{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e56178d9",
   "metadata": {},
   "source": [
    "# Autoregressive Integrated Moving Average (ARIMA) Tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "147712e3",
   "metadata": {},
   "source": [
    "This notebook demonstrates a practical implementation of ARIMA using real-world macroeconomic data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3be53bf9",
   "metadata": {},
   "source": [
    "The AutoRegressive Integrated Moving Average (ARIMA) model is one of the most widely used approaches in time-series forecasting. In a nutshell, ARIMA forecasts a time-series' future values based on past values and past forecast errors. As shown by its name, ARIMA consists of three main components:\n",
    "- AR (AutoRegressive): the model uses past values to predict the current value\n",
    "- I (Integrated): the series is differenced $d$ times to achieve stationarity\n",
    "- MA: it represents the moving average components (past errors), indicating that the forecast error is a linear combination of past respective errors.\n",
    "In mathematical terms, the ARIMA(p,d,q) model can be written as:\n",
    "\n",
    "$$\n",
    "\\Delta^d y_t = c + \\sum_{i=1}^{p} \\phi_i \\Delta^d y_{t-i} + \\sum_{j=1}^{q} \\theta_j \\epsilon_{t-j} + \\epsilon_t\n",
    "$$\n",
    "\n",
    "where:\n",
    "\n",
    "- $y_t$: value of the time series at time $t$\n",
    "- $\\Delta^d$: differencing operator applied $d$ times\n",
    "- $\\phi_i$: autoregressive coefficients\n",
    "- $\\theta_j$: moving average coefficients\n",
    "- $\\epsilon_t$: error term\n",
    "\n",
    "As the equation highlights, there are three parameters defining ARIMA:\n",
    "\n",
    "- **Autoregressive order (p)**: amount of past data point used to predict the future value\n",
    "- **(Nonseasonal) differencing order (d)**: Differencing order of the target. Stationarity tests help understanding whether a first or a second differencing is needed.\n",
    "- **Order of the moving average (q)**: number of lagged errors in the prediction equations, i.e the moving average window used to forecast future values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4c03b4cd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:50.500933100Z",
     "start_time": "2026-07-24T14:06:45.571520400Z"
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    "execution": {
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "from statsmodels.datasets import macrodata\n",
    "\n",
    "# ACF and PACF\n",
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "\n",
    "# ARIMA\n",
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "\n",
    "# ADF test\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "\n",
    "sns.set_style(\"darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a84a84f9",
   "metadata": {},
   "source": [
    "## Loading the data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bda4754",
   "metadata": {},
   "source": [
    "This tutorial consider the statsmodels macrodata dataset. It collects various macro data recorded quarterly from 1959 to 2009. \n",
    "\n",
    "In details, we consider real GDP (\"realGDP\"), as it is easy to interpret and it is a well-known macrodata.\n",
    "\n",
    "To begin with, we load the data, assign a year+quarter index and perform a short Exploratory Data Analysis (EDA)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "362f555d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:50.553039Z",
     "start_time": "2026-07-24T14:06:50.518304900Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:36.206003Z",
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     "shell.execute_reply": "2026-07-28T19:10:36.226593Z"
    }
   },
   "outputs": [],
   "source": [
    "# load the dataset\n",
    "data = macrodata.load_pandas().data\n",
    "# select the realgdp ts\n",
    "ts = data[[\"year\", \"quarter\", \"realgdp\"]]\n",
    "# build a quarterly period index\n",
    "ts.index = pd.PeriodIndex(\n",
    "    ts[\"year\"].astype(int).astype(str) + \"Q\" + ts[\"quarter\"].astype(int).astype(str),\n",
    "    freq=\"Q\",\n",
    ")\n",
    "ts.index.name = \"quarter\"\n",
    "# drop old columns if needed\n",
    "ts = ts.drop(columns=[\"year\", \"quarter\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "55426e0a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:50.662076100Z",
     "start_time": "2026-07-24T14:06:50.554038900Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:36.232857Z",
     "iopub.status.busy": "2026-07-28T19:10:36.229864Z",
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     "shell.execute_reply": "2026-07-28T19:10:36.251625Z"
    }
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>realgdp</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quarter</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1959Q1</th>\n",
       "      <td>2710.349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1959Q2</th>\n",
       "      <td>2778.801</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          realgdp\n",
       "quarter          \n",
       "1959Q1   2710.349\n",
       "1959Q2   2778.801"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show first 2 rows\n",
    "ts.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d1872242",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:51.179518200Z",
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    "execution": {
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>realgdp</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quarter</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2009Q2</th>\n",
       "      <td>12901.504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009Q3</th>\n",
       "      <td>12990.341</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           realgdp\n",
       "quarter           \n",
       "2009Q2   12901.504\n",
       "2009Q3   12990.341"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show last 2 rows\n",
    "ts.tail(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "70cff48a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:52.202984200Z",
     "start_time": "2026-07-24T14:06:52.149298200Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:36.270849Z",
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     "shell.execute_reply": "2026-07-28T19:10:36.289172Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Real GDP summary statistics:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>realgdp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>203.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>7221.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3214.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2710.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>4440.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6559.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>9629.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>13415.27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        realgdp\n",
       "count    203.00\n",
       "mean    7221.17\n",
       "std     3214.96\n",
       "min     2710.35\n",
       "25%     4440.10\n",
       "50%     6559.59\n",
       "75%     9629.35\n",
       "max    13415.27"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ts summary statistics\n",
    "print(\"Real GDP summary statistics:\")\n",
    "ts.describe().map(\"{:.2f}\".format)  # show it w/ 2 decimals"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "920d543f",
   "metadata": {},
   "source": [
    "The time-series has 203 observation, a median of 6559.59 and an average of 7221.17. Since the median and the average are close, probably there are not outliers in the series.\n",
    "\n",
    "The standard deviation is 3214.9."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "576bee30",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:52.685941800Z",
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   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set the index as timestamp for plotting\n",
    "ts_plot = ts.to_timestamp()\n",
    "# plot ts\n",
    "plt.plot(ts_plot)\n",
    "plt.title(\"Real GDP: quarterly frequence\")\n",
    "plt.xlabel(\"Year\")\n",
    "plt.ylabel(\"Real GDP\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24fe323b",
   "metadata": {},
   "source": [
    "The data is plotted as a time series with years (quarterly frequence) on the x-axis and real GDP on the y-axis.\n",
    "\n",
    "As the chart highlights, there is no clear seasonal pattern and an evident upward trend in real GDP. This suggests the time series is not-stationary, and it needs differencing (of at least order = 1) to become stationary. That is, d is likely to be >= 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0aca6611",
   "metadata": {},
   "source": [
    "## Train-testing splitting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d612e851",
   "metadata": {},
   "source": [
    "In order to assess ARIMA performances and avoid overfitting, we divide data into training and testing sets. In this specific case, 90% of data is used for training. This leaves out around 5 years for validation purposes.\n",
    "\n",
    "As real GDP has time-dependencies, it is crucial to keep data's temporal alignment (*i.e* chronological order) when splitting between train and test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1725a801",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:53.105489800Z",
     "start_time": "2026-07-24T14:06:53.092977500Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:36.594268Z",
     "iopub.status.busy": "2026-07-28T19:10:36.594037Z",
     "iopub.status.idle": "2026-07-28T19:10:36.604748Z",
     "shell.execute_reply": "2026-07-28T19:10:36.599630Z"
    }
   },
   "outputs": [],
   "source": [
    "# define the training %\n",
    "split_index = int(len(ts) * 0.90)\n",
    "# training set\n",
    "train = ts.iloc[:split_index]\n",
    "# validation set\n",
    "val = ts.iloc[split_index:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa0ce43a",
   "metadata": {},
   "source": [
    "## Parameter Definition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d2fff85",
   "metadata": {},
   "source": [
    "ARIMA requires specifying (p,d,q). \n",
    "\n",
    "Augmented Dickey-Fuller (ADF) test, autocorrelation (ACF) and partial autocorrelation (PACF) plots help in determining them. However, the most efficient approach is to set up the simplest ARIMA configuration and eventually adding complexity by trial-and-errors.\n",
    "\n",
    "Let's begin with d. We will difference our time series until it becomes stationary. To test for it, we will employ an Augmented Dickey-Fuller test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7fccb0cd",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:53.159990300Z",
     "start_time": "2026-07-24T14:06:53.108488900Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:36.608215Z",
     "iopub.status.busy": "2026-07-28T19:10:36.607998Z",
     "iopub.status.idle": "2026-07-28T19:10:36.629222Z",
     "shell.execute_reply": "2026-07-28T19:10:36.628509Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF p-value: 0.000000\n"
     ]
    }
   ],
   "source": [
    "# Apply first differencing\n",
    "ts_diff = train.diff().dropna()\n",
    "# ADF test\n",
    "adf_test = adfuller(ts_diff)\n",
    "# show p-values\n",
    "print(f\"ADF p-value: {adf_test[1]:.6f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1eb6d34e",
   "metadata": {},
   "source": [
    "The series becomes stationary by differencing by 1, as the ADF test and the plot remark. Therefore d = 1. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16e0b9b3",
   "metadata": {},
   "source": [
    "Turning to p and q, We now consider the auto-correlation and partial auto-correlation plots to assess p and q maximum values. ACF helps in identifying MA(q), while PACF helps in defining AR(p)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "20a8ae30",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:53.358148500Z",
     "start_time": "2026-07-24T14:06:53.170991700Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:36.631666Z",
     "iopub.status.busy": "2026-07-28T19:10:36.631308Z",
     "iopub.status.idle": "2026-07-28T19:10:36.907006Z",
     "shell.execute_reply": "2026-07-28T19:10:36.906543Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot ACF\n",
    "plt.show(plot_acf(ts_diff, lags=30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "234b51e0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:53.557233500Z",
     "start_time": "2026-07-24T14:06:53.359149200Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:36.910889Z",
     "iopub.status.busy": "2026-07-28T19:10:36.910487Z",
     "iopub.status.idle": "2026-07-28T19:10:37.202049Z",
     "shell.execute_reply": "2026-07-28T19:10:37.201412Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot PACF\n",
    "plt.show(plot_pacf(ts_diff, lags=30))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc4bd86b",
   "metadata": {},
   "source": [
    "Both ACF and PACF show significant spikes at the first few lags, suggesting the presence of a short-term correlation. Altogether, the plots highlighting a time-series with an initial correlation that lose importance after the very first few lags.\n",
    "\n",
    "The maximum AR() order will be defined by the PACF last significant order. On the other hand, the maximum MA() order is determined by ACF last-significant lag.\n",
    "\n",
    "To keep this tutorial straightforward, we will set up the simplest option: an ARIMA(1,1,1) configuration.\n",
    "In practice, model selection is often refined using information criteria such as AIC or BIC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca8e16a3",
   "metadata": {},
   "source": [
    "## Model implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b7b40fd",
   "metadata": {},
   "source": [
    "Once p, d and q are defined, it is time to implement the model.\n",
    "\n",
    "Firstly, we initialize an ARIMA model through the ARIMA() function and specify p, d and q (order) and trend. Adding drift (trend = \"t\") allows the model to capture long-term growth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f48918d1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:53.577225600Z",
     "start_time": "2026-07-24T14:06:53.561234700Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:37.206738Z",
     "iopub.status.busy": "2026-07-28T19:10:37.206518Z",
     "iopub.status.idle": "2026-07-28T19:10:37.217238Z",
     "shell.execute_reply": "2026-07-28T19:10:37.216744Z"
    }
   },
   "outputs": [],
   "source": [
    "# define the model\n",
    "arima = ARIMA(train, order=(1, 1, 1), trend=\"t\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd5b83df",
   "metadata": {},
   "source": [
    "Secondly, the model is trained on the train dataset. This is done through the fit() function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "62e468b9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:53.767067800Z",
     "start_time": "2026-07-24T14:06:53.579225400Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:37.220846Z",
     "iopub.status.busy": "2026-07-28T19:10:37.219028Z",
     "iopub.status.idle": "2026-07-28T19:10:37.512115Z",
     "shell.execute_reply": "2026-07-28T19:10:37.511580Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                               SARIMAX Results                                \n",
      "==============================================================================\n",
      "Dep. Variable:                realgdp   No. Observations:                  182\n",
      "Model:                 ARIMA(1, 1, 1)   Log Likelihood                -964.154\n",
      "Date:                Tue, 28 Jul 2026   AIC                           1936.308\n",
      "Time:                        19:10:37   BIC                           1949.102\n",
      "Sample:                    03-31-1959   HQIC                          1941.495\n",
      "                         - 06-30-2004                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "x1            52.5377      7.754      6.776      0.000      37.341      67.735\n",
      "ar.L1          0.7489      0.102      7.339      0.000       0.549       0.949\n",
      "ma.L1         -0.4723      0.138     -3.426      0.001      -0.742      -0.202\n",
      "sigma2      2475.9130    213.673     11.587      0.000    2057.121    2894.705\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   0.18   Jarque-Bera (JB):                 9.61\n",
      "Prob(Q):                              0.67   Prob(JB):                         0.01\n",
      "Heteroskedasticity (H):               1.99   Skew:                             0.09\n",
      "Prob(H) (two-sided):                  0.01   Kurtosis:                         4.11\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "# fit the ARIMA model\n",
    "arima_fit = arima.fit()\n",
    "# show model summary\n",
    "print(arima_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc0aa6d9",
   "metadata": {},
   "source": [
    "The table summarizes ARIMA estimation.\n",
    "\n",
    "At the top-left, we can see description of both the variable and the model. On the top-right, instead, are displayed metrics to assess performances and used for comparison.\n",
    "\n",
    "In the middle, the table shows variables' coefficent, along with their standard error, z-statistic, p-values and 95% confidence interval. In this specific case, x1 is the constant term (drift), ar.L1 is the autoregressive term and sigma2 is the variance of residuals (i.e error)-\n",
    "\n",
    "At the bottom, several residuals diagnostics tests are presented. These are crucial to evaluate properties as errors autocorrelation, normality and homoskedasticity, allowing to evaluate the overall model's reliability."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a518bb7b",
   "metadata": {},
   "source": [
    "## Forecasting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45db82db",
   "metadata": {},
   "source": [
    "Thirdly, future values are forecasted. This is done thanks to the get_forecast() function. Here, we will predict future GDP values along with its 95% confidence interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d93759f2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:53.804213900Z",
     "start_time": "2026-07-24T14:06:53.770070300Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:37.518217Z",
     "iopub.status.busy": "2026-07-28T19:10:37.518003Z",
     "iopub.status.idle": "2026-07-28T19:10:37.549757Z",
     "shell.execute_reply": "2026-07-28T19:10:37.544558Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Real GDP predictions:\n",
      "-------------------------------------\n",
      "2004Q3    12287.849231\n",
      "2004Q4    12356.483090\n",
      "2005Q1    12421.074946\n",
      "2005Q2    12482.639812\n",
      "2005Q3    12541.937817\n",
      "2005Q4    12599.538206\n",
      "2006Q1    12655.867280\n",
      "2006Q2    12711.244286\n",
      "2006Q3    12765.908304\n",
      "2006Q4    12820.038378\n",
      "2007Q1    12873.768590\n",
      "2007Q2    12927.199352\n",
      "2007Q3    12980.405861\n",
      "2007Q4    13033.444430\n",
      "2008Q1    13086.357231\n",
      "2008Q2    13139.175848\n",
      "2008Q3    13191.923932\n",
      "2008Q4    13244.619194\n",
      "2009Q1    13297.274899\n",
      "2009Q2    13349.900980\n",
      "2009Q3    13402.504877\n",
      "Freq: Q-DEC, Name: predicted_mean, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# predict real GDP values (avg + confidence interval)\n",
    "predictions = arima_fit.get_forecast(steps=len(val))\n",
    "# get point prediction\n",
    "predictions_mean = predictions.predicted_mean\n",
    "# build the confidence interval\n",
    "conf_int = predictions.conf_int()\n",
    "# show prediction\n",
    "print(\"Real GDP predictions:\")\n",
    "print(\"-------------------------------------\")\n",
    "print(predictions_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de7cb848",
   "metadata": {},
   "source": [
    "## Model Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0850ba6c",
   "metadata": {},
   "source": [
    "Finally, it is time to assess model performances by comparing prediction with actual values (the test set) considering both RMSE and predicted-vs-actual plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7eb9fe71",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:53.847109Z",
     "start_time": "2026-07-24T14:06:53.808214400Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:37.554618Z",
     "iopub.status.busy": "2026-07-28T19:10:37.554368Z",
     "iopub.status.idle": "2026-07-28T19:10:37.566717Z",
     "shell.execute_reply": "2026-07-28T19:10:37.565430Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Validation RMSE:\n",
      "----------------\n",
      " 254.661\n"
     ]
    }
   ],
   "source": [
    "# trasform validation into a series\n",
    "val_series = val.squeeze()\n",
    "# compute rmse\n",
    "rmse = np.sqrt(np.mean((val_series - predictions_mean.values) ** 2))\n",
    "# Note: Ensure predictions and actual values are aligned before computing errors\n",
    "# show it\n",
    "print(\"Validation RMSE:\")\n",
    "print(\"----------------\")\n",
    "print(f\"{rmse: .3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e8a3620",
   "metadata": {},
   "source": [
    "The RMSE corresponds to roughly 3.5% of the average GDP level, underscoring that the model captures the general trend reasonably well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "146d5e88",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-07-24T14:06:54.115969400Z",
     "start_time": "2026-07-24T14:06:53.851110300Z"
    },
    "execution": {
     "iopub.execute_input": "2026-07-28T19:10:37.569863Z",
     "iopub.status.busy": "2026-07-28T19:10:37.568615Z",
     "iopub.status.idle": "2026-07-28T19:10:37.985847Z",
     "shell.execute_reply": "2026-07-28T19:10:37.982863Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert train to timestamp\n",
    "train_plot = train.to_timestamp()\n",
    "# Convert val to timestamp\n",
    "val_plot = val.to_timestamp()\n",
    "# Align the prediction series w/ validation\n",
    "predictions_mean.index = val_plot.index\n",
    "# Align the CI w/ validation\n",
    "conf_int.index = val_plot.index\n",
    "# keep only last 30 points\n",
    "train_tail = train_plot[-30:]\n",
    "# Bridge first validation points to make plot continuous\n",
    "bridge_point = val_plot.iloc[:1]\n",
    "train_tail = pd.concat([train_tail, bridge_point])\n",
    "\n",
    "# plot\n",
    "plt.figure(figsize=(12, 6))\n",
    "# last 30 train points\n",
    "plt.plot(train_tail, label=\"Train\", color=\"blue\")\n",
    "# actual validation points\n",
    "plt.plot(val_plot, label=\"Actual\", color=\"orange\")\n",
    "# forecast\n",
    "plt.plot(predictions_mean, label=\"Forecast\", color=\"red\")\n",
    "# confidence interval\n",
    "plt.fill_between(\n",
    "    conf_int.index,\n",
    "    conf_int.iloc[:, 0],\n",
    "    conf_int.iloc[:, 1],\n",
    "    color=\"pink\",\n",
    "    alpha=0.3,\n",
    "    label=\"Confidence Interval\",\n",
    ")\n",
    "# labels & title\n",
    "plt.title(\"ARIMA Forecast vs Actual\")\n",
    "plt.xlabel(\"Year\")\n",
    "plt.ylabel(\"Real GDP\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5304f43c",
   "metadata": {},
   "source": [
    "As the RMSE and the actual-vs-predicted plot reveal, the model captures the real-GDP upward trend reasonably well. However, it fails in catching some short-term fluctuations along with some temporal dynamics.\n",
    "\n",
    "This is expected, as ARIMA(1,1,1) is a simple model and does not capture all GDP dynamics."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90b721b3",
   "metadata": {},
   "source": [
    "**Note**: ARIMA assumes linear relationships and may struggle with structural breaks or non-linear dynamics. More advanced models (e.g., SARIMA, VAR, or ML-based models) may be more appropriate in such cases."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9542d4b7",
   "metadata": {},
   "source": [
    "## Common Pitfalls"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a95ed39",
   "metadata": {},
   "source": [
    "Below a list of common pitfalls when implementing an ARIMA model:\n",
    "- Forget to test for stationarity before fitting. Data stationarity and integration order defines *d*, and if data are not stationary ARIMA will produce misleading results.\n",
    "- Using random train-test split instead of time-based splits. Time based splits ensure data time dependency, splitting randomly completely break the chronological order.\n",
    "- Misinterpreting predict(), forecast() and get_forecast(): Forecast() is specialized for future out-of-sample points; predict() works both for in-sample and out-of-sample data and needs a data range; get_forecast() provides the richest output with and confidence intervals\n",
    "- Overfitting with overly complex p and q. Always assess model performances on a set-aside validation test."
   ]
  }
 ],
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   "language": "python",
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