Assume p(t)follows a random walk process.“ What he means is that the price at any time t equals the price at time t - 1, plus a completely random "shock.” The shock is modeled as a random variable with mean zero and a certain variance.
Notice already that this approach has given up on trying to explain how real-world prices are actually formed. In reality, today’s prices have no causal connection with tomorrow’s prices. Every day, the price of a stock is formed afresh by decisions on the part of investors to buy or sell. The stock price today seems to be partially “dependent” on the stock price yesterday only because the underlying factors that caused yesterday’s price are largely the same today. The case of a stock price is completely different from, say, the balance of one’s bank account, which does remain constant from day to day, except for “autoregressive” changes due to interest compounding, or “shocks” due to deposits and withdrawals.
The econometric approach to stock price movements is analogous to a meteorologist who looks for correlations between various measurements of atmospheric conditions. For example, he might find that the temperature on any given day is a very good predictor of the temperature on the following day. But no meteorologist would believe that the reading on the thermometer one day somehow caused the reading the next day; he knows that the correlation is due to the fact that the true causal factors—such as the angle of the earth relative to its orbital plane around the sun—do not change much from one day to the next.
Unfortunately, this distinction between causation and correlation is not stressed in econometrics. Indeed, for economists truly committed to the positive method, there can be no such distinction. Although the econometric pioneers may understand why certain assumptions are made and can offer a priori justifications such as “rational expectations” for the details of a particular model, the students of such pioneers are often caught up in the mathematical technicalities and lose sight of the true causes of economic phenomena.