Identify-Randomwalk-Time-series-forecasting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "febd8964-bb69-4d13-8f55-89ff622928ab",
   "metadata": {},
   "source": [
    "# Time Series Forecasting - Identifying a random walk"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91609cf5-c5aa-4124-89ea-2e11ef3cc53f",
   "metadata": {},
   "source": [
    "## This notebook is to show how a random walk can be identified in gold prices dataset from https://www.kaggle.com/datasets/jishnukoliyadan/gold-price-1979-present"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "28dc9d13",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "from statsmodels.tsa.stattools import adfuller"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1d02984-912b-4c20-aac6-e6abecdaf878",
   "metadata": {},
   "source": [
    "## Read Monthly gold prices file. There are two other files in this dataset - Yearly and Quarterly gold prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b24febd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "monthly_gold_price = pd.read_csv(filepath_or_buffer='Monthly_Gold_Price_on_World.csv', sep=',', header=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a51c2ae-1747-4564-949c-81291e99e2dd",
   "metadata": {},
   "source": [
    "## There are 512 consecutive timesteps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "96e2c051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(518, 20)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monthly_gold_price.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a8e4be64",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>US dollar (USD)</th>\n",
       "      <th>Euro (EUR)</th>\n",
       "      <th>Japanese yen (JPY)</th>\n",
       "      <th>Pound sterling (GBP)</th>\n",
       "      <th>Canadian dollar (CAD)</th>\n",
       "      <th>Swiss franc (CHF)</th>\n",
       "      <th>Indian rupee (INR)</th>\n",
       "      <th>Chinese renmimbi (CNY)</th>\n",
       "      <th>Turkish lira (TRY)</th>\n",
       "      <th>Saudi riyal (SAR)</th>\n",
       "      <th>Indonesian rupiah (IDR)</th>\n",
       "      <th>UAE dirham (AED)</th>\n",
       "      <th>Thai baht THB)</th>\n",
       "      <th>Vietnamese dong (VND)</th>\n",
       "      <th>Egyptian pound (EGP)</th>\n",
       "      <th>Korean won (KRW)</th>\n",
       "      <th>Russian ruble (RUB)</th>\n",
       "      <th>South African rand (ZAR)</th>\n",
       "      <th>Australian dollar (AUD)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1979-01-31</td>\n",
       "      <td>233.7</td>\n",
       "      <td>144.84</td>\n",
       "      <td>45160.33</td>\n",
       "      <td>117.44</td>\n",
       "      <td>267.10</td>\n",
       "      <td>379.32</td>\n",
       "      <td>1840.82</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>745.20</td>\n",
       "      <td>139739.28</td>\n",
       "      <td>856.14</td>\n",
       "      <td>4511.27</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>108235.82</td>\n",
       "      <td>0.0</td>\n",
       "      <td>194.53</td>\n",
       "      <td>197.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1979-02-28</td>\n",
       "      <td>251.3</td>\n",
       "      <td>154.64</td>\n",
       "      <td>50209.08</td>\n",
       "      <td>124.19</td>\n",
       "      <td>295.50</td>\n",
       "      <td>413.61</td>\n",
       "      <td>2011.68</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>827.84</td>\n",
       "      <td>154683.13</td>\n",
       "      <td>946.62</td>\n",
       "      <td>4985.70</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>119929.27</td>\n",
       "      <td>0.0</td>\n",
       "      <td>209.36</td>\n",
       "      <td>219.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1979-03-30</td>\n",
       "      <td>240.1</td>\n",
       "      <td>148.04</td>\n",
       "      <td>50274.29</td>\n",
       "      <td>116.22</td>\n",
       "      <td>278.16</td>\n",
       "      <td>406.20</td>\n",
       "      <td>1940.16</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>796.73</td>\n",
       "      <td>148844.15</td>\n",
       "      <td>910.39</td>\n",
       "      <td>4812.88</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>116123.63</td>\n",
       "      <td>0.0</td>\n",
       "      <td>202.37</td>\n",
       "      <td>214.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1979-04-30</td>\n",
       "      <td>245.3</td>\n",
       "      <td>152.76</td>\n",
       "      <td>54144.57</td>\n",
       "      <td>118.82</td>\n",
       "      <td>278.53</td>\n",
       "      <td>420.01</td>\n",
       "      <td>2013.10</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>819.39</td>\n",
       "      <td>152453.63</td>\n",
       "      <td>930.21</td>\n",
       "      <td>4890.99</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>117423.25</td>\n",
       "      <td>0.0</td>\n",
       "      <td>206.91</td>\n",
       "      <td>221.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1979-05-31</td>\n",
       "      <td>274.6</td>\n",
       "      <td>172.00</td>\n",
       "      <td>61057.09</td>\n",
       "      <td>132.69</td>\n",
       "      <td>321.62</td>\n",
       "      <td>478.01</td>\n",
       "      <td>2253.41</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>933.26</td>\n",
       "      <td>171656.12</td>\n",
       "      <td>1048.41</td>\n",
       "      <td>5560.75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>133889.58</td>\n",
       "      <td>0.0</td>\n",
       "      <td>233.65</td>\n",
       "      <td>250.72</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Date  US dollar (USD)  Euro (EUR)  Japanese yen (JPY)  \\\n",
       "0  1979-01-31            233.7      144.84            45160.33   \n",
       "1  1979-02-28            251.3      154.64            50209.08   \n",
       "2  1979-03-30            240.1      148.04            50274.29   \n",
       "3  1979-04-30            245.3      152.76            54144.57   \n",
       "4  1979-05-31            274.6      172.00            61057.09   \n",
       "\n",
       "   Pound sterling (GBP)  Canadian dollar (CAD)  Swiss franc (CHF)  \\\n",
       "0                117.44                 267.10             379.32   \n",
       "1                124.19                 295.50             413.61   \n",
       "2                116.22                 278.16             406.20   \n",
       "3                118.82                 278.53             420.01   \n",
       "4                132.69                 321.62             478.01   \n",
       "\n",
       "   Indian rupee (INR)  Chinese renmimbi (CNY)  Turkish lira (TRY)  \\\n",
       "0             1840.82                     0.0                 0.0   \n",
       "1             2011.68                     0.0                 0.0   \n",
       "2             1940.16                     0.0                 0.0   \n",
       "3             2013.10                     0.0                 0.0   \n",
       "4             2253.41                     0.0                 0.0   \n",
       "\n",
       "   Saudi riyal (SAR)  Indonesian rupiah (IDR)  UAE dirham (AED)  \\\n",
       "0             745.20                139739.28            856.14   \n",
       "1             827.84                154683.13            946.62   \n",
       "2             796.73                148844.15            910.39   \n",
       "3             819.39                152453.63            930.21   \n",
       "4             933.26                171656.12           1048.41   \n",
       "\n",
       "   Thai baht THB)  Vietnamese dong (VND)  Egyptian pound (EGP)  \\\n",
       "0         4511.27                    0.0                   0.0   \n",
       "1         4985.70                    0.0                   0.0   \n",
       "2         4812.88                    0.0                   0.0   \n",
       "3         4890.99                    0.0                   0.0   \n",
       "4         5560.75                    0.0                   0.0   \n",
       "\n",
       "   Korean won (KRW)  Russian ruble (RUB)  South African rand (ZAR)  \\\n",
       "0         108235.82                  0.0                    194.53   \n",
       "1         119929.27                  0.0                    209.36   \n",
       "2         116123.63                  0.0                    202.37   \n",
       "3         117423.25                  0.0                    206.91   \n",
       "4         133889.58                  0.0                    233.65   \n",
       "\n",
       "   Australian dollar (AUD)  \n",
       "0                   197.17  \n",
       "1                   219.63  \n",
       "2                   214.55  \n",
       "3                   221.12  \n",
       "4                   250.72  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monthly_gold_price.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c54af4d1-4fe1-48a8-aaaa-48bb6a2f115e",
   "metadata": {},
   "source": [
    "## Verify if there is only entry for each timestep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "463ed867",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(monthly_gold_price['Date'].unique()) == monthly_gold_price.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b002312c-04a6-428f-9851-1c3d58265faa",
   "metadata": {},
   "source": [
    "## We're interested only in the timestep and the data value which is gold price in USD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1465b1d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "monthly_gold_price = monthly_gold_price[['Date', 'US dollar (USD)']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "adcbf077",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>US dollar (USD)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1979-01-31</td>\n",
       "      <td>233.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1979-02-28</td>\n",
       "      <td>251.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1979-03-30</td>\n",
       "      <td>240.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1979-04-30</td>\n",
       "      <td>245.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1979-05-31</td>\n",
       "      <td>274.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "         Date  US dollar (USD)\n",
       "0  1979-01-31            233.7\n",
       "1  1979-02-28            251.3\n",
       "2  1979-03-30            240.1\n",
       "3  1979-04-30            245.3\n",
       "4  1979-05-31            274.6"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monthly_gold_price.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "226f3b47-cb7c-46d0-b883-69ef67ae8c63",
   "metadata": {},
   "source": [
    "## Set test data size to 20%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a11e5566",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_dataset_count = int(np.ceil(len(monthly_gold_price)*0.2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0407b4c3-2ea3-4dc2-834d-33d77728b7f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "104"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_dataset_count"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21105cc8-dc86-4785-8d37-1aa6395a2b19",
   "metadata": {},
   "source": [
    "## Plot entire dataset, shading the test dataset in grey"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "070d0630",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.plot(monthly_gold_price['Date'], monthly_gold_price['US dollar (USD)'])\n",
    "ax.set_xlabel('Timesteps')\n",
    "ax.set_ylabel('Gold Price (USD)')\n",
    "ax.axvspan(\n",
    "            min(monthly_gold_price.index.to_list()[-test_dataset_count:]), \n",
    "            max(monthly_gold_price.index.to_list()[-test_dataset_count:]), \n",
    "            color='#808080', \n",
    "            alpha=0.2\n",
    "          )\n",
    "\n",
    "plt.xticks(np.arange(0, len(monthly_gold_price)+1, 48))\n",
    "\n",
    "fig.autofmt_xdate()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24ae8ca6-b52e-40d6-8c83-e7c93fb0212f",
   "metadata": {},
   "source": [
    "## Separate into train and test. In time series, data points have to be consecutive, so we don't do any shuffling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2d4dff31",
   "metadata": {},
   "outputs": [],
   "source": [
    "train = monthly_gold_price[:-test_dataset_count]\n",
    "test = monthly_gold_price[-test_dataset_count:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0137137e-6731-44d6-b220-cdbe0b7413f2",
   "metadata": {},
   "source": [
    "# TEST FOR A RANDOM WALK :-\n",
    "## Get ADF statistic (Augmented Dickey-Fuller Test) to test whether our data (train dataset) is stationary or not.\n",
    "## The null hypothesis is that data is not stationary. Alternative hypothesis is that data is stationary. When ADF statistic is a large negative number and p-value is less than 0.05, we reject the null hypothesis and conclude that data is stationary.\n",
    "## If data is not stationary, we one-difference the data and recheck for ADF statistic. \n",
    "## After data becomes stationary, we plot ACF (Auto-correlation Function) to see if there are any significant coefficients. If Yes, then the data is not a random walk, If No, then we conclude that data is a random walk. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "68d1caed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -2.2925730827429494\n",
      "p-value: 0.17437448974055464\n"
     ]
    }
   ],
   "source": [
    "ADF_result = adfuller(train['US dollar (USD)'])\n",
    "\n",
    "print(f'ADF Statistic: {ADF_result[0]}')\n",
    "print(f'p-value: {ADF_result[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec2435b5-47b8-4e87-a603-2fd66b4cb7f5",
   "metadata": {},
   "source": [
    "## We see that p-value is not less than 0.05, so we cannot reject the null hypothesis (i.e. data is not stationary). Just for sake of curiosity, our ACF plot looks as below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f56ea742",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(train['US dollar (USD)'], lags=20);\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "638a9967-b09e-4dfa-82f9-5503577b55f5",
   "metadata": {},
   "source": [
    "## Difference the data. If we difference once, we lose one data point due to differencing. If we do it twice, we lose two data points, and so on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4f53cfaf-ffd9-4141-8197-b1b7874e43f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "diff_random_walk = np.diff(train['US dollar (USD)'], n=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaa06d7c-5d7b-4cbb-af8d-a1ea1c0904db",
   "metadata": {},
   "source": [
    "## Plot the differenced data. We see below, that the trend has been removed from the data. We can roughly assume that the data is not stationary. But let's still find the ADF statistic. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1ce10978-e4bd-43ec-a5c3-8c0dd742b692",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(diff_random_walk)\n",
    "plt.title('Differenced Random Walk')\n",
    "plt.xlabel('Timesteps')\n",
    "plt.ylabel('Value')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b19f160-7035-484a-910f-942a5e942fa3",
   "metadata": {},
   "source": [
    "## Find ADF statistic. The p-value is less than 0.05, so we can reject null hypothesis and conclude that the differences data is stationary. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b5eb4738-e9b1-4d27-b8af-40f8b15c4c1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADF Statistic: -3.7372816150475585\n",
      "p-value: 0.0036182885641485134\n"
     ]
    }
   ],
   "source": [
    "ADF_result = adfuller(diff_random_walk)\n",
    "print(f'ADF Statistic: {ADF_result[0]}')\n",
    "print(f'p-value: {ADF_result[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81be07e2-fc99-4189-882a-516ad92c2bec",
   "metadata": {},
   "source": [
    "## Plot ACF. We see that, although there are significant coefficients at lag = 1, 3, 6, 11, there are no consecutive significant coefficients between 0 and any of these lags. We can conclude that there are no significant coefficients. Hence, the data is a random walk, which cannot be predicted with any forecasting methodology. Some very crude ways to create predictions could be average of the last N values, or average of the values in the past for the same period, or a simple linear regression. However, none of these predictions would be backed by a robust model.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f93d760e-6289-43b1-a950-67ecc891678f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(diff_random_walk, lags=20);\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d4bb560-0b54-4925-8c4d-ca73fd4e27b8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}