Time Series Projects: White Noise Process
Updated: April 7, 2006
Jacob: If the time series itself is a white noise process, have we made an error?
Rachel: Some time series are white noise processes.
~ If the time series is the number of earthquakes each year in the U.S., a white noise process is reasonable.
~ If the time series is the number of hurricanes each month in the Gulf Coast or the number of tornadoes in the mid-West, we don’t expect a white noise process, since hurricanes and tornadoes have strong seasonality and possibly long-term cycles.
Jacob: What about interest rates? Might they be a white noise process?
Rachel: Interest rates themselves are not a white noise process. But if interest rates are a random walk, the first differences are a white noise process. Random walks are common in financial and actuarial work, so an ARIMA(0,1,0) model is reasonable.
Jacob: Are the interest rates on the NEAS web site a random walk that should be modeled as ARIMA(0,1,0)?
Rachel: For all eras combined, the interest rates are clearly not ARIMA(0,1,0). In the first era, the drift is positive, and in the third era, the drift is negative. But the interest rates in sub-periods may be a random walk, depending on the time period.
Jacob: If the observed interest rates have a drift, is the process not a random walk?
Rachel: Random walks can have drifts. Stock prices are often presumed to be random walks, but they have strong drifts.
Jacob: Do financial economists assume interest rates are a random walk?
Rachel: That depends on the time period, the country, and the actions of the central bank. One reason we use interest rates for the student project is that they are hard to model.