How to use ARRAYS in Pine Script V4 to calculate CORRELATION & COVARIANCE

hi traders welcome back my name is
matthew from the art of trading today's
lesson
is going to be covering how to use
arrays in pinescript
we're not going to do anything too
complicated we're just going to
introduce you to the basics but we are
going to create something pretty useful
we're going to create a correlation
meter which is going to determine
exactly how correlated two different
markets are and we're going to achieve
that using arrays so if that sounds like
something you'd be interested in please
stick around hit the like button while
the intro rolls and we'll get started in
a second
so the script we're going to be working
with today does a couple of different
things
the first thing it does is it stores the
past
x amount of price data so in this case
we're going to use candle closes by
default
but you can change that here but we're
going to save the last
20 candle closes on the current market
and on our reference market we're going
to save those values
into two separate arrays and then we are
going to use some inbuilt
pinescript functions to analyze that
data
we're going to get the correlation
between
these two data sets and we're also going
to get the covariance well we need to
get the covariance first
and then we'll use the covariance to
calculate our correlation coefficient
now if all of that sounds like gibberish
to you don't worry
i literally learned most of this stuff
this morning it's not rocket science but
it is quite advanced for
a fool like me i have the equivalent of
math dyslexia
so if i can handle this you should be
able to too
and as we go through the lesson i'm
going to explain all of these concepts
hopefully in a way that makes sense
to you whether you are experienced with
this stuff or a complete beginner
so with all that said let's get started
so right now i have euro yen weekly
chart
up on my trading view charts the script
is drawing these red lines here these
red bars
are the s p 500 closes so if it closes
positive
that means the s p 500 closed higher and
if it closes
negative that means it closed lower and
by closers i mean
percentage gains so each bar on this
indicator box here represents the
percentage
change from the previous bar on the s p
500
but we can change this to whatever we
want so we could we could change this to
aussie yen for example
and now we're comparing the euro yen's
weekly candles to the aussie yen's
weekly candles
and as you can see here we have quite a
high correlation
the closer this black number is to 1 1.0
the more positively correlated these
markets are which just means that if one
market is moving up
then the other market is also likely to
be moving up
and the micro movements might not be the
same but the correlation number here the
correlation coefficient
can give you a rough idea of just how
correlated a market
is and what this would be useful for
there's a few uses you could use this
for
in forex trading the way i would use
this is i would
use it to determine which currency pairs
are likely to be
correlated so that i can manage my risk
accordingly so for example if i'm
trading the euro yen
and i'm long on the euro yen let's say i
have a high probability set up and i'm
aggressive with it i have two or three
percent
of my total capital involved in that
trade
it's probably not a good idea for me to
then open a trade on aussie yen
with the same amount of risk if these
two pairs are highly correlated because
all that means is that if one trade
loses
the other trade is likely to lose as
well and then i'm taking a double hit
for nothing what would be better in that
scenario if i do have two trading
opportunities on two highly correlated
pairs
would be to split my risk so if i have
one position on euro yen
that might be 1.5 percent risk and on
aussie yen i might have 1.5 percent risk
as well that way in the
unlikely or off chance that one of them
wins and one loses
i don't double my loss by taking a large
position on a correlated market
and there are other use cases for this
as well which we'll go into later
but anyway let's get into the code and
i'll explain what we're doing as we go
and if you're already lost don't worry
this should make sense by the end
hopefully this makes sense by the end of
the lesson
i'm going to do my best to explain all
of this stuff in detail
so let's get into the pine editor and
start this lesson just really quickly
before we get into the pine editor
i thought i should probably show you a
visual representation of what an array
is
it's basically just a list of data so
here we have
our values and they can be anything
so we saw that here they can be a float
an integer a boolean a color a string
and they're stored in these little boxes
which correspond
to a array index
so similar to historical operators for
price action like
referencing previous bars you can do the
same thing with arrays
now dealing with them in partnership is
slightly different to using the
historical operator
which if you're not sure what that is
that's the square brackets
to reference previous bars so you could
reference the previous closing price
like this you could also reference the
value corresponding with the array index
of one it's the same concept in theory
and arrays in partscript have a maximum
size of 100 000
data values which is quite large i don't
think there's many cases where you would
need to exceed that many
data entries into an array so that's
what an array is in pinescript just
think of it as a data set
with each uh entry corresponding to
a array index which starts at 0
and counts up from there in increments
of one and so in this particular case we
have
nine values an array length of nine
but the array index for the final entry
in this array
is eight because we do start at zero so
keep that in mind that takes a little
bit of practice
to get used to if you're not used to
dealing with arrays anyway let's jump
over to the pine editor and get into
this script first thing i'm going to do
is delete all of this code
and we're going to start from scratch so
that you can follow along
and see what i'm doing and i'll explain
what i'm doing
line by line all right so first things
first we just have a blank script here
we just have our study annotation
function you can call this title
whatever you want
i've set overlay to false because i want
to be drawing into my own oscillator box
or indicator box
and the first thing i'm going to do here
is always is get some user input
i'm just going to copy this code over
here because
hopefully by now if you've followed
enough of my lessons you should know how
getting user input works we're getting
three user inputs here we're getting a
look back period
our price source and our reference
market
so we're using the inbuilt in input
function just titling them
accordingly so the user knows what they
correspond to
and i'm setting the types our lookback
is going to be an integer this is how
many bars to look back
our source is a price source which can
be anything if i
minimize this and open this up here is
our price sources
and you can also choose from price
sources on indicators or markets that
you've
added to your chart so if we wanted to
we could calculate
all of this data based on an average of
the open the high the low and the close
or just the high the low and the close
for today's lesson i'm sticking i'm
keeping it simple i'm sticking with
close
and then the final input we're getting
is our reference market that's just the
type of input dot string
and this default value here if you've
never used the security function to
reference other markets other than the
one that you've loaded onto your chart
the format of this is you can either
just put in the string i could have just
put in spx 500 usd here
and that would reference that market
that ticker id this is the ticker id
but i like to also specify which
brokerage or exchange
i want to get that data from so in this
particular case
we're referencing the oanda exchange i'm
using the
semicolon to then reference the ticker
id
so this is the broker or exchange this
is the market
i want to reference and this works with
any
exchange if you go up into here and we
type in apple for example
you could write nasdaq apple so i could
change that to nasdaq and apple if i
wanted to
and then this would reference apple's
price from the nasdaq exchange
so that's it for our user inputs so the
first thing we need to do before we
continue is get the percentage
change of our reference data
so the way we do that i'm going to
create a variable here that
references the security function and the
security function takes a minimum
of three parameters or arguments
we need to specify the symbol we want to
reference
we need to specify the resolution or
time frame we want to reference
and we need to give it an expression
that we want to reference
so this could be anything this could be
an indicator expression
this could be any number of
code expressions that you could use in
pinescript
but for today's lesson we're going to be
keeping it really simple and we're just
going to be referencing
the source input so by default this is
going to be the closing price
so our symbol is going to be our
reference input
and our resolution is going to be our
time frame
dot period so that's whatever time frame
we've currently set
our chart to so right now i'm on the
weekly chart this would just
reference the weekly chart on our
reference market
so hopefully that makes sense so now
just to make sure that we're getting
the right data here let's plot our
reference data
to the chart say the script make sure
there's no compile errors
and there we go everything's working
fine if i go to spx 500 us dollar
this blue line should mimic the closing
price of this chart
i'll get rid of that don't need that so
um
it's on percentage right now three nine
three five
and three nine three five perfect so
so far so good and get rid of that plot
so the next thing we need to do
is get the percentage change of
the current bar on our reference market
compared to the previous bar
so to do that i'm going to create a new
variable called reference
change that is going to be set to i'm
going to open two
parentheses here i'm going to say
reference data
subtracted from our previous
bars reference data divided by our
previous
reference close multiplied by 100
this line of code here this expression
will give us
our reference markets change as a
percentage
so now if i plot this to the chart
reference change save the script oops
and i have a typo here
hopefully that's the only one there we
go minimize that
so now this blue line here is printing
the percentage change so up here you can
see that the current bar has a plus
0.84 percent change from the previous
bar and down here we have
0.8 or positive 0.8 so we are
calculating an accurate reading so
that's how we get the percentage
change in price next thing we need to do
is get the percentage change of our
current market
so to do that i'm going to create a new
variable called current data and this is
going to be set to our source
input so we want to compare the same
source
across our reference market and our
current market so if you were to change
this
default value to something like
ohlc 4 or open high low close
then it will compare the average of our
open high low close on our reference
market
to the average of our open high low
close on the current market
and again to get our percentage we can
pretty much copy this
line of code here i'm going to change
this to current
change copy current data we can paste
that across there
and now we're getting the exact same
percentage
change calculation but on the current
market instead of our reference
market so now we have our two value data
sets
all that's left to do is input these
into an array
and then once we have some data to work
with we can start calculating
our correlation coefficient so now we
have our two data sets we're getting our
reference markets change and our current
markets change all that's left to do is
input this data into two different
arrays
and then we can use those arrays to
perform some
statistical calculations so to declare
an array
it's extremely simple i'm just going to
comment this here
we're going to use the var operator and
if you're unfamiliar with the var
operator all that does
is it makes sure that this variable
we're about to declare does not get
reset on each new bar
it's only declared once on the very
first bar on our chart
as opposed to these variables here which
are not var variables
and these get recalculated on every new
bar on our chart
but since we're using arrays the whole
purpose of arrays
is to store data across all of the bars
on our charts so that we can perform
calculations
and analyze that data so if we don't
create these as var
arrays then these arrays will be cleared
and reset on every new bar in our chart
we don't want that so we use the var
operator to make sure that doesn't
happen and we're going to create two
arrays here
one's going to be called reference array
and the other other one
i'm going to call current array so
reference array
is an array or a list of our reference
markets
change in percentages and current array
is exactly the same but for the current
market
that we've loaded onto our chart and let
me change this market
so that we have two different data sets
here to work with so to declare an array
you need to use the array inbuilt array
object or um class and this array
operator just contains the list of all
the inbuilt array functions that we can
work with
in pine script so arrays behave very
similarly in pinescript to
lines and labels so if we were creating
a label here you would
write label dot new or line
dot new but for today we're using arrays
the main difference with arrays is that
there is a number of different
data types that we can reference so you
can make a color array
you can make a float array or decimal
point number array you can make an
integer array or whole number array
you can make a label array a line array
or a string
array today we're only going to be
working with floats
so floats are just any number with a
decimal place
such as a price or a percentage value so
the array
dot new float function if we click
control click
on this name this function name we can
get a rundown
on exactly how this function works this
function
can take either a single input parameter
or function parameter or
two function parameters so one is the
size
of the array if you're unfamiliar with
arrays
think of them like lists with the main
difference being that we need to specify
the length of the list before we start
working with it and
initial value is the initial value of
all array elements so this think of this
as like a default value
for your arrays we're not going to be
using the default value today
we're just going to be using the array
size and for our array size we're going
to reference our lookback
input parameter so i paste look back in
there
by default these two arrays will be
initialized as floating point arrays
with a look back period of 20 or a size
of 20 meaning that these arrays these
two arrays will hold
20 historical price
changes as percentages by default if you
don't change
this variable here in your script
settings then these two arrays will be
initialized with a length of 20
and so these arrays will store the past
20 bar changes as percentages
so because we have an array length of 20
here our look back is set to 20 by
default
so our array length is only 20
data values we need to make sure that
every time we add a new value
to our array we delete a previous value
to make room for it so the way we're
going to approach this
today in this script is we are going to
use a first in
first out approach if you're not sure
what that means there's a little diagram
here that's quite helpful
so we're creating a q version of an
array
you could also create a stack version
today's version is going to be q
so the first value that goes in gets
shifted down until we hit our array size
in this case will be 20. so when we have
20 values
in our array the first value that
entered this array
will be the first one to be deleted and
so we basically cycle through
with a first in first out approach an
alternative method
for using arrays is a last in first out
approach which is like a stack
so think of it like a stack of papers
you stack up a bunch of values
for whatever reason and there are some
cases where you don't want
to remove the very first value you want
to remove the last value that went in
first but for today's lesson we are just
focusing on a q
array so the first variable that goes
into our array is the first one to be
deleted when the array's maximum
capacity is reached
so in order to achieve that we need to
shift or remove
the last or the first entered
value from our arrays which is a
first in first out approach or fifo for
short
and to do that we need to use the array
dot shift
function and then we need to input our
array id
so id stands for our array variable name
so paste that in there that will delete
the very first data value we entered
into our reference array
before we add a new variable into this
array so this will make sense in one
second
because the next thing we're going to do
is
add the current values to
our arrays in order to add a value to an
array
we need to use the push function so the
array.push function you can think of
this as an array.add
function this will add our data value
to the specified array so the array
we're going to add to first is our
reference
array and the data value we're going to
add to this array
is our reference change so our
percentage change for the current bar
and by current bar i mean the current
bar that this script is running on so
this happens to be a historical bar then
that bar's
percentage change will be added to the
array and once our array hits our
maximum capacity
of 20 it will start deleting or removing
the first value that was added like a
queue and will cycle through those
values
as more data is printed to our chart so
i can copy this line of code here
and we can push to our current array
our current change is a percentage so
these four lines of code here handle all
of our array
operations we are first removing the
oldest
data value from our array before we add
any new
data values to our array
give me a second my cat wants to come in
here he doesn't like being locked out of
the office you want to help me
are you going to be annoying huh
this is hunter hunter s thompson if
anyone's wondering
what his name is there you go entertain
yourself for a bit
so now that we've set up our array
commands or functions
the next thing we need to do is
determine and plot
our covariance relationship so
covariance
i found a pretty good definition here on
investopedia
so first what is covariance
covariance measures the directional
relationship
between the returns on two assets a
positive
covariance means that asset returns move
together
while a negative covariance means they
move inversely or apart
covariance is calculated by analyzing at
return surprises or standard deviations
from the expected return or by
multiplying the correlation between the
two variables by the standard deviation
of each variable
now some of you will understand what all
of that means i don't
but the good news is we don't need to
understand this in order to use it in
our script
so let's go back to the pine editor and
determine
our covariance best of all we don't even
need to write the code
ourselves i'm going to create a new
variable here called covariance
and that's going to be set to array dot
co variance so this inbuilt function
will perform all of that calculation for
us
in a single line of code couldn't be
easier which is perfect for
dummies like me that have no idea how to
calculate this stuff
so to get the covariance we need to
reference two arrays
so that we can get the variance between
the two of them so we're going to
input our reference array here and our
current
array and we're done we're getting the
covariance
but before we continue we should
probably plot that data to the chart so
that we can
visually see what's going on so i'm
going to plot our covariance
value i'm going to give it a color of
color dot purple
i'm going to give it a style of plot dot
style
underscore area i'm going to give it a
transparency of 0
and i'm going to title it our co
variance
so now i'm going to save my script and
make sure everything compiles
and there we go working perfectly so as
you can see
throughout this period here which was
the peak of the covert
pandemic outbreak so if we have a quick
look
if we look at the 16th
of march on gold and we go over to the s
p 500 and look at the
16th of march from there you can see
that
since that day both these markets
have moved higher so
during this period we had a high a
positive covariance
or a directional correlation so these
markets were moving in sync
but that's not always the case there are
occasions when
we have a negative covariance and that
means that these markets
are moving in opposite directions so
anyway
our script is working as we wanted to so
let's finish writing our code and then
we'll go and look over a few different
covariance and correlation examples over
various markets
so before we calculate the correlation
coefficient
between these two data sets let's plot
our reference
market data to the chart just for visual
representation
so here i'm going to say plot our
reference data
we're going to use two plot functions
here one is going to plot our reference
change the other is going to plot our
current markets change and then we're
going to set the color of our reference
market to red our style to plot
dot style columns we're going to set
transparency to 10
i'm going to give this a title of
reference market
and then for our current markets price
change we're going to set the color to
blue
we're going to set the style to plot dot
style
histogram we're going to set the line
width to 4
and then i'm going to title this one our
current
market so now if i save the script we
should get a little bit of a different
visual representation
on the chart so the red bars here is our
reference markets percentage change
so each bar on our chart this red bar is
representing
our reference mark of the s p 500 its
percentage change on that same bar
and the blue number here is the
percentage
change of the current bar so you can see
here we had a 0.73 percent change on the
current bar
that corresponds to the same number up
here
so far so good let's wrap up this script
by calculating
our correlation coefficient before i do
that i should probably explain what that
is
so here we are back on investopedia i'll
leave these links in the video
description
and here's a short summary definition of
correlation coefficient the correlation
coefficient is a statistical measure
of the strength of the relationship
between the relative movements of two
variables
or two markets the coefficient values
range between
negative one and positive one if they
fall outside that range then there's
been an error
in the calculation so correlation of
negative one shows a perfect
negative correlation meaning that for
every dollar a market goes up
the other market goes down a dollar and
a correlation coefficient
of positive one shows a perfect positive
correlation
meaning that for every dollar a market
goes up the reference market
also goes up a dollar and finally a
correlation of zero
means there is no correlation no direct
correlation between the two
markets or two variable data sets so
ideally in your portfolio
depending how you've set it up you would
hedge your positions by
trading a market with a negative
correlation to whatever market you're
investing in and from a trading
perspective if you
are creating a trading strategy across a
portfolio of different markets
ideally you'd want a correlation as
close to zero as possible
because if you have a high correlation
between two markets that you're trading
uh it's the equivalent of doubling your
risk and obviously you can double your
reward that way as well but
it's just magnifying your trading
results if you can find two markets that
have
zero correlation or as close to zero as
possible
that's a good deal as far as portfolio
theory goes
or in other words the closer to zero
your correlation coefficient
is across all the markets you trade and
invest in
the more diversified your portfolio is
and so for investors your portfolio
might be a
bunch of stocks you want those stocks to
have as little correlation as possible
and for a trader you want your
strategies and the markets you trade
to have as little correlation as
possible at least in a perfect world
with currencies that can be a little bit
difficult which will show at the end of
the lesson
where we finish our script i will show
you the correlation
between several different markets so
before we calculate
our correlation coefficient between
these two arrays
or these two different markets we need
to get a little bit more information
first thing we need to do is determine
the standard
deviation of our two arrays or two data
sets
again just like this inbuilt function
here
pinescript has made this extremely easy
for us we don't need to even know what a
standard deviation is
it probably helps to know but we don't
need to because we can just use the
array.stdev
function which will get that value for
us so for our reference
market i'm going to create a new
variable called reference dev
short for deviation and we're going to
pass
our reference array into this standard
deviation
function and this line of code will get
our standard deviation
for our reference market copy this line
of code
change this to current deviation
and paste that in there change this to
current
array now we're getting the
standard deviation of our reference
market and our current markets data set
now that we have that information we can
calculate our correlation coefficient
which is
extremely easy there's no inbuilt
function for this as far as i know for
buying script
but it's easy enough to calculate all we
need to do is divide our covariance
by our reference deviation multiplied
by our current deviation that's it
this formula here will give us our
correlation ranging between negative one
and positive one so to prove that is the
case let's plot this
to the chart we're going to plot our
correlation
value to the chart it's going to have a
color of color dot black
a line width of two and a style of plot
dot um i'm gonna use a step line
for this just for something different
you could use plot this as anything you
want
but i'm trying to keep this varied here
and show you
multiple different ways to plot this
data to your chart
while we're at it and then finally i'm
going to title this our
correlation strength so this is the
strength of the correlation between the
two markers
oscillating so it's a form of an
oscillator i suppose between
negative one and positive one so that's
it our script is complete if i save the
script
hopefully it compiles without any errors
there we go
and now our black line here is plotting
the correlation coefficient
of these two markets so this number here
this black number
is our correlation coefficient between
the s p 500
and gold on the weekly chart and this
value is being calculated over the past
20 bars on our chart pretty cool pretty
easy
so that's the power of pine script the
concepts that we're working with here
may be very advanced this mathematical
concept may be quite advanced
but to achieve it in panscript couldn't
be simpler
so one last thing before we continue
this was something i did that
i thought was interesting i'm gonna just
paste this in here
i'm just creating three horizontal lines
here h lines
at positive one negative one and zero
if i save the script here i minimize the
editor
and let's just look at this visually
basically the
purple area here is our covariance
there's not a lot we can do with this
information in particular
but we needed to get that information in
order to calculate
our correlation coefficient now this
correlation coefficient
is much more useful than the covariance
because we can use this
as a gauge to determine just how
correlated two different markets are
and i'm going to show you exactly what i
mean right now i'm going to come up to
the settings menu
of our correlation meter go to style i'm
going to turn off covariance
and our reference market and current
market so now this black line
represents the correlation between
whichever markets we've set up here
so just to confirm that this is indeed
working
right now we're on the chart for gold
let's change our ticker to silver
and let's just see how correlated gold
is
to silver so now you can see this black
line
hovers very close to one which means
these two markets gold and silver are
extremely correlated
it stays above zero uh almost
indefinitely if we zoom out our chart uh
all the way to the beginning
of price action this market has
maintained extremely high correlation
directional correlation
to silver in layman's terms
that just means when gold goes up silver
goes up when gold goes down
silver goes down when gold goes sideways
silver goes sideways
in practical terms that means that if
you're putting
a lot of risk on gold you do not want to
put a lot of risk
on silver in the same direction because
then you're doubling your risk
essentially and for just a couple more
examples let's check the correlation
between
silver and the s
p 500
click ok uh we'll go to the weekly chart
i feel like the weekly chart shows the
best
representation so again after that
initial
panic sell silver has rallied quite
aggressively to the upside
so did the u.s stock market and so we
had a high
correlation coefficient between those
two markets
let's do something a little bit
different let's try a stock
so here is apple compared to
the s p 500 again during
the panic everything sold off and then
we had this strong rally
during this period we had a high
correlation coefficient
between apple and the s p 500
so hopefully now you're seeing how this
could be quite useful
in your trading process to identify just
exactly how correlated certain markets
are
let's look at one last example before i
wrap this video up let's go to a
currency pair like the euro dollar
and right now you can see that the
correlation between
the us dollar and the s p 500 is all
over the place there is no direct
correlation here
we hover around zero most of the time
but if we were to change our market to
let's say
euro yen now we have a high
positive correlation you can see that
this black line
stays above zero most of the time that
indicates a high positive correlation
let's change this to australian dollar
against the swiss franc
now we have a high negative correlation
so this black line stays below zero most
of the time
that means that often when euro dollar
is selling off
aussie swiss is rallying so there's an
interesting
correlation statistic there that you
would probably not recognize
if it wasn't for this sort of
information being plotted onto your
chart
so that brings me to the end of today's
lesson i hope you found that interesting
this was the most practical example i
could think of to use arrays
for there are obviously many different
ways you can use arrays
you could use them to calculate support
and resistance
zones potentially you could use it to
store
information so for example you could use
it to
store pivots or you know tests of
support
and resistance and you can check if a
certain zone gets tested more than three
times
maybe you can draw a h line across your
chart if
current price action is within an x
amount of percentage
of that zone that's a good example of
a way you could use arrays but there are
many many different use cases for these
most of them are quite obscure
and so i don't think i'll be going into
arrays much more
on youtube if you want to learn a lot
more about arrays and go into more
detail about them
check out pinescriptmastery.com i have a
course there the punch punishment
mastery course
where i'll be going into more detail
about this if and when students request
that
over the months to come as i become more
familiar with arrays myself
well that's it for today's lesson thanks
for sticking around to the end i
appreciate it if you found it valuable
please hit the like button
hit the subscribe button if you haven't
already i'll be back soon with more
lessons
on pinescript and uh yeah that's it for
today
uh good luck with your trading stay away
from exposing yourself
too much on correlated markets and i
will see you in the next one
take care goodbye