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"content": "To plot the given sequence of numbers and extrapolate it using the statsmodels library, you can use the following steps:\n\n1. Install the required libraries: statsmodels and matplotlib (if you haven't done so)\n2. Import the required libraries and functions.\n3. Load the data.\n4. Fit the model using statsmodels' SARIMAX function.\n5. Predict the extrapolated values.\n6. Plot the results.\n\nHere's the code:\n\n```python\n# Step 1: Install libraries (run this line in your command line, not in the Python file)\n# pip install statsmodels matplotlib\n\n# Step 2: Import required libraries and functions\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport statsmodels.api as sm\n\n# Step 3: Load the data\ndata = np.array([2, 3, 15, 14, 9.2, 11, 9, 12.1, 15, 16])\n\n# Step 4: Fit the model (SARIMAX)\n# Order and seasonal_order parameters are (p, d, q) and (P, D, Q, s) respectively, chosen by trial and error\n# Here, we use an ARIMA model with order (1, 0, 0), which means 1 autoregressive, 0 differencing and 0 moving average component\nmodel = sm.tsa.SARIMAX(data, order=(1, 0, 0), seasonal_order=(0, 0, 0, 0))\nresults = model.fit()\n\n# Step 5: Predict the extrapolated values (here, we extrapolate 5 new values)\nextrapolate_steps = 5\npredictions = results.get_prediction(start=len(data), end=len(data) + extrapolate_steps - 1, dynamic=True)\n\n# Step 6: Plot the results\nplt.plot(data, label='Original data')\nplt.plot(np.arange(len(data), len(data) + extrapolate_steps), predictions.predicted_mean, label='Extrapolated data')\nplt.xlabel('Time step')\nplt.ylabel('Value')\nplt.legend()\nplt.show()\n```\n\nThis code will generate a plot showing the original data and the extrapolated data using an ARIMA model from the statsmodels library. Note that you might need to adjust the ARIMA model's order and seasonal_order parameters depending on your specific time series.",
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