A stock share price is the market price of one traded share, commonly represented by its closing price for a trading interval. Treating prices as a dated time series supports visualization, forecasting, and risk analysis. section 7.2.1 section 7.2.3
A practical price-analysis workflow includes:
- Fetch historical prices, select the Close column, and optionally replace timestamp labels with trading-day indices for clearer charts. section 7.2.1
- Plot closing prices to inspect trends, volatility, support and resistance levels, trading volume, and market sentiment. section 7.2.3
- Forecast future prices with ARIMA or exponential smoothing, then compare predictions with subsequent observed prices. section 7.2.3
- Use Monte Carlo simulation to estimate log-return parameters, generate compounded price paths, and examine a distribution of possible outcomes. section 9.5.1 section 9.5.6
Apple and General Motors
An Apple series from October 2023 through April 2024 began and ended near $173 but reached nearly $198 and fell to about $165, illustrating substantial volatility. A General Motors simulation used July–December 2023 prices to forecast January 2024, producing 500 paths over 20 trading days; 219 ended above the starting price and 281 below it. section 7.2.3 section 9.5.2 section 9.5.8
>>> simulation_df = pd.DataFrame() #1 >>> for i in range(num_simulations): >>> sampled_returns = \ >>> np.random.normal(mu, sigma, num_days) #2 >>> price_list = [last_price_23] #3 >>> for r in sampled_returns: >>> price_list.append(price_list[-1] * \ >>> np.exp(r)) #4 >>> simulation_df[i] = price_list #5
The simulation listing shows how normally sampled daily log returns are compounded from the last observed price into separate future price paths. section 9.5.6
