From Modern Fortran by Milan Curcic

Stock price analysis and prediction has been an increasingly popular topic since the early days of high-level programming, and Fortran has been used in the bowels of many financial trading and banking systems, mainly thanks to its robustness, reliability, and efficiency. In this article, we’ll work with a dataset that is freely available, small enough to be easily downloaded, and yet large enough to demonstrate the power of Fortran arrays.


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Part 1: Declaring and initializing arrays for stock price data

I’m no trader and I won’t go into the details of true technical stock market analysis. Therefore I recommend that you don’t use this article as trading advice. Instead, I will merely show you how you can leverage the power of Fortran arrays to perform any kind of time series analysis that you can think of, whether it’s stock or commodity prices, measurements, or signal processing.

Introduction

An array is a sequence of data elements of same type that are also contiguous in memory. While this may at first seem restrictive, it does come with advantages. First, it allows you to write simpler code with expressive one-liners that can work on millions of elements at once. While arrays have been part of Fortran since its birth, whole-array operators and arithmetic have been introduced in Fortran 90, allowing programmers to write cleaner, shorter, and less error-prone code. In a nutshell, arrays allow you to easily work on large datasets and apply functions and arithmetic operators on whole arrays without resorting to loops or other verbose syntax.

In this article, we’ll take a dive into Fortran arrays and learn the mechanics of declaring arrays, allocating them in memory, and using them with familiar arithmetic operators. We’ll do this by writing a small stock price analysis app. You will learn how to declare, allocate and initialize dynamic arrays, read and store data into them, and then perform whole-array arithmetic to quantify stock performance, volatility, and other metrics. Let’s get started by setting some objectives for our application, and looking at the data that we’ll work with.

Objectives

Let’s set some tangible goals for this exercise. We can think of them as challenges.

  1. Find the best and worst performing stocks. We’ll first evaluate which stock grew (or lost value) the most, relative to its starting price. To do this, we’ll need to know the stock price from the start and the end of the time series, and calculate the difference relative to the initial price. In this challenge, you will learn how to declare, allocate, and initialize dynamic arrays, calculate the size of an array, and reference individual array elements.
  2. Identify risky stocks. Some stocks are just riskier than others. This can be quantified by the so-called stock volatility, which is related to the standard deviation of the stock price. Standard deviation is a statistical measure of how much do the values deviate from the average value, and it can be defined over arbitrary time periods. In this challenge, you will learn how to slice arrays and perform whole-array arithmetic.
  3. Identify good times to buy and sell. Traders commonly use a technique called the moving average crossover to decide whether it is a good time to buy or sell a certain stock. The moving average crossover tells us when the stock price crosses the moving average (average over a limited time window), and is an indicator of a change in longer term trend of the stock price, despite the high-frequency fluctuations. In this challenge, you will learn how to search the arrays for specific values and extract elements that meet any criteria that you want.

Before we dive into implementing the solutions to these challenges, let’s first get familiar with the data that we’ll work with.

About the data

We’ll work on daily stock price time series from 10 technology companies, including Apple, Amazon, and Intel. The data is stored in the comma-separated value (CSV) format. Here’s a sample of the Apple stock daily data. Rows are ordered from newest to oldest:

  
 timestamp,open,high,low,close,adjusted_close,volume,dividend_amount,split_coefficient
 2018-05-14,189.0100,189.5300,187.8600,188.1500,188.1500,20364542,0.0000,1.0000
 2018-05-11,189.4900,190.0600,187.4500,188.5900,188.5900,26212221,0.7300,1.0000
 2018-05-10,187.7400,190.3700,187.6500,190.0400,189.3072,27989289,0.0000,1.0000
 2018-05-09,186.5500,187.4000,185.2200,187.3600,186.6376,23211241,0.0000,1.0000
 2018-05-08,184.9900,186.2200,183.6650,186.0500,185.3326,28402777,0.0000,1.0000
 ...
  

The columns in each CSV file are:

  • timestamp: Date in YYYY-mm-dd format.
  • open: Opening price at the start of the trading day.
  • high: Highest price that the stock reached during the trading day.
  • low: Lowest price that the stock reached during the trading day.
  • close: Closing price at the end of the trading day. This reflects the price of the last stock that was traded that day.
  • adjusted_close: Closing price that has been retroactively adjusted for stock splits (see split coefficient below).
  • volume: The total number of shares traded during the day.
  • dividend_amount: The amount of dividend paid per share.
  • split_coefficient: Occasionally, a stock can be split for various reasons, and the split coefficient indicates the factor by which the stock was split. If split_coefficient is 1, the stock was not split. If it is 0.5, the stock price is halved due to the split.

For a birds-eye view of how these stocks performed since 2000, I plotted the adjusted close price against time:


Figure 1: Adjusted close stock prices (USD) of 10 technology companies. The y-axis on each panel has different scale.


Most of the companies had their stock grow in the overall. We can even spot some trends. For example, IBM grew considerably from 2009 to 2012 following the growth of cloud-based technologies and expansion in that area. Nvidia (NVDA) entered a period of explosive growth in early 2016 thanks to the mass adoption of their GPUs for machine learning.

You may be wondering, why use the adjusted close and not just the closing price? Occasionally, a company splits its stock, resulting in a much different closing price than the day before. We could see this in effect in June of 2014 when Apple split its stock sevenfold:

  
 timestamp,open,high,low,close,adjusted_close,volume,dividend_amount,split_coefficient
 2014-06-09,92.7000,93.8800,91.7500,93.7000,87.1866,75414997,0.0000,7.0000
 2014-06-06,649.9000,651.2600,644.4700,645.5700,85.8134,12497800,0.0000,1.0000
  

On June 6, the closing price was $645.57, while on the next trading day, June 9 (exchange markets close on weekends), the opening price was $92.70. Notice that the split coefficient on this day is 7, indicating the factor by which the stock price was divided. If we analyzed long time series of closing prices, we would also capture occasional large increases or drops due to these events that do not reflect the market value of the stock. Adjusted closing price retroactively accounts for all stock splits that occured, and results in price time series that are consistent with actual stock value. It is thus useful when analyzing long-term historical performance of a stock.

Getting the data and code

The full code for the stock analysis exercise is available on Github. If you use git, you can clone it directly from the command line:

  
 git clone https://github.com/modern-fortran/stock-prices
  

Otherwise, you can download it as a zip file.

The repository already includes the stock price data needed for this exercise in the stock-prices/data directory. However, if this exercise leaves you hungry for more in-depth analysis or larger stock price datasets, there’s an easy way to get more.

To download the stock data in CSV format for this exercise, I used the free service Alpha Vantage (https://alphavantage.co) which provides an HTTP API to obtain data in JSON or CSV format. To download your own data beyond that used in this article, you will need to register for the API key at their website. Once you have one, you can make your own API requests to get various stock data. For an example, see the download script that I used to download the daily data for this exercise in stock-prices/data/get_data.sh.

Cloning the repository (or downloading the zip file) will also get you the complete code that implements the 3 data analysis challenges. We’ll implement these step-by-step in the following sections, so if you want to follow along, defer reading the final code until the end of the article.

Finding the best and worst performing stocks

Let’s start from the basics. Before we do any data analysis, we need to take care of the logistics. The following steps will generally apply to each of the three challenges in this exercise:

  1. Define the arrays to hold the data. We’ll learn how to declare dynamic arrays whose size is not known at compile time. In this article, we’ll still rely on core numeric types: real for stock prices and character for time stamps.
  2. Read data from the CSV files. We’ll implement a custom subroutine to read the files and store the data into arrays defined in step 1.
  3. Calculate statistics from raw data. Most of the crunchy stuff described in this article will deal with this step.

For a start, we can estimate the performance of different stocks by calculating their gain over the whole period of the time series data – from January 2000 to May 2018. When we implement the solution to our first challenge, the output of the program will look like this:

  
 2000-01-03 through 2018-05-14
  Symbol, Gain (USD), Relative gain (%)
  -------------------------------------
  AAPL   184.594589            5192
  AMZN   1512.16003            1692
  CRAY   9.60000038              56
  CSCO   1.71649933               4
  HPQ    1.55270004               7
  IBM    60.9193039              73
  INTC   25.8368015              89
  MSFT   59.4120979             154
  NVDA   251.745300            6964
  ORCL   20.3501987              77
  

For each stock, we’ll calculate its gain, that is, the difference between the closing price at the end of the beginning of the time series, and the gain in percent relative to the starting price. The main program (not including the utility functions) looks like this:

  
 program stock_gain
  
   use mod_arrays, only: reverse
   use mod_io, only: read_stock
  
   implicit none
  
   character(len=4), allocatable :: symbols(:)
   character(len=:), allocatable :: time(:)
   real, allocatable :: open(:), high(:), low(:),&
                        close(:), adjclose(:), volume(:)
   integer :: i, im, n
   real :: gain
  
   symbols = ['AAPL', 'AMZN', 'CRAY', 'CSCO', 'HPQ ',&
              'IBM ', 'INTC', 'MSFT', 'NVDA', 'ORCL']
  
   do n = 1, size(symbols)
  
     call read_stock('data/' // trim(symbols(n)) //  '.csv', time,&
       open, high, low, close, adjclose, volume)
  
     adjclose = reverse(adjclose)
     gain = (adjclose(size(adjclose)) - adjclose(1))
  
     if (n == 1) then
       print *, time(size(time)) // ' through ' // time(1)
       print *, 'Symbol, Gain (USD), Relative gain (%)'
       print *, '-------------------------------------'
     end if
  
     print *, symbols(n), gain, nint(gain / adjclose(1) * 100)
  
   end do
  
 end program stock_gain
  

In this program, we first declare the dynamic (allocatable) arrays to hold the list of stock symbols, and time stamps and stock price data for each stock. We then loop over each stock, and read the data from CSV files one at a time. Finally, we calculate the difference between end and start price, and print the results to screen. The following few sections go into details of how dynamic Fortran arrays work, specifically, how to declare them, allocate in memory, initialize their values, and finally clear them from memory when done.

Declaring arrays

The basic way to declare a Fortran array of fixed size is by indicating the size in the parentheses:

  
 real :: u(100) ! declare a real array u with 100 elements
  

When you specify the size of the array at the declaration line, like I did in the snippet above, you tell the compiler to declare a static array. The size of the array is known at compile time, and the compiler can use this information to generate more efficient machine code. Effectively, when you declare a static array, it is allocated in memory when you run the program.

However, you will not always know the size of the arrays ahead of time. It just so happens that each stock data CSV file has the same number of records (4620), but this may not always be the case, as some companies may have much longer presence in the public markets than others. Furthermore, if you choose to later work on a different or larger stock prices dataset, it would be unwieldy to have to hardcode the size of the arrays every time. This is where the dynamic, or in Fortran lingo, allocatable arrays, come in. Whenever the size of the array is not known ahead of time, or, you anticipate that it will change at any time during the life of the program, declare it as allocatable:

  
 real, allocatable :: u(:) ! declare a dynamic array u
  

Writing more general and flexible apps will also require allocating arrays at run-time.

Notice that there are two key changes here relative to declaring a static array. We added the allocatable attribute, and we used the colon (:) as a placeholder for the array size. At this point in the code, we did not allocate this array in memory, but simply stated “We’ll use a real, 1-dimensional array u, whose size is yet to be determined.”

You’re likely wondering when to use dynamic over static arrays? Use dynamic over static arrays whenever you don’t know the size of the arrays ahead of time, or know that it will change. A few examples come to mind:

  • Storing user-input data, entered either by standard input (keyboard) or read from an input file;
  • Reading data from multiple files of different length;
  • Arrays that will be re-used across datasets;
  • Arrays that may grow or shrink during the lifetime of the program.

Dynamic arrays will help you write more general and flexible code, but may carry a performance penalty as allocation of memory is a slow operation compared to, say, floating-point arithmetic.

It does seem that for our use case, we should use dynamic arrays. Following the data description from the previous section, we’ll need:

  • An array of character strings to hold stock symbols (AAPL, AMZN, etc.)
  • An array of character strings to hold the time stamps (2018-05-15, 2018-05-14, etc.)
  • Arrays of real numbers to hold the actual stock data, such as opening and closing prices, and others.

We can apply the dynamic array declaration syntax to declare these arrays:

  
 program stock_gain
  
   implicit none
  
   character(len=4), allocatable :: symbols(:)
   character(len=:), allocatable :: time(:)
   real, allocatable :: open(:), high(:), low(:), close(:),&
                        adjclose(:), volume(:)
  
 end program stock_gain
  

Notice that for symbols I declared an array of character strings of length, while for the time array I didn’t specify the length ahead of time (len=:). This is because we’ll determine the length of timestamps in the subroutine that is in charge of reading the data files, and we don’t need to hardcode the length here. For the rest of the data, I declared real (floating point) arrays. Even though the volume is an integer quantity (number of shares traded), real will work just fine for typical volume values and will help simplify the code. You can compile and run this program, but it won’t do anything useful at this point since it only declares the arrays that we’ll use. To loop over stock symbols and print each to screen, we’ll use an array constructor to initialize the array symbols.

Array constructors

Let’s begin with a modest first step – initializing the stock symbols that we’ll work on. When we properly initialize the stock symbols, loop over them and print each to screen, the output will look like this:

  
  Working on AAPL
  Working on AMZN
  Working on CRAY
  Working on CSCO
  Working on HPQ
  Working on IBM
  Working on INTC
  Working on MSFT
  Working on NVDA
  Working on ORCL
  

As you can imagine, specific symbols depend on what data we have. Since in this exercise we’ll work with only 10 stocks, we can type these directly in code:

  
 program stock_gain
   ...
   integer :: n
  
   symbols = ['AAPL', 'AMZN', 'CRAY', 'CSCO', 'HPQ ',&
              'IBM ', 'INTC', 'MSFT', 'NVDA', 'ORCL']
  
   do n = 1, size(symbols)
     write(*,*) 'Working on ' // symbols(n)
   end do
  
 end program stock_gain
  

Here for the first time I invoke the intrinsic function size, which returns an integer size of an input array, in this case 10. I will show you how size works in more details a bit later in this article.

I also introduce a new syntax element, the so-called array constructor, to assign stock symbols to the symbols array. Array constructors allow you to create arrays on the fly and assign them to array variables:

  
 integer :: a(5) = [1, 2, 3, 4, 5]
  

In the example above, I used the square brackets to enclose a sequence of five integers. Together, this syntax forms a literal constant array that is then assigned to a. For static arrays, the size and shape of the array constructor must match the size and shape of the array variable on the left-hand side.

In this above snippet, I initialized a on the declaration line. This makes for an easy and concise declaration and initialization of a small array. However, there’s one exception case in which you’re not allowed to do this: pure procedures. In that case, you have no choice but to declare and initialize on separate statements:

  
 integer :: a(5)
 a = [1, 2, 3, 4, 5]
  

This is no big deal, but you may rightfully ask, why this restriction? It stems from a historical feature of Fortran called implicit save behavior.

 

Implicit save

Adding a save attribute to the declaration statement in a procedure causes the value of the declared variable to be saved between calls. In other words, the procedure would “remember” the value of that saved variable. Now, here’s the twist: If you initialize a variable in the declaration statement, this will implicitly add the save attribute to the declaration. A variable with the save attribute will maintain its value in memory between procedure calls. Since this is a side effect, it can’t be used in pure procedures.

I don’t recommend using the save attribute, or relying on implicit save feature to maintain state between calls. In main programs and modules, it’s harmless and you can safely initialize on declaration. In procedures (if not pure), you can initialize on declaration, but I recommend not exploiting the implicit save behavior as it results in more stateful and bug-prone code.

There is another, more general way of constructing an array. In the trivial example above, I assigned to a an array of 5 elements, and they were easy to type in by hand. However, what if you wanted to assign a hundred or a thousand elements? This is where we can use the so-called implied do-loop constructor:

  
 integer, allocatable :: a(:)
 integer :: i
  
 a = [(i, i = 1, 100)]
  

The above syntax is called an implied do-loop because (i, i = 1, 100) is just syntactic sugar for an explicit do-loop:

  
 do i = 1, 100
   a(i) = i
 end do
  

With an implied do-loop array constructor, you are not restricted to just the loop counter. You can use it to assign array values from arbitrary functions or expressions:

  
 real, allocatable :: a(:)
 integer :: i
 real, parameter :: pi = 3.14159256
  
 a = [(sin(2 * pi * i / 1000), i = 0, 1000)]
  

Here, I used the integer index i to construct an array of sines with arguments that go from 0 to 2π in 1000 steps. However, you don’t have to use the index in the expression, but merely as a way to repeat the same element over and over again. For example, initializing an array of thousand zeros is trivial:

  
 a = [(0, i = 1, 1000)]
  

Finally, Fortran also lets you create empty arrays using [integer ::] or [real ::]. In practice, these could be useful if invoking a generator – a kind of function that adds an element to an array on every call.

 

Combining different numeric types in expressions

Notice that in the above listing I have mixed integer and real variables in a single expression: sin(2 * pi * i / 1000). What is the type of the result then? Integer or real? Fortran follows two simple rules:

  1. The expression is first evaluated to the strongest (most precise) type. For example, multiplying a real with an integer always results in a real, and multiplying a complex number with either real or integer always results in a complex number. Same goes for kinds of different precision – adding a real32 to a real64 results in a real64 value.
  2. If you’re assigning the result of the expression to a variable, its type is automatically promoted (or downgraded!) to the type of the variable.

In this specific example, 2, i, and 1000 are integers, and pi is a real. The whole expression is thus a real number. This is generally known as type coercion.

Reading stock data from files

Now that we have the list of stock symbols that we’ll work on, let’s use this information to load the data from file and store it in our newly declared dynamic arrays. The prototype of our main loop should look like this:

  
 do n = 1, size(symbols)
   call read_stock('data/' // trim(symbols(n)) //  '.csv', time,&
     open, high, low, close, adjclose, volume)
 end do
  

However, we haven’t implemented the read_stock subroutine yet! Based on the calling signature, we should pass the file name as the first argument, an array of times as the second, and 6 real arrays to hold the stock data as the remaining arguments. At this point, we are passing arrays that have not been allocated yet. As we iterate over the stocks, we’ll need to explicitly allocate our arrays before loading the data from files. The declaration of data in our read_stock subroutine prototype may thus look something like this:

  
 subroutine read_stock(filename, time, open, high, low,&
                       close, adjclose, volume)
   character(len=*), intent(in) :: filename
   character(len=:), allocatable, intent(in out) :: time(:)
   real, allocatable, intent(in out) :: open(:), high(:), low(:),&
     close(:), adjclose(:), volume(:)
   ...
 end subroutine read_stock
  

Let’s look at our arguments in this subroutine definition. filename is declared as character(len=*). This is the so-called assumed-length character string. It says, whatever the length of the string is passed to the subroutine, this argument will accept and assume that length. This is useful whenever you want to pass character strings that are of either varying or unpredictable length. time, however, is declared as character(len=:) allocatable array to match the declaration in the calling program. Finally, the arrays to hold the actual stock data are declared as real and allocatable. We’re using intent(in out) for all subroutine arguments, which means that they will be passed back and forth between the main program and the subroutine. Notice also that here we’ve matched the data type and allocatable attributes for the stock data with those declared in the main program.

Summary

In this article, we covered the essentials of declaring and initializing Fortran arrays. Specifically, we focused on the so-called allocatable (dynamic) arrays, whose size and range isn’t known at compile time, and is determined at run time instead. You’ll find yourself to rely on allocatable arrays whenever you need to work with real-world data with records of varying shape and size. Finally, I’ve introduced the concept of array constructors, which is a convenient way of allocating and initializing Fortran arrays at the same time. In Part 2 of this article, we’ll dive into the details of how explicit allocation and deallocation works. This will allow you to specify custom index range for your arrays, as well as use built-in exception handling to make your code more robust and fault-tolerant. We’ll also cover slicing arrays with arbitrary range and stride. We’ll use these techniques to tackle the first stock price analysis challenge – finding the best and worst performing stocks.

If you want to learn more about the book, check it out on liveBook here and see this slide deck.