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Generate a Random Walk

Whereas stock returns are often modeled as white noise, stock prices closely follow a random walk. In other words, today's price is yesterday's price plus some random noise.

You will simulate the price of a stock over time that has a starting price of 100 and every day goes up or down by a random amount. Then, plot the simulated stock price. If you hit the "Run Code" code button multiple times, you'll see several realizations.

This is a part of the course

“Time Series Analysis in Python”

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Exercise instructions

  • Generate 500 random normal "steps" with mean=0 and standard deviation=1 using np.random.normal(), where the argument for the mean is loc and the argument for the standard deviation is scale.
  • Simulate stock prices P:
    • Cumulate the random steps using the numpy .cumsum() method
    • Add 100 to P to get a starting stock price of 100.
  • Plot the simulated random walk

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Generate 500 random steps with mean=0 and standard deviation=1
steps = np.random.normal(loc=___, scale=___, size=___)

# Set first element to 0 so that the first price will be the starting stock price
steps[0]=0

# Simulate stock prices, P with a starting price of 100
P = ___ + np.cumsum(___)

# Plot the simulated stock prices
plt.plot(___)
plt.title("Simulated Random Walk")
plt.show()
Edit and Run Code

This exercise is part of the course

Time Series Analysis in Python

IntermediateSkill Level
4.5+
19 reviews

In this four-hour course, you’ll learn the basics of analyzing time series data in Python.

In this chapter you'll learn about some simple time series models. These include white noise and a random walk.

Exercise 1: Autocorrelation FunctionExercise 2: Taxing Exercise: Compute the ACFExercise 3: Are We Confident This Stock is Mean Reverting?Exercise 4: White NoiseExercise 5: Can't Forecast White NoiseExercise 6: Random WalkExercise 7: Generate a Random Walk
Exercise 8: Get the DriftExercise 9: Are Stock Prices a Random Walk?Exercise 10: How About Stock Returns?Exercise 11: StationarityExercise 12: Is it Stationary?Exercise 13: Seasonal Adjustment During Tax Season

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