Threshold to wake up signal

Question

I have a sketch to put to sleep and wake up an arduino mini pro 5V, but the problem is that sometimes when it is moved fast it wakes up itself, thing that I do not want. I have it configure to be waken up in the pin 2 by a rising signal using an interruption:

#define wakePin 2        // pin used for waking up


void wakeUpNow()        // here the interrupt is handled after wakeup
{
  // execute code here after wake-up before returning to the loop() function
  // timers and code using timers (serial.print and more...) will not work here.
  // we don't really need to execute any special functions here, since we
  // just want the thing to wake up
}

void setup() 
{
  Serial.begin(115200);

  pinMode(RLEDPIN, OUTPUT);
  pinMode(GLEDPIN, OUTPUT);
  pinMode(BLEDPIN, OUTPUT);
  pinMode(wakePin, INPUT);

  attachInterrupt(0, wakeUpNow, RISING );
}

void sleepNow()         // here we put the arduino to sleep
{

    set_sleep_mode(SLEEP_MODE_PWR_DOWN);   // sleep mode is set here

    sleep_enable();          // enables the sleep bit in the mcucr register  // so sleep is possible. just a safety pin

    attachInterrupt(0,wakeUpNow, RISING); // use interrupt 0 (pin 2) and run function  // wakeUpNow when pin 2 gets LOW

    sleep_mode();            // here the device is actually put to sleep!! // THE PROGRAM CONTINUES FROM HERE AFTER WAKING UP

    sleep_disable();         // first thing after waking from sleep: // disable sleep...

    detachInterrupt(0);      // disables interrupt 0 on pin 2 so the // wakeUpNow code will not be executed  // during normal running time.

}


void loop() 
{
    digitalWrite(GLEDPIN, HIGH); //set green led high
    digitalWrite(BLEDPIN, HIGH); //set blue led high
    digitalWrite(RLEDPIN, HIGH); //set red led high

  times = millis();

  if((times-times_f)>=12000)
  {
    times_f=times;
    Serial.println(times-times_f);
    digitalWrite(GLEDPIN, LOW); //Reset the LED's
    digitalWrite(BLEDPIN, LOW);
    digitalWrite(RLEDPIN, LOW);
    sleepNow();
  }
}

I think the problem is that it has a bit of rising signal while moving, so a solution could be to have a threshold in the reception of the signal, can it be done?