Stationary and Nonstationary Time Series
"Anyone who tries to analyse a time series without plotting it first is asking for trouble"
1. A time series is an exampe of what is called a stochastic process, which is a sequence of random variables ordered in time
2. A time series is said to stationary if its mean and variance are constant over time and the value of the covariance between two time periods depends only on the distance between the time periods and not the actual time at which the covariance is computed
3. Why should we worry whether a time series is stationary or not ?
Random walk without drift
"Anyone who tries to analyse a time series without plotting it first is asking for trouble"
1. A time series is an exampe of what is called a stochastic process, which is a sequence of random variables ordered in time
2. A time series is said to stationary if its mean and variance are constant over time and the value of the covariance between two time periods depends only on the distance between the time periods and not the actual time at which the covariance is computed
3. Why should we worry whether a time series is stationary or not ?
- If a time series is nonstationary, we can study for the period under consideration. As a result it is not possible to generalize it to other time periods. For forecasting purposes, nonstationary time series will be of little practical value
- If we have two or more nonstationary time series, regression analysis involving such time series may lead to phenomenon of suprious or nonsense regression.
4. Tests of Stationarity
- There are three ways to examine stationarity of a time series (1) graphical analysis (2) correlogram and (3) unit root analysis
- Auto correlation function and correlogram
A plot of
against k, the lag lenght, is called the correlogram
- White noise: Special type of time series namely a purely random or white nosie. Such a time series has constant mean, constant variance and is serially uncorrelated; its mean value is often assumed to be zero.
- Gaussian white noise: The error term in LRM is assumed to be white noise (stochastic) process, which we denote as U ~ IID (0, sigma^2). If U is normally distributed, it is called a Gaussian white noise process
The unit root test of stationarity
where 
that is the first difference of the log of the exchange rate, t is the time or trend variable taking value of 1, 2, till the end of the sample and 
is the error term.
Null hypothesis is that B3 is zero, the coefficient of
The random walk model
Asset prices, such as stock prices and exchanges rates follow a random walk, that is they are nonstationary. We distinguis two types of random walk: (1) random walk without drift (2) random walk with drift
Null hypothesis is that B3 is zero, the coefficient of
The random walk model
Asset prices, such as stock prices and exchanges rates follow a random walk, that is they are nonstationary. We distinguis two types of random walk: (1) random walk without drift (2) random walk with drift
Random walk without drift