def ljungbox(
vdf: vDataFrame,
column: str,
ts: str,
by: list = [],
p: int = 1,
alpha: float = 0.05,
box_pierce: bool = False,
):
"""
---------------------------------------------------------------------------
Ljung–Box test (whether any of a group of autocorrelations of a time series
are different from zero).
Parameters
----------
vdf: vDataFrame
Input vDataFrame.
column: str
Input vcolumn to test.
ts: str
vcolumn used as timeline. It will be to use to order the data. It can be
a numerical or type date like (date, datetime, timestamp...) vcolumn.
by: list, optional
vcolumns used in the partition.
p: int, optional
Number of lags to consider in the test.
alpha: float, optional
Significance Level. Probability to accept H0.
box_pierce: bool
If set to True, the Box-Pierce statistic will be used.
Returns
-------
tablesample
An object containing the result. For more information, see
utilities.tablesample.
"""
check_types(
[
("ts", ts, [str],),
("column", column, [str],),
("by", by, [list],),
("p", p, [int, float],),
("alpha", alpha, [int, float],),
("box_pierce", box_pierce, [bool],),
("vdf", vdf, [vDataFrame,],),
],
)
columns_check([column] + [ts] + by, vdf)
column = vdf_columns_names([column], vdf)[0]
ts = vdf_columns_names([ts], vdf)[0]
by = vdf_columns_names(by, vdf)
acf = vdf.acf(column=column, ts=ts, by=by, p=p, show=False)
if p >= 2:
acf = acf.values["value"]
else:
acf = [acf]
n = vdf[column].count()
name = (
"Ljung–Box Test Statistic" if not (box_pierce) else "Box-Pierce Test Statistic"
)
result = tablesample(
{"index": [], name: [], "p_value": [], "Serial Correlation": []}
)
Q = 0
for k in range(p):
div = n - k - 1 if not (box_pierce) else 1
mult = n * (n + 2) if not (box_pierce) else n
Q += mult * acf[k] ** 2 / div
pvalue = chi2.sf(Q, k + 1)
result.values["index"] += [k + 1]
result.values[name] += [Q]
result.values["p_value"] += [pvalue]
result.values["Serial Correlation"] += [True if pvalue < alpha else False]
return result
def plot_acf_pacf(
vdf: vDataFrame,
column: str,
ts: str,
by: list = [],
p: (int, list) = 15,
**style_kwds,
):
"""
---------------------------------------------------------------------------
Draws the ACF and PACF Charts.
Parameters
----------
vdf: vDataFrame
Input vDataFrame.
column: str
Response column.
ts: str
vcolumn used as timeline. It will be to use to order the data.
It can be a numerical or type date like (date, datetime, timestamp...)
vcolumn.
by: list, optional
vcolumns used in the partition.
p: int/list, optional
Int equals to the maximum number of lag to consider during the computation
or List of the different lags to include during the computation.
p must be positive or a list of positive integers.
**style_kwds
Any optional parameter to pass to the Matplotlib functions.
Returns
-------
tablesample
An object containing the result. For more information, see
utilities.tablesample.
"""
check_types([
(
"column",
column,
[str],
),
(
"ts",
ts,
[str],
),
(
"by",
by,
[list],
),
(
"p",
p,
[int, float],
),
(
"vdf",
vdf,
[
vDataFrame,
],
),
])
tmp_style = {}
for elem in style_kwds:
if elem not in ("color", "colors"):
tmp_style[elem] = style_kwds[elem]
if "color" in style_kwds:
color = style_kwds["color"]
else:
color = gen_colors()[0]
columns_check([column, ts] + by, vdf)
by = vdf_columns_names(by, vdf)
column, ts = vdf_columns_names([column, ts], vdf)
acf = vdf.acf(ts=ts, column=column, by=by, p=p, show=False)
pacf = vdf.pacf(ts=ts, column=column, by=by, p=p, show=False)
result = tablesample(
{
"index": [i for i in range(0, len(acf.values["value"]))],
"acf": acf.values["value"],
"pacf": pacf.values["value"],
"confidence": pacf.values["confidence"],
}, )
fig = plt.figure(figsize=(10,
6)) if isnotebook() else plt.figure(figsize=(10,
6))
plt.rcParams["axes.facecolor"] = "#FCFCFC"
ax1 = fig.add_subplot(211)
x, y, confidence = (
result.values["index"],
result.values["acf"],
result.values["confidence"],
)
plt.xlim(-1, x[-1] + 1)
ax1.bar(
x,
y,
width=0.007 * len(x),
color="#444444",
zorder=1,
linewidth=0,
)
param = {
"s": 90,
"marker": "o",
"facecolors": color,
"edgecolors": "black",
"zorder": 2,
}
ax1.scatter(
x,
y,
**updated_dict(
param,
tmp_style,
),
)
ax1.plot(
[-1] + x + [x[-1] + 1],
[0 for elem in range(len(x) + 2)],
color=color,
zorder=0,
)
ax1.fill_between(x, confidence, color="#FE5016", alpha=0.1)
ax1.fill_between(x, [-elem for elem in confidence],
color="#FE5016",
alpha=0.1)
ax1.set_title("Autocorrelation")
y = result.values["pacf"]
ax2 = fig.add_subplot(212)
ax2.bar(x, y, width=0.007 * len(x), color="#444444", zorder=1, linewidth=0)
ax2.scatter(
x,
y,
**updated_dict(
param,
tmp_style,
),
)
ax2.plot(
[-1] + x + [x[-1] + 1],
[0 for elem in range(len(x) + 2)],
color=color,
zorder=0,
)
ax2.fill_between(x, confidence, color="#FE5016", alpha=0.1)
ax2.fill_between(x, [-elem for elem in confidence],
color="#FE5016",
alpha=0.1)
ax2.set_title("Partial Autocorrelation")
plt.show()
return result
