Statsmodels state space: forecasting using `simulate`

sm_ss_forecast_sim.ipynb

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   "source": [
    "%matplotlib inline\n",
    "\n",
    "from importlib import reload\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from statsmodels.tsa import _ar_model, ar_model_old as ar_old\n",
    "\n",
    "dta = sm.datasets.macrodata.load_pandas().data\n",
    "dta.index = pd.PeriodIndex(start='1959Q1', end='2009Q3', freq='Q')\n",
    "endog = np.log(dta[['realgdp', 'cpi']]).diff(1).iloc[1:]\n",
    "\n",
    "np.set_printoptions(suppress=True, linewidth=120)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod = sm.tsa.VARMAX(endog, order=(1, 0))\n",
    "res = mod.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: forecasting without shocks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     realgdp       cpi\n",
      "0   0.007656  0.009244\n",
      "1   0.007840  0.009464\n",
      "2   0.007863  0.009605\n",
      "3   0.007850  0.009695\n",
      "4   0.007833  0.009754\n",
      "5   0.007820  0.009791\n",
      "6   0.007811  0.009816\n",
      "7   0.007805  0.009831\n",
      "8   0.007801  0.009842\n",
      "9   0.007799  0.009848\n",
      "10  0.007797  0.009853\n",
      "11  0.007796  0.009855\n",
      "\n",
      "fcast_simulate = fcast ?  True\n"
     ]
    }
   ],
   "source": [
    "steps = 12\n",
    "initial_state = res.predicted_state[..., -1]\n",
    "state_shocks = np.zeros((steps, mod.k_states))\n",
    "\n",
    "fcast = res.forecast(steps)\n",
    "fcast_simulate = res.simulate(steps, state_shocks=state_shocks, initial_state=initial_state)\n",
    "\n",
    "print(fcast_simulate)\n",
    "print()\n",
    "print('fcast_simulate = fcast ? ', np.all(fcast.values == fcast_simulate.values))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forecasting with shocks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     realgdp       cpi\n",
      "0   0.007656  0.009244\n",
      "1   0.007840  0.009464\n",
      "2   0.007863  1.009605\n",
      "3   0.867706  0.653800\n",
      "4   0.170115  0.419310\n",
      "5  -0.001913  0.272586\n",
      "6  -0.031876  0.179143\n",
      "7  -0.027582  0.119141\n",
      "8  -0.017911  0.080467\n",
      "9  -0.009651  0.055497\n",
      "10 -0.003726  0.039363\n",
      "11  0.000276  0.028934\n"
     ]
    }
   ],
   "source": [
    "steps = 12\n",
    "initial_state = res.predicted_state[..., -1]\n",
    "state_shocks = np.array([\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "])\n",
    "\n",
    "print(res.simulate(steps, state_shocks=state_shocks, initial_state=initial_state))"
   ]
  }
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