\n",
+ "\n",
+ "This notebook covers different types of **Exponential Smoothing** techniques for time series forecasting:\n",
+ "\n",
+ "1. **Simple Exponential Smoothing (SES)** \n",
+ "2. **Double Exponential Smoothing (Holt’s Method)** \n",
+ "3. **Triple Exponential Smoothing (Holt-Winters Method)**\n",
+ "\n",
+ "---\n",
+ "\n",
+ "
Objectives
\n",
+ "\n",
+ "- Understand the core idea of exponential smoothing \n",
+ "- Learn how each method builds on the previous:\n",
+ " - SES handles **level**\n",
+ " - Holt’s method handles **level + trend**\n",
+ " - Holt-Winters method handles **level + trend + seasonality**\n",
+ "- Apply Holt-Winters method to forecast daily revenue \n",
+ "- Visualize and interpret the forecast results\n",
+ "\n",
+ "---\n",
+ "\n",
+ "
Dataset
\n",
+ "\n",
+ "We will use a **daily revenue time series**, where each row corresponds to a revenue value recorded on a specific date. This data will help us:\n",
+ "\n",
+ "- Visualize time-based patterns \n",
+ "- Train smoothing models \n",
+ "- Forecast future values \n",
+ "\n",
+ "---\n",
+ "\n",
+ "
Introduction to Exponential Smoothing
\n",
+ "\n",
+ "Exponential Smoothing is a classic and widely used **time series forecasting** technique that originated in the **1950s**. Robert G. Brown introduced it in **1956**, and it was further developed by Charles C. Holt (1957) and Peter Winters (1960).\n",
+ "\n",
+ "---\n",
+ "\n",
+ "
Why the \"Exponential\" in Exponential Smoothing?
\n",
+ "\n",
+ "The method assigns weights to past observations that **decrease exponentially** as the observations get older:\n",
+ "\n",
+ "- Most recent data points have the **highest weight**\n",
+ "- Older data points’ influence **decays geometrically** with time\n",
+ "- This gives the method a “memory” that prioritizes **recent changes**, while still considering historical patterns\n",
+ "\n",
+ "---\n",
+ "\n",
+ "
Position Between Naïve and Mean Forecasting
\n",
+ "\n",
+ "- **Naïve forecast**: Uses only the most recent observation to project the next value \n",
+ "- **Mean forecast**: Uses the average of all past observations \n",
+ "- **Exponential Smoothing**: Strikes a balance between these two by:\n",
+ " - Using **all past data**\n",
+ " - Giving **more weight to recent values**\n",
+ " - Allowing forecasts to be **more responsive** to recent changes\n",
+ "\n",
+ "---\n",
+ "\n",
+ "
Key Strengths
\n",
+ "\n",
+ "- **Computationally lightweight**: Requires only the previous forecast and the latest data point \n",
+ "- **Highly adaptable**, with extensions to handle:\n",
+ " - **Level only** → Simple Exponential Smoothing (SES)\n",
+ " - **Level + Trend** → Holt’s Linear Trend Method\n",
+ " - **Level + Trend + Seasonality** → Holt–Winters Method (Triple Exponential Smoothing)\n",
+ "\n",
+ "---\n",
+ "\n",
+ "
"
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### Observation:\n",
+ "- From the above graph a clear yearly seasonal pattern and an increading upward trend is evident"
+ ],
+ "metadata": {
+ "id": "mT6pECGcO13P"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **Seasonal Decomposition** \n",
+ "\n",
+ "This reveals the structure of the series by separating it into three main components:\n",
+ "\n",
+ "### Components of Time Series\n",
+ "\n",
+ "- **Trend** \n",
+ " The long-term progression of the series — it shows the overall direction (increasing, decreasing, or stable) over time.\n",
+ "\n",
+ "- **Seasonal** \n",
+ " The repeating short-term cycle or pattern at fixed intervals, such as daily, weekly, monthly, or quarterly.\n",
+ "\n",
+ "- **Residual (Irregular or Noise)** \n",
+ " The random variation or \"leftover\" part of the data after removing both trend and seasonal components.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "### Things to Consider Before Performing Seasonal Decomposition\n",
+ "\n",
+ "##### 1. Model Selection\n",
+ "\n",
+ "Before decomposing the series, it's important to choose the correct model type:\n",
+ "\n",
+ "- **Additive Model**: Use when the seasonal fluctuations are roughly constant over time.\n",
+ "- **Multiplicative Model**: Use when the seasonal variation increases or decreases with the level of the trend.\n",
+ "\n",
+ "##### 2. Identify the Seasonality Period\n",
+ "\n",
+ "You need to determine the correct **seasonal period** (e.g., 12 for monthly seasonality, 365 for yearly seasonality in daily data). This can be guided by:\n",
+ "\n",
+ "- Domain knowledge \n",
+ "- Visual inspection of time series plots \n",
+ "- Autocorrelation and partial autocorrelation plots \n",
+ "- Spectral analysis\n",
+ "\n",
+ "---"
+ ],
+ "metadata": {
+ "id": "Id8RMlK6TVCC"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Plotting the autocorrelation to determine seasonal period.\n",
+ "fig, ax = plt.subplots(figsize = (10,4))\n",
+ "plot_acf(daily_revenue_df['revenue'], lags = 730, ax = ax)\n",
+ "plt.show()"
+ ],
+ "metadata": {
+ "id": "daANxB6I3sSf",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 372
+ },
+ "outputId": "0008b837-ff68-4a71-ce61-1322d0f69fd3"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ "
"
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### Observation :\n",
+ " Repeaitng spikes after every 365 interval indicate repeating seasonal patterns."
+ ],
+ "metadata": {
+ "id": "3LPdPT9Na3Sm"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "\n",
+ "# In our case, we use: #model=multiplicative and period= 365\n",
+ "# This is because our daily revenue dataset exhibits **yearly seasonality** which is increasing with the trend, as observed in the earlier visualization and also in the ACF plot\n",
+ "result = seasonal_decompose(daily_revenue_df['revenue'],model = 'mul',period = 365)\n",
+ "\n",
+ "result.plot()\n",
+ "plt.show()\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "L0tqOeNZ0Z4u",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 487
+ },
+ "outputId": "cebaf44e-ccc6-49e2-8c8b-37832f3b8e9e"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "execution_count": 12
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **Lets Begin with Modeling by Simple Exponential Smoothing** \n",
+ "\n",
+ "Simple Exponential Smoothing (SES) is a basic yet powerful method for forecasting time series data that shows **no clear trend or seasonality**. It works by assigning exponentially decreasing weights to past observations, emphasizing more recent data.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "\n",
+ "This method uses a single parameter, **alpha (α)**, known as the **smoothing factor**. It controls how much weight is placed on the most recent observation versus the historical average.\n",
+ "\n",
+ "- If **α** is close to 1, the model gives more importance to recent data (fast adaptation).\n",
+ "- If **α** is close to 0, the model smooths more slowly, giving more weight to past observations.\n",
+ "\n",
+ "The smoothing factor **α** typically ranges between **0 and 1**.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "\n",
+ "## Mathematical Formula\n",
+ "\n",
+ "The update rule for Simple Exponential Smoothing is given by:\n",
+ "\n",
+ "\\[\n",
+ "s_t = \\alpha x_t + (1 - \\alpha) s_{t-1}\n",
+ "\\]\n",
+ "\n",
+ "Or equivalently:\n",
+ "\n",
+ "\\[\n",
+ "s_t = s_{t-1} + \\alpha(x_t - s_{t-1})\n",
+ "\\]\n",
+ "\n",
+ "Where:\n",
+ "\n",
+ "- \\( s_t \\) = Smoothed statistic at time \\( t \\) \n",
+ "- \\( x_t \\) = Actual value at time \\( t \\) \n",
+ "- \\( s_{t-1} \\) = Smoothed statistic at time \\( t-1 \\) \n",
+ "- \\( \\alpha \\) = Smoothing factor ( \\( 0 < \\alpha < 1 \\) )\n",
+ "\n",
+ "---\n",
+ "\n",
+ "## Intuition\n",
+ "\n",
+ "Think of SES as a weighted moving average where **weights decay exponentially** into the past. It’s a middle ground between:\n",
+ "\n",
+ "- **Naive forecasting**: using only the most recent value.\n",
+ "- **Simple averaging**: using the mean of all past values equally.\n",
+ "\n",
+ "---"
+ ],
+ "metadata": {
+ "id": "WdT3l0uWEaR4"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "\n",
+ "SES_model = SimpleExpSmoothing(train).fit()\n",
+ "\n",
+ "ses_model_predictions = SES_model.forecast(len(test))"
+ ],
+ "metadata": {
+ "id": "Yn3XyldX__-M",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "outputId": "29b81180-061d-4500-d0b1-a84c445c9b5e"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stderr",
+ "text": [
+ "/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: No frequency information was provided, so inferred frequency D will be used.\n",
+ " self._init_dates(dates, freq)\n"
+ ]
+ }
+ ]
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "\n",
+ "plt.figure(figsize = (10,4))\n",
+ "\n",
+ "plt.plot(train, label = 'Train')\n",
+ "plt.plot(test, label = 'Test')\n",
+ "plt.plot(ses_model_predictions, label = \"Forecast\")\n",
+ "plt.title(\"Simple Exponential smoothing\")\n",
+ "plt.legend()\n",
+ "plt.show()"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 387
+ },
+ "id": "csW61d4ZFL9Z",
+ "outputId": "bd70b7bd-499b-47da-b70a-098af6de1f57"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ "
"
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "\n",
+ "# **Next we are implementing Double Exponential Smoothing (Holt's Linear Smoothing)** \n",
+ "\n",
+ "Double Exponential Smoothing, also known as **Holt’s Trend Method**, **Second-Order Smoothing**, or **Holt’s Linear Smoothing**, extends Simple Exponential Smoothing to capture data with a **trend**. It is used when the time series data exhibits a trend but **not seasonality**.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "## Purpose\n",
+ "\n",
+ "The core idea behind Double Exponential Smoothing is to model both the **level** and the **trend** of the series:\n",
+ "\n",
+ "- The **level** is the smoothed estimate of the series.\n",
+ "- The **trend** captures the increasing or decreasing movement over time.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "## Parameters\n",
+ "\n",
+ "This method introduces an additional parameter:\n",
+ "\n",
+ "- **Alpha (α)**: Smoothing factor for the level (same as in Simple Exponential Smoothing).\n",
+ "- **Beta (β)**: Smoothing factor for the trend. Controls how quickly the trend component is updated over time.\n",
+ "\n",
+ "Both α and β range between 0 and 1.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "## Intuition\n",
+ "\n",
+ "Simple Exponential Smoothing works well when data has no trend, but it falls short when the data shows a consistent **upward or downward movement** over time.\n",
+ "\n",
+ "Double Exponential Smoothing solves this by:\n",
+ "\n",
+ "- Keeping track of **how fast the series is changing** using a trend component.\n",
+ "- Adjusting the forecast not just based on the most recent value, but also based on how the series has been increasing or decreasing.\n",
+ "- Using two smoothing equations: one for the level and one for the trend, so it can adapt as the trend grows stronger or weaker.\n",
+ "\n",
+ "This means the model doesn't just \"follow\" the data—it learns and **projects the direction** the data is going.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "## When to Use\n",
+ "\n",
+ "- Data contains a **trend**, but **no seasonality**.\n",
+ "- Useful for **short- to medium-term forecasting** where trend behavior is observed.\n",
+ "\n",
+ "---\n",
+ "\n",
+ "## Mathematical Formulas\n",
+ "\n",
+ "Let:\n",
+ "\n",
+ "- \\( s_t \\): Smoothed value (level) at time \\( t \\)\n",
+ "- \\( b_t \\): Estimated trend at time \\( t \\)\n",
+ "- \\( x_t \\): Actual observation at time \\( t \\)\n",
+ "\n",
+ "### Update equations:\n",
+ "\n",
+ "\\[\n",
+ "s_t = \\alpha x_t + (1 - \\alpha)(s_{t-1} + b_{t-1})\n",
+ "\\]\n",
+ "\n",
+ "\\[\n",
+ "b_t = \\beta (s_t - s_{t-1}) + (1 - \\beta) b_{t-1}\n",
+ "\\]\n",
+ "\n",
+ "---\n",
+ "\n",
+ "### Explanation of Terms\n",
+ "\n",
+ "- \\( \\alpha \\): Controls how much weight is given to the latest observation versus the past level plus trend.\n",
+ "- \\( \\beta \\): Controls how quickly the trend component is updated.\n",
+ "- \\( s_t \\): Represents the smoothed value (forecasted level).\n",
+ "- \\( b_t \\): Represents the best estimate of the trend at time \\( t \\).\n",
+ "\n",
+ "---\n",
+ "\n",
+ "\n",
+ "\n",
+ "Double Exponential Smoothing is ideal for time series data that shows a **trend but no seasonality**. It learns both the current level and the trend of the data and uses both to make accurate forecasts."
+ ],
+ "metadata": {
+ "id": "KU362TxPItBW"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "\n",
+ "DES_model = ExponentialSmoothing(train,trend = 'mul',seasonal = None).fit()\n",
+ "des_model_predictions = DES_model.forecast(len(test))\n",
+ "des_model_predictions\n"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 582
+ },
+ "id": "9aveMxj5Iv2Q",
+ "outputId": "5d50e9e0-977e-4dfc-8063-228890552d91"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stderr",
+ "text": [
+ "/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/base/tsa_model.py:473: ValueWarning: No frequency information was provided, so inferred frequency D will be used.\n",
+ " self._init_dates(dates, freq)\n",
+ "/usr/local/lib/python3.11/dist-packages/statsmodels/tsa/holtwinters/model.py:85: RuntimeWarning: overflow encountered in matmul\n",
+ " return err.T @ err\n",
+ "/usr/local/lib/python3.11/dist-packages/scipy/optimize/_numdiff.py:596: RuntimeWarning: invalid value encountered in subtract\n",
+ " df = fun(x1) - f0\n"
+ ]
+ },
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ "2021-12-01 2.609419e+07\n",
+ "2021-12-02 2.588051e+07\n",
+ "2021-12-03 2.566858e+07\n",
+ "2021-12-04 2.545838e+07\n",
+ "2021-12-05 2.524991e+07\n",
+ " ... \n",
+ "2022-11-26 1.352041e+06\n",
+ "2022-11-27 1.340969e+06\n",
+ "2022-11-28 1.329988e+06\n",
+ "2022-11-29 1.319097e+06\n",
+ "2022-11-30 1.308296e+06\n",
+ "Freq: D, Length: 365, dtype: float64"
+ ],
+ "text/html": [
+ "