Random Walk With Drift

As per Investopedia, the random walk theory suggests that stock price changes have the same distribution and are independent of each other, so the past movement or trend of a stock price or market cannot be used to predict its future movement. In short, this is the idea that stocks take a random and unpredictable path.

As for a random walk with drift, the best forecast of tomorrow’s price is today’s price plus a drift term. One could think of the drift as measuring a trend in the price (perhaps reflecting long-term inflation). Given the drift is usually assumed to be constant. Reference

Visual differences between the trend / cycles / types of random walks is nicely shown below:

AT-Stationary1.gif

Source: http://www.investopedia.com/articles/trading/07/stationary.asp

Assuming FBMKLCI has the property of a random walk (with drift), what would be its predictable forecast range?

The following are the key parameters assumed for the random walk with drift forecasting method:

  • Training Set Data Jan 17 – Jul 17
  • Testing Data Aug 17

FBMKLCI.pngIt is observed that the actual data points are within the confidence bands as per the random walk with drift forecasting method:

Actual vs Forecast Table.png

Residual Error

Nevertheless, the random walk with drift method is a very simplistic method of forecasting future prices. I believe that having the confidence bands will assist in ascertaining whether a security is in ‘over-extended’ position. One should also ask oneself whether he or she believes in the random walk theory.

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