PACF function in statsmodels.tsa.stattools gives numbers greater than 1 when using ywunbiased?

Question

I have a dataframe which is of length 177 and I want to calculate and plot the partial auto-correlation function (PACF).

I have the data imported etc and I do:

from statsmodels.tsa.stattools import pacf
ys = pacf(data[key][array].diff(1).dropna(), alpha=0.05, nlags=176, method="ywunbiased")
xs = range(lags+1)
plt.figure()
plt.scatter(xs,ys[0])
plt.grid()
plt.vlines(xs, 0, ys[0])
plt.plot(ys[1])

The method used results in numbers greater than 1 for very long lags (90ish) which is incorrect and I get a RuntimeWarning: invalid value encountered in sqrtreturn rho, np.sqrt(sigmasq) but since I can't see their source code I don't know what this means.

To be honest, when I search for PACF, all the examples only carry out PACF up to 40 lags or 60 or so and they never have any significant PACF after lag=2 and so I couldn't compare to other examples either.

But when I use:

method="ols"
# or
method="ywmle"

the numbers are corrected. So it must be the algo they use to solve it.

I tried importing inspect and getsource method but its useless it just shows that it uses another package and I can't find that.

If you also know where the problem arises from, I would really appreciate the help.

For your reference, the values for data[key][array] are:

[1131.130005, 1144.939941, 1126.209961, 1107.300049, 1120.680054, 1140.839966, 1101.719971, 1104.23999, 1114.579956, 1130.199951, 1173.819946, 1211.920044, 1181.27002, 1203.599976, 1180.589966, 1156.849976, 1191.5, 1191.329956, 1234.180054, 1220.329956, 1228.810059, 1207.01001, 1249.47998, 1248.290039, 1280.079956, 1280.660034, 1294.869995, 1310.609985, 1270.089966, 1270.199951, 1276.660034, 1303.819946, 1335.849976, 1377.939941, 1400.630005, 1418.300049, 1438.23999, 1406.819946, 1420.859985, 1482.369995, 1530.619995, 1503.349976, 1455.27002, 1473.98999, 1526.75, 1549.380005, 1481.140015, 1468.359985, 1378.550049, 1330.630005, 1322.699951, 1385.589966, 1400.380005, 1280.0, 1267.380005, 1282.829956, 1166.359985, 968.75, 896.23999, 903.25, 825.880005, 735.090027, 797.869995, 872.8099980000001, 919.1400150000001, 919.320007, 987.4799800000001, 1020.6199949999999, 1057.079956, 1036.189941, 1095.630005, 1115.099976, 1073.869995, 1104.48999, 1169.430054, 1186.689941, 1089.410034, 1030.709961, 1101.599976, 1049.329956, 1141.199951, 1183.26001, 1180.550049, 1257.640015, 1286.119995, 1327.219971, 1325.829956, 1363.609985, 1345.199951, 1320.640015, 1292.280029, 1218.890015, 1131.420044, 1253.300049, 1246.959961, 1257.599976, 1312.410034, 1365.680054, 1408.469971, 1397.910034, 1310.329956, 1362.160034, 1379.319946, 1406.579956, 1440.670044, 1412.160034, 1416.180054, 1426.189941, 1498.109985, 1514.680054, 1569.189941, 1597.569946, 1630.73999, 1606.280029, 1685.72998, 1632.969971, 1681.550049, 1756.540039, 1805.810059, 1848.359985, 1782.589966, 1859.449951, 1872.339966, 1883.949951, 1923.569946, 1960.22998, 1930.6700440000002, 2003.369995, 1972.290039, 2018.050049, 2067.560059, 2058.899902, 1994.9899899999998, 2104.5, 2067.889893, 2085.51001, 2107.389893, 2063.110107, 2103.840088, 1972.180054, 1920.030029, 2079.360107, 2080.409912, 2043.939941, 1940.2399899999998, 1932.22998, 2059.73999, 2065.300049, 2096.949951, 2098.860107, 2173.600098, 2170.949951, 2168.27002, 2126.149902, 2198.810059, 2238.830078, 2278.8701170000004, 2363.639893, 2362.719971, 2384.199951, 2411.800049, 2423.409912, 2470.300049, 2471.649902, 2519.360107, 2575.26001, 2584.840088, 2673.610107, 2823.810059, 2713.830078, 2640.8701170000004, 2648.050049, 2705.27002, 2718.3701170000004, 2816.290039, 2901.52002, 2913.97998]

Answer 1

Your time series is pretty clearly not stationary, so that Yule-Walker assumptions are violated.

More generally, PACF is usually appropriate with stationary time series. You might difference your data first, before considering the partial autocorrelations.