Time Series for Python with PyFlux

Posted on 2018-12-20 Edited on 2024-09-28 In Finance

Merry Christmas buddy!

It's been quite a while without writing anything. Today, we are going to introduce PyFlux for time seriers analysis. Cannonical models are to be directly adopted from PyFlux Documents and tested in this blog.

Get Started

Copy and paste that piece of code from PyFlux Documents with trivial modifications as follows:

import pandas as pd
import numpy as np
from pandas_datareader.data import DataReader
from datetime import datetime
import pyflux as pf
import matplotlib.pyplot as plt


a = DataReader('JPM',  'yahoo', datetime(2006,6,1), datetime(2016,6,1))
a_returns = pd.DataFrame(np.diff(a['Adj Close'].values))
a_returns.index = a.index.values[1:a.index.values.shape[0]]
a_returns.columns = ["JPM Returns"]

print(a_returns.head())

plt.figure(figsize=(15, 5))
plt.ylabel("Returns")
plt.plot(a_returns)
plt.show()

pf.acf_plot(a_returns.values.T[0])
pf.acf_plot(np.square(a_returns.values.T[0]))

After running the above piece of code, we'll get the following time series loaded:

            JPM Returns
2006-06-02     0.167995
2006-06-05    -0.613506
2006-06-06    -0.430914
2006-06-07    -0.094942
2006-06-08     0.073048

and the following resultant figures:

Cannonical Models

ARIMA

We can load and test ARIMA model using the following piece of code:

my_model = pf.ARIMA(data=a_returns, ar=4, ma=4, family=pf.Normal())
print(my_model.latent_variables)

result = my_model.fit("MLE")
result.summary()

my_model.plot_z(figsize=(15,5))
my_model.plot_fit(figsize=(15,10))
my_model.plot_predict_is(h=50, figsize=(15,5))
my_model.plot_predict(h=20,past_values=20,figsize=(15,5))

ARIMA's latent variables are printed as:

Index    Latent Variable           Prior           Prior Hyperparameters     V.I. Dist  Transform
======== ========================= =============== ========================= ========== ==========
0        Constant                  Normal          mu0: 0, sigma0: 3         Normal     None
1        AR(1)                     Normal          mu0: 0, sigma0: 0.5       Normal     None
2        AR(2)                     Normal          mu0: 0, sigma0: 0.5       Normal     None
3        AR(3)                     Normal          mu0: 0, sigma0: 0.5       Normal     None
4        AR(4)                     Normal          mu0: 0, sigma0: 0.5       Normal     None
5        MA(1)                     Normal          mu0: 0, sigma0: 0.5       Normal     None
6        MA(2)                     Normal          mu0: 0, sigma0: 0.5       Normal     None
7        MA(3)                     Normal          mu0: 0, sigma0: 0.5       Normal     None
8        MA(4)                     Normal          mu0: 0, sigma0: 0.5       Normal     None
9        Normal Scale              Flat            n/a (non-informative)     Normal     exp

And the fitting result is summarized as:

Normal ARIMA(4,0,4)
======================================================= ==================================================
Dependent Variable: JPM Returns                         Method: MLE
Start Date: 2006-06-08 00:00:00                         Log Likelihood: -3106.9508
End Date: 2016-06-02 00:00:00                           AIC: 6233.9016
Number of observations: 2514                            BIC: 6292.1979
==========================================================================================================
Latent Variable                          Estimate   Std Error  z        P>|z|    95% C.I.
======================================== ========== ========== ======== ======== =========================
Constant                                 0.0126     0.0136     0.9273   0.3538   (-0.0141 | 0.0394)
AR(1)                                    0.0596     0.198      0.3008   0.7635   (-0.3284 | 0.4475)
AR(2)                                    -0.3591    0.1858     -1.9331  0.0532   (-0.7231 | 0.005)
AR(3)                                    -0.2205    0.2687     -0.8208  0.4118   (-0.7471 | 0.3061)
AR(4)                                    0.5272     0.1373     3.8406   0.0001   (0.2581 | 0.7962)
MA(1)                                    -0.1667    0.1995     -0.8354  0.4035   (-0.5578 | 0.2244)
MA(2)                                    0.3234     0.202      1.6008   0.1094   (-0.0726 | 0.7193)
MA(3)                                    0.1603     0.2396     0.6692   0.5033   (-0.3093 | 0.63)
MA(4)                                    -0.5817    0.1618     -3.5942  0.0003   (-0.8989 | -0.2645)
Normal Scale                             0.8331
==========================================================================================================

And 4 images are to be produced as:

GARCH

We can load and test GARCH model using the following piece of code:

my_model = pf.GARCH(p=1, q=1, data=a_returns)
print(my_model.latent_variables)

my_model.adjust_prior(1, pf.TruncatedNormal(0.01, 0.5, lower=0.0, upper=1.0))
my_model.adjust_prior(2, pf.TruncatedNormal(0.97, 0.5, lower=0.0, upper=1.0))

result = my_model.fit('M-H', nsims=20000)
result.summary()

my_model.plot_z([1,2])
my_model.plot_fit(figsize=(15,5))
my_model.plot_sample(nsims=10, figsize=(15,7))

from scipy.stats import kurtosis
my_model.plot_ppc(T=kurtosis)
my_model.plot_predict(h=30, figsize=(15,5))

GARCH's latent variables are printed as:

Index    Latent Variable           Prior           Prior Hyperparameters     V.I. Dist  Transform
======== ========================= =============== ========================= ========== ==========
0        Vol Constant              Normal          mu0: 0, sigma0: 3         Normal     exp
1        q(1)                      Normal          mu0: 0, sigma0: 0.5       Normal     logit
2        p(1)                      Normal          mu0: 0, sigma0: 0.5       Normal     logit
3        Returns Constant          Normal          mu0: 0, sigma0: 3         Normal     None