{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# ETS models\n", "\n", "The ETS models are a family of time series models with an underlying state space model consisting of a level component, a trend component (T), a seasonal component (S), and an error term (E).\n", "\n", "This notebook shows how they can be used with statsmodels. For a more thorough treatment we refer to [1], chapter 8 (free online resource), on which the implementation in statsmodels and the examples used in this notebook are based.\n", "\n", "statsmodels implements all combinations of:\n", "- additive and multiplicative error model\n", "- additive and multiplicative trend, possibly dampened\n", "- additive and multiplicative seasonality\n", "\n", "However, not all of these methods are stable. Refer to [1] and references therein for more info about model stability.\n", "\n", "[1] Hyndman, Rob J., and George Athanasopoulos. *Forecasting: principles and practice*, 3rd edition, OTexts, 2019. https://www.otexts.org/fpp3/7" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2022-05-09T08:18:13.899215Z", "iopub.status.busy": "2022-05-09T08:18:13.898836Z", "iopub.status.idle": "2022-05-09T08:18:15.643994Z", "shell.execute_reply": "2022-05-09T08:18:15.643442Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "\n", "%matplotlib inline\n", "from statsmodels.tsa.exponential_smoothing.ets import ETSModel" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2022-05-09T08:18:15.647498Z", "iopub.status.busy": "2022-05-09T08:18:15.647131Z", "iopub.status.idle": "2022-05-09T08:18:15.650464Z", "shell.execute_reply": "2022-05-09T08:18:15.650064Z" } }, "outputs": [], "source": [ "plt.rcParams[\"figure.figsize\"] = (12, 8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple exponential smoothing\n", "\n", "The simplest of the ETS models is also known as *simple exponential smoothing*. In ETS terms, it corresponds to the (A, N, N) model, that is, a model with additive errors, no trend, and no seasonality. The state space formulation of Holt's method is:\n", "\n", "\\begin{align}\n", "y_{t} &= y_{t-1} + e_t\\\\\n", "l_{t} &= l_{t-1} + \\alpha e_t\\\\\n", "\\end{align}\n", "\n", "This state space formulation can be turned into a different formulation, a forecast and a smoothing equation (as can be done with all ETS models):\n", "\n", "\\begin{align}\n", "\\hat{y}_{t|t-1} &= l_{t-1}\\\\\n", "l_{t} &= \\alpha y_{t-1} + (1 - \\alpha) l_{t-1}\n", "\\end{align}\n", "\n", "Here, $\\hat{y}_{t|t-1}$ is the forecast/expectation of $y_t$ given the information of the previous step. In the simple exponential smoothing model, the forecast corresponds to the previous level. The second equation (smoothing equation) calculates the next level as weighted average of the previous level and the previous observation." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2022-05-09T08:18:15.653151Z", "iopub.status.busy": "2022-05-09T08:18:15.652825Z", "iopub.status.idle": "2022-05-09T08:18:15.926256Z", "shell.execute_reply": "2022-05-09T08:18:15.925450Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Annual oil production in Saudi Arabia (Mt)')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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