\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": [
"# Autocorrelation and Partial Autocorrelation Functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Autocorrelation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can calculate the correlation for time series observations with observations in previous time steps, called lags. Because the correlation of the time series observations is calculated with values of the same series at previous times, this is called a serial correlation, or an autocorrelation. If a series is significantly autocorrelated, then the previous values of the series (lags) may be helpful in predicting the current value."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Partial Autocorrelation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A partial autocorrelation is a summary of the relationship between an observation in a time series with observations at prior time steps with the relationships of intervening observations removed (i.e., excluding the correlation contributions from the intermediate lags). The partial autocorrelation at lag $k$ is the correlation that results after removing the effect of any correlations due to the terms at shorter lags.\n",
"\n",
"The partial autocorrelation of lag (k) of a series is the coefficient of that lag in the autoregression equation of Y. The autoregressive equation of Y is nothing but the linear regression of Y with its own lags as predictors. For example, let $Y_t$ be the current value, then the partial autocorrelation of lag 3 ($Y_{t-3}$) is the coefficient $\\alpha_3$ in the following equation:\n",
"\n",
"$$Y_t = \\alpha_0 + \\alpha_1 Y_{t-1} + \\alpha_2 Y_{t-2} + \\alpha_3 Y_{t-3}$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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