Each Array dimension uses only one int inside a bracket as its index:
previousCoordinates[3] = mouseX;

If you need to store more than 1 related value, you're gonna need an extra Array to store it.
Also, you need to instantiate an Object before using it with keyword new:

final static int NUM = 1000;
int[] coordsMX = new int[NUM];
int[] coordsMY = new int[NUM];

However, since you dunno how many elements gonna be stored, you'd better off using an ArrayList;
or something similar to it, like an IntList:

final IntList coordsMX = new IntList();
final IntList coordsMY = new IntList();

Processing's references:
http://processing.org/reference/Array.html
http://processing.org/reference/IntList.html

A similar post about it:
// http://forum.processing.org/topic/saving-mouseevent-data-in-an-array

1. // array should be initialized, either here or in setup()
   int [] previousCoordinates = new int[] {0,0};
   void setup() {
     size(500, 500);
   }
2. void draw() {
     background(128);
     if(mousePressed) {
       previousCoordinates = new int [] {mouseX, mouseY};
     }
     for(int i = 0; i < previousCoordinates.length; i++) {
       text(previousCoordinates[i], 10, 14 + 14 * i);
     }
   }

PS. You could use the new in the mouse capture, but why? It is more economical to just re-store the values.

previousCoordinates[0] = mouseX;
previousCoordinates[1] = mouseY;

Even better: There is a data type (class) PVector designed to hold X and Y values which is perfect for mouse coords. This class also has methods to set and add/sub the values, find related angles and magnitudes, rotate, and much more, which is often very helpful dealing with mouse events.

PS You could use the new PVector in the mouse capture, but as before, why? Just use set().

Also, PVector hold floats, not ints. this is necessary to provide the math functions. You can cast to int anytime as shown on the Y value below.

PVector previousCoordinates = new PVector();
void setup() {
  size(500, 500);
}

void draw() {
  background(128);
  if(mousePressed) {
    previousCoordinates.set(mouseX, mouseY);
  }
    text(previousCoordinates.x, 10, 14);
    text((int) previousCoordinates.y, 10, 28);
}

Oops! I haven't paid too much attention of what was being asked.
I was thinking too much ahead as if he was needing some kinda List for mouse coordinates.

It turns out he's just asking for some kinda tuple to store previous mouse coordinates only.
Although for such meager storage, I'd choose 2 int variables for them. It's better speed-wise.

PVector is OK as a container for mouseX & mouseY. A pity it's of float data-type.
Well, here's my custom PVectorI; which stores int in place of float:

/** 
 * Mini PVector Class Storage for Ints (v1.01)
 * by GoToLoop (2013/Aug)
 * 
 * http://forum.processing.org/topic/can-pvector-work-with-doubles
 */

class PVectorI {
  int x, y, z;

  PVectorI(double xx, double yy) {
    set((int) xx, (int) yy);
  }

  PVectorI(double xx, double yy, double zz) {
    set((int) xx, (int) yy, (int) zz);
  }

  PVectorI(PVector p) {
    set(p);
  }

  PVectorI(int[] a) {
    set(a);
  }

  PVectorI(float[] a) {
    set(int(a));
  }

  void clear() {
    x = y = z = 0;
  }

  void set(int xx, int yy) {
    x = xx;
    y = yy;
  }

  void set(int xx, int yy, int zz) {
    x = xx;
    y = yy;
    z = zz;
  }

  void set(PVector p) {
    x = (int) p.x;
    y = (int) p.y;
    z = (int) p.z;
  }

  void set(int[] a) {
    final int len = a.length;

    if (len > 0)  x = a[0];
    if (len > 1)  y = a[1];
    if (len > 2)  z = a[2];
  }

  void set(float[] a) {
    set(int(a));
  }

  PVectorI get() {
    return new PVectorI(x, y, z);
  }

  PVector toPVector() {
    return new PVector(x, y, z);
  }

  int[] toArray() {
    return new int[] {
      x, y, z
    };
  }

  String toString() {
    return "[ " + x + ", " + y + ", " + z + " ]";
  }
}