object...
Adding factor 6 to flash object...
Adding factor 7 to flash object...
Adding factor 8 to flash object...
Factor doesn't significantly increase objective and won't be added.
Wrapping up...
Done.
Backfitting 7 factors (tolerance: 5.17e-04)...
Difference between iterations is within 1.0e+03...
Difference between iterations is within 1.0e+02...
Difference between iterations is within 1.0e+01...
Difference between iterations is within 1.0e+00...
Difference between iterations is within 1.0e-01...
Difference between iterations is within 1.0e-02...
Difference between iterations is within 1.0e-03...
Wrapping up...
Done.
Nullchecking 7 factors...
Done.for(i in 1:7){
barplot(fit.f3$loadings.pm[[2]][,i], names.arg=names(prices), horiz=TRUE,las=2, main=paste0("Factor ",i))
}
for(i in 1:7){
plot(fit.f3$loadings.pm[[1]][,i], main=paste0("Factor ",i))
}
Wavelet transformed data
Since these are time series it would be nice to try wavelet transforming them before applying flashier. Here I explore some of these ideas.
First define haar transform functions
haar = function(x,scale= sqrt(2)){
if(length(x)==1){
return(x)
}
else{
x = matrix(x,nrow=2)
diff = (x[1,]-x[2,])/scale
sum = (x[1,]+x[2,])/scale
return(c(diff, haar(sum)))
}
}
haar_inv = function(x,scale=sqrt(2)){
n=length(x)
if(n==1){
return(x)
}
x = matrix(scale*x,nrow=2,byrow=TRUE)
smoothed = haar_inv(x[2,])
return(as.vector(rbind(smoothed+x[1,], smoothed-x[1,]))/2)
}Now I plot the above fitted factors after haar transform. As expected they are sparser in that basis.
for(i in 1:7){
plot(haar(fit.f3$loadings.pm[[1]][1:2048,i]), main=paste0("Factor ",i, " (transformed space)"))
}
Compute the haar transform of log returns:
lp.h = log_returns[1:2048,]
# do haar wavelet decomposition on log-returns and save in lp.h
for(i in 1:ncol(log_prices)){
lp.h[,i] = haar(log_returns[1:2048,i])
}Quick look at correlations of the transformed data.
S.h = cor(lp.h)
heatmap(S.h, xlab = names(prices), symm=TRUE)
Maybe it makes sense just to do the higher scales?
low_res = 2048-(0:255)
S.h = cor(lp.h[low_res,])
heatmap(S.h, xlab = names(prices), symm=TRUE)
I’m not quite sure of the right way to proceed here… I’m just going to apply flash to the wavelet transformed data, even though that does not really seem quite right (the iid prior on wavelet coefficients at different scales does not really seem sensible.)
lp.h.f = flashier::flash(lp.h)Adding factor 1 to flash object...
Adding factor 2 to flash object...
Adding factor 3 to flash object...
Adding factor 4 to flash object...
Adding factor 5 to flash object...
Adding factor 6 to flash object...
Adding factor 7 to flash object...
Adding factor 8 to flash object...
Adding factor 9 to flash object...
Factor doesn't significantly increase objective and won't be added.
Wrapping up...
Done.
Nullchecking 8 factors...
Done.for(i in 1:8){
barplot(lp.h.f$loadings.pm[[2]][,i], names.arg=names(prices), horiz=TRUE,las=2, main=paste0("Factor ",i))
}
for(i in 1:8){
plot(lp.h.f$loadings.pm[[1]][,i], main=paste0("Factor ",i," (transformed space)"))
}
for(i in 1:8){
plot(haar_inv(lp.h.f$loadings.pm[[1]][,i]), main=paste0("Factor ",i),type="l")
}
Well this certainly made a difference: the first factors are no longer the time series type trends etc….Also they are not very spatially smooth. We may need to work on that.
sessionInfo()R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS 10.16
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] flashier_0.2.7 ebnm_0.1-24
loaded via a namespace (and not attached):
[1] Rcpp_1.0.6 pillar_1.4.6 compiler_3.6.0 later_1.1.0.1
[5] git2r_0.27.1 workflowr_1.6.2 tools_3.6.0 digest_0.6.27
[9] evaluate_0.14 lifecycle_1.0.0 tibble_3.0.4 lattice_0.20-41
[13] pkgconfig_2.0.3 rlang_0.4.10 Matrix_1.2-18 rstudioapi_0.13
[17] parallel_3.6.0 yaml_2.2.1 xfun_0.16 invgamma_1.1
[21] stringr_1.4.0 knitr_1.29 fs_1.5.0 vctrs_0.3.8
[25] rprojroot_1.3-2 grid_3.6.0 glue_1.4.2 R6_2.4.1
[29] rmarkdown_2.3 mixsqp_0.3-43 irlba_2.3.3 ashr_2.2-51
[33] magrittr_1.5 whisker_0.4 backports_1.1.10 promises_1.1.1
[37] ellipsis_0.3.1 htmltools_0.5.0 httpuv_1.5.4 stringi_1.4.6
[41] truncnorm_1.0-8 SQUAREM_2020.3 crayon_1.3.4