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    "# Set Specific Lags\n",
    "\n",
    "Example created by Wilson Rocha Lacerda Junior\n",
    "\n",
    "> **Looking for more details on NARMAX models?**\n",
    "> For comprehensive information on models, methods, and a wide range of examples and benchmarks implemented in SysIdentPy, check out our book:\n",
    "> [*Nonlinear System Identification and Forecasting: Theory and Practice With SysIdentPy*](https://sysidentpy.org/book/0%20-%20Preface/)\n",
    ">\n",
    "> This book provides in-depth guidance to support your work with SysIdentPy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different ways to set the maximum lag for input and output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pip install sysidentpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sysidentpy.model_structure_selection import FROLS\n",
    "from sysidentpy.basis_function import Polynomial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting lags using a range of values\n",
    "\n",
    "If you pass int values for *ylag* and *xlag*, the lags are defined as a range from 1-*ylag* and 1-*xlag*. \n",
    "\n",
    "For example: if *ylag=4* then the candidate regressors are $y_{k-1}, y_{k-2}, y_{k-3}, y_{k-4}$"
   ]
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   "source": [
    "basis_function = Polynomial(degree=1)\n",
    "\n",
    "model = FROLS(\n",
    "    order_selection=True,\n",
    "    ylag=4,\n",
    "    xlag=4,\n",
    "    info_criteria=\"aic\",\n",
    "    basis_function=basis_function,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting specific lags using lists\n",
    "\n",
    "If you pass the *ylag* and *xlag* as a list, only the lags related to values in the list will be created.\n",
    "$y_{k-1}, y_{k-4}$,  $x_{k-1}, x_{k-4}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FROLS(\n",
    "    order_selection=True,\n",
    "    ylag=[1, 4],\n",
    "    xlag=[1, 4],\n",
    "    info_criteria=\"aic\",\n",
    "    basis_function=basis_function,\n",
    ")"
   ]
  },
  {
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   "source": [
    "## Setting lags for Multiple Input Single Output (MISO) models\n",
    "\n",
    "The following example shows how to define specific lags for each input. One should notice that we have to use a nested list in that case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The example considers a model with 2 inputs, but you can use the same for any amount of inputs.\n",
    "\n",
    "model = FROLS(\n",
    "    order_selection=True,\n",
    "    ylag=[1, 4],\n",
    "    xlag=[[1, 2, 3, 4], [1, 7]],\n",
    "    info_criteria=\"aic\",\n",
    "    basis_function=basis_function,\n",
    ")\n",
    "# The lags defined are:\n",
    "# x1(k-1), x1(k-2), x(k-3), x(k-4)\n",
    "# x2(k-1), x1(k-7)"
   ]
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