\n",
"\n",
"show code\n",
"\"\"\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"hide_input": true,
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" show code\n",
" "
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%run ../../notebooks/loadtsfuncs.py\n",
"%matplotlib inline\n",
"toggle()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Exponential Smoothing Forecasts"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simple Exponential Smoothing\n",
"\n",
"The simple exponential smoothing method is defined by the following two equations, where\n",
"\n",
"- $L_t$, called the level of the series at time $t$, is not observable but can only be estimated. Essentially, it is an estimate of where the series would be at time $t$ if there were no random noise.\n",
"\n",
"- $F_{t+k}$ is the forecast of $Y_{t+k}$ made at time $t$.\n",
"\n",
"\\begin{align}\n",
"L_t &= \\alpha Y_t + (1-\\alpha) L_{t-1} \\tag{1}\\\\\n",
"F_{t+k} &= L_t \\nonumber\n",
"\\end{align}\n",
"\n",
"\n",
"The level $\\alpha \\in [0,1]$. If you want the method to react quickly to movements in the series, you should choose a large $\\alpha$; otherwise a small $\\alpha$.\n",
"\n",
"- If $\\alpha$ is close to 0, observations from the distant past continue to have a large influence on the next forecast. This means that the graph of the forecasts will be relatively smooth.\n",
"\n",
"- If $\\alpha$ is close to 1, only very recent observations have much influence on the next forecast. In this case, forecasts react quickly to sudden changes in the series.\n",
"\n",
"Simple exponential smoothing offers \"flat\" forecasts. That is, all forecasts take the same value, equal to the last level component. Remember that these forecasts will only be suitable if the time series has no trend or seasonal component."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Why exponential smoothing?**\n",
"\n",
"Note that\n",
"\n",
"\\begin{align}\n",
"L_{t-1} &= \\alpha Y_{t-1} + (1-\\alpha) L_{t-2} \\tag{2} \\\\\n",
"\\end{align}\n",
"\n",
"By substituting equation (2) into equation (1), we get\n",
"\n",
"\\begin{align*}\n",
"L_{t} &= \\alpha Y_{t-1} + (1-\\alpha) \\big( \\alpha Y_{t-1} + (1-\\alpha) L_{t-2} \\big) \\\\\n",
"&= \\alpha Y_{t-1} + \\alpha(1-\\alpha) Y_{t-1} + (1-\\alpha)^2 L_{t-2}\n",
"\\end{align*}\n",
"\n",
"If we substitute recursively into the equation (1), we obtain\n",
"\n",
"\\begin{align*}\n",
"L_{t} &= \\alpha Y_{t-1} + \\alpha(1-\\alpha) Y_{t-1} + \\alpha(1-\\alpha)^2 Y_{t-2} + \\alpha(1-\\alpha)^3 Y_{t-3} + \\cdots\n",
"\\end{align*}\n",
"\n",
"where exponentially decaying weights are assigned to historical data."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "d72dc2f3e9c74b6690588d438f9ab80d",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(BoundedIntText(value=12, description='Forecasts:', min=1), BoundedIntText(value=0, descr…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"widgets.interact_manual.opts['manual_name'] = 'Run Forecast'\n",
"interact_manual(ses_forecast,\n",
" forecasts=widgets.BoundedIntText(value=12, min=1, description='Forecasts:', disabled=False),\n",
" holdouts=widgets.BoundedIntText(value=0, min=0, description='Holdouts:', disabled=False),\n",
" level=widgets.BoundedFloatText(value=0.2, min=0, max=1, step=0.05, description='Level:', disabled=False),\n",
" optimized=widgets.Checkbox(value=False, description='Optimize Parameters', disabled=False));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Holt's Model for Trend\n",
"\n",
"Holt extended simple exponential smoothing to allow the forecasting of data with a trend. This method involves a forecast equation and two smoothing equations where one for the level and one for the trend.\n",
"\n",
"Besides the smoothing constant $\\alpha$ for the level, Holt's requires a new smoothing constant $\\beta$ for the trend to control how quickly the method reacts to observed changes in the trend.\n",
"\n",
"- If $\\beta$ is small, the method reacts slowly,\n",
"\n",
"- If $\\beta$ is large, the method reacts more quickly.\n",
"\n",
"Some practitioners suggest using a small value of $\\alpha$ (such as 0.1 to 0.2) and setting $\\beta = \\alpha$. Others suggest using an optimization option to select the optimal smoothing constant."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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