1. Time series econometrics is concerns with the estimation of difference equations containing stochastic components[1]. A day to day change in the price of a stock can be tested for the random walk hypothesis.
   1. (+2.5pts.) Write down a stochastic difference equation that shows how the day to day price of a stock should evolve.

2. (+2.5pts.) If you assume that the error term in your previous equation is a white noise, what do you know about its expected value, its variance, and covariance?

3. (+2.5pts.)Provide a more general stochastic difference equation for Dy_t (Hint: Using y_t-1and error term)

4. (+2.5pts.)Based on the equation above what would be they null hypothesis you would set up for the random walk hypothesis?

[1]In its most general form, a difference equation expresses the value of a variable as function its own lagged values, time, and other variables.

2. (+2 pts.) What are the necessary conditions for weakly stationary time series?