diff --git "a/sarima.ipynb" "b/sarima.ipynb"
new file mode 100644--- /dev/null
+++ "b/sarima.ipynb"
@@ -0,0 +1,1258 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "f029aeea",
+ "metadata": {},
+ "source": [
+ "# Forecasting Inflation rates with SARIMA \n",
+ "\n",
+ "\n",
+ "**SARIMA** is an extension of the regular ARIMA model that adds a seasonality component to the model. This allows us to better capture seasonal affects that the regular ARIMA model does not permit.\n",
+ "To produce SARIMA(p, d, q)(P, D, Q)m, a seasonality component is added to each factor of the classic ARIMA equation \n",
+ "\n",
+ "$$\n",
+ "y_t' = c + \\sum_{n=1}^{p} \\phi_n y_{t-n}' + \\sum_{n=1}^{q} \\theta_n \\varepsilon_{t-n} \n",
+ "+ \\sum_{n=1}^{P} \\eta_n y_{t-mn}' + \\sum_{n=1}^{Q} \\omega_n \\varepsilon_{t-mn} + \\varepsilon_t\n",
+ "$$\n",
+ " Where:\n",
+ "\n",
+ "y’: differenced time series, through both regular, d, and seasonal, D, differencing\n",
+ "P: number of seasonal auto-regressors\n",
+ "ω: coefficients of the seasonal autoregressive components\n",
+ "Q: number of seasonal moving-average components\n",
+ "η: coefficients of the seasonal forecast errors\n",
+ "m: length of season\n",
+ "\n",
+ "\n",
+ "### Limitation of SARIMA\n",
+ "\n",
+ "One key limitation of the **SARIMA** model is that it **cannot handle multiple seasonalities**. \n",
+ "It is designed to capture only a **single seasonal pattern** (e.g., monthly or weekly), making it unsuitable for datasets that exhibit **more than one seasonal cycle** (e.g., both daily and yearly patterns).\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "87ea7b85",
+ "metadata": {},
+ "source": [
+ "## Key Considerations\n",
+ "\n",
+ "### 1. Stationarity Requirement\n",
+ "\n",
+ "SARIMA models require the time series to be **stationary**, meaning:\n",
+ "- No long-term trend or persistent seasonality\n",
+ "- Constant mean and variance over time\n",
+ "\n",
+ "To achieve stationarity:\n",
+ "- **Mean stabilization** is done through differencing:\n",
+ " - Regular differencing → order \\( d \\)\n",
+ " - Seasonal differencing → order \\( D \\)\n",
+ "- **Variance stabilization** can be achieved using:\n",
+ " - Log transformation\n",
+ " - Box-Cox transformation \n",
+ "These help normalize the amplitude of seasonal fluctuations across time.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "### 2. Order Selection\n",
+ "\n",
+ "Once the series is stationary, we determine the model orders:\n",
+ "\n",
+ "#### a. Differencing Orders \n",
+ "- \\( d \\): Number of regular differences \n",
+ "- \\( D \\): Number of seasonal differences \n",
+ "Use the **Augmented Dickey-Fuller (ADF)** test to assess whether differencing is required.\n",
+ "\n",
+ "#### b. AR and MA Orders \n",
+ "- Regular terms: \\( p \\) (AR), \\( q \\) (MA) \n",
+ "- Seasonal terms: \\( P \\) (SAR), \\( Q \\) (SMA) \n",
+ "Analyze:\n",
+ "- **Partial Autocorrelation Function (PACF)** → identifies AR (p, P) \n",
+ "- **Autocorrelation Function (ACF)** → identifies MA (q, Q) \n",
+ "\n",
+ "\n",
+ "\n",
+ "---\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7eb25e04",
+ "metadata": {},
+ "source": [
+ "# `Data Loading and Visualization`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "f19ee008",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import matplotlib.pyplot as plt\n",
+ "import pandas as pd"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "59d09afb",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "infl_df = pd.read_csv('I:/CQAI/TSA/Notebooks/inflation rates dataset.csv')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "bfeb00f9",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# infl_df[\"Date\"] =pd.to_datetime(infl_df['Year'].astype(str) + '-' + infl_df['Month'].astype(str) + '-01')\n",
+ "infl_df[\"Date\"]= pd.to_datetime(infl_df[\"Date\"])\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "27f5528e",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Unnamed: 0 | \n",
+ " Monthly_Inflation | \n",
+ "
\n",
+ " \n",
+ " | Date | \n",
+ " | \n",
+ " | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 1960-01-01 | \n",
+ " 0 | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 1960-02-01 | \n",
+ " 1 | \n",
+ " 1.000000 | \n",
+ "
\n",
+ " \n",
+ " | 1960-03-01 | \n",
+ " 2 | \n",
+ " 0.991323 | \n",
+ "
\n",
+ " \n",
+ " | 1960-04-01 | \n",
+ " 3 | \n",
+ " 1.008753 | \n",
+ "
\n",
+ " \n",
+ " | 1960-05-01 | \n",
+ " 4 | \n",
+ " 1.006508 | \n",
+ "
\n",
+ " \n",
+ " | ... | \n",
+ " ... | \n",
+ " ... | \n",
+ "
\n",
+ " \n",
+ " | 2019-09-01 | \n",
+ " 716 | \n",
+ " 1.006250 | \n",
+ "
\n",
+ " \n",
+ " | 2019-10-01 | \n",
+ " 717 | \n",
+ " 1.009317 | \n",
+ "
\n",
+ " \n",
+ " | 2019-11-01 | \n",
+ " 718 | \n",
+ " 1.009231 | \n",
+ "
\n",
+ " \n",
+ " | 2019-12-01 | \n",
+ " 719 | \n",
+ " 1.006098 | \n",
+ "
\n",
+ " \n",
+ " | 2020-01-01 | \n",
+ " 720 | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
721 rows × 2 columns
\n",
+ "