Technically, it is Java (a name, rather than a capitalised acronym).

That would probably be best until you get the hang of the groups,
though you seem to be doing that rather quickly.

Close.  Note that you could move all the imports to the top,
demote the second class to 'default' (see code) and compile it
all in the same file.  

Look closely at the comments I put in, they explain further..
<sscce>
import javax.swing.*;
import java.awt.*;
import java.util.*;

public class ProgramSetup
{

   private double temp;
   private Random random;
   private int[] yvalues;
   private int[] xvalues;

   /** For sticking with my original advice, I'll add two
   arrays of arrays. */
   private int[][] shape1;
   private int[][] shape2;

   private int times = 750;

   /** this is actually a sub-class of JPanel. If you declare
   it as an JPanel, Java will assume that only JPanel methods
   are present, rather than the extra ones you defined for
   setShapes() etcetera. */
   // private JPanel primaryPanel;
   private DrawPanel primaryPanel;

   public ProgramSetup()
   {
       makeGUI();
   }

   public void calculate()
   {
       random = new Random();
       xvalues = new int[times];
       yvalues = new int[times];

       shape1 = new int[2][];
       shape1[0] = xvalues;
       shape1[1] = yvalues;

       shape2 = new int[2][];
       shape2[0] = xvalues;
       shape2[1] = yvalues;

       temp = 0;

       for(int j = 0; j != times; j++)
       {
           xvalues[j] = j;
       }

       for(int j = 0; j != times; j++)
       {
               yvalues[j] = (int) (temp - 1 - 5 * random.nextGaussian());
               temp = yvalues[j];

       }

       primaryPanel.setShapes(shape1, shape2);
   }

   public void makeGUI()
   {
       JFrame frame = new JFrame("Graph");
       frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

       primaryPanel = new DrawPanel();

       frame.getContentPane().add(primaryPanel);
       frame.pack();
       frame.setVisible(true);
   }
}

class DrawPanel extends JPanel
{
   private int[] xvalues;
   private int[] yvalues;
   private int times;

   int[][] shape1, shape2;

   public DrawPanel()
   {
       setup();
   }

   /** Note that this method currently accepts two arrays of
   arrays (often referred to as multi-dimensional arrays).
   It might make more sense to hand two single arrays of
   Point objects.  Each Point object possesses an x and y
   attribute. Though that is another story. */
   public void setShapes(int[][] shape1, int[][] shape2)
   {
       this.shape1 = shape1;
       this.shape2 = shape2;
   }

   public void setup()
   {
       setPreferredSize(new Dimension(800,450));
       setBackground(Color.red);
   }

   public void paintComponent(Graphics e)
   {
       super.paintComponent(e);

       e.translate(50,400);

       e.setColor(Color.white);    

       if (xvalues!=null)
       {
           e.drawPolyline(xvalues, yvalues, xvalues.length);
       }
   }
}
</sscce>

HTH