Tropical cyclones are among the most destructive natural disasters of the world. The long coastline of peninsular India is frequently affected by cyclonic storms originating in the Bay of Bengal and Arabian Sea resulting in loss of life and property in the affected region. Hence there is a need for prediction and forecasting methods for minimizing the disastrous effects of tropical cyclones. The time series data of the annual cyclonic disturbance records (for the time period 1901 - 2004) over the North Indian Ocean (comprising of Bay of Bengal and Arabian Sea) has been analyzed. It is found that the behavior of the cyclonic intensity exhibits perfect power law behavior. Local changes of scaling exponents are examined. It is found that the calculated scaling exponent is larger than 0.5 indicating that cyclonic disturbance data have long-range correlations.